lisp/calc/calc-ext.el

   1 ;;; calc-ext.el --- various extension functions for Calc
   2
   3 ;; Copyright (C) 1990-1993, 2001-2015 Free Software Foundation, Inc.
   4
   5 ;; Author: David Gillespie <daveg@synaptics.com>
   6 ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
   7
   8 ;; This file is part of GNU Emacs.
   9
  10 ;; GNU Emacs is free software: you can redistribute it and/or modify
  11 ;; it under the terms of the GNU General Public License as published by
  12 ;; the Free Software Foundation, either version 3 of the License, or
  13 ;; (at your option) any later version.
  14
  15 ;; GNU Emacs is distributed in the hope that it will be useful,
  16 ;; but WITHOUT ANY WARRANTY; without even the implied warranty of
  17 ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  18 ;; GNU General Public License for more details.
  19
  20 ;; You should have received a copy of the GNU General Public License
  21 ;; along with GNU Emacs.  If not, see <http://www.gnu.org/licenses/>.
  22
  23 ;;; Commentary:
  24
  25 ;;; Code:
  26
  27 (require 'calc)
  28 (require 'calc-macs)
  29
  30 ;; Declare functions which are defined elsewhere.
  31 (declare-function math-clip "calc-bin" (a &optional w))
  32 (declare-function math-round "calc-arith" (a &optional prec))
  33 (declare-function math-simplify "calc-alg" (top-expr))
  34 (declare-function math-simplify-extended "calc-alg" (a))
  35 (declare-function math-simplify-units "calc-units" (a))
  36 (declare-function calc-set-language "calc-lang" (lang &optional option no-refresh))
  37 (declare-function calc-flush-caches "calc-stuff" (&optional inhibit-msg))
  38 (declare-function calc-save-modes "calc-mode" ())
  39 (declare-function calc-embedded-modes-change "calc-embed" (vars))
  40 (declare-function calc-embedded-var-change "calc-embed" (var &optional buf))
  41 (declare-function math-mul-float "calc-arith" (a b))
  42 (declare-function math-arctan-raw "calc-math" (x))
  43 (declare-function math-sqrt-raw "calc-math" (a &optional guess))
  44 (declare-function math-sqrt-float "calc-math" (a &optional guess))
  45 (declare-function math-exp-minus-1-raw "calc-math" (x))
  46 (declare-function math-normalize-polar "calc-cplx" (a))
  47 (declare-function math-normalize-hms "calc-forms" (a))
  48 (declare-function math-normalize-mod "calc-forms" (a))
  49 (declare-function math-make-sdev "calc-forms" (x sigma))
  50 (declare-function math-make-intv "calc-forms" (mask lo hi))
  51 (declare-function math-normalize-logical-op "calc-prog" (a))
  52 (declare-function math-possible-signs "calc-arith" (a &optional origin))
  53 (declare-function math-infinite-dir "calc-math" (a &optional inf))
  54 (declare-function math-calcFunc-to-var "calc-map" (f))
  55 (declare-function calc-embedded-evaluate-expr "calc-embed" (x))
  56 (declare-function math-known-nonzerop "calc-arith" (a))
  57 (declare-function math-read-expr-level "calc-aent" (exp-prec &optional exp-term))
  58 (declare-function math-read-big-rec "calc-lang" (math-rb-h1 math-rb-v1 math-rb-h2 math-rb-v2 &optional baseline prec short))
  59 (declare-function math-read-big-balance "calc-lang" (h v what &optional commas))
  60 (declare-function math-format-date "calc-forms" (math-fd-date))
  61 (declare-function math-vector-is-string "calccomp" (a))
  62 (declare-function math-vector-to-string "calccomp" (a &optional quoted))
  63 (declare-function math-format-radix-float "calc-bin" (a prec))
  64 (declare-function math-compose-expr "calccomp" (a prec &optional div))
  65 (declare-function math-abs "calc-arith" (a))
  66 (declare-function math-format-bignum-binary "calc-bin" (a))
  67 (declare-function math-format-bignum-octal "calc-bin" (a))
  68 (declare-function math-format-bignum-hex "calc-bin" (a))
  69 (declare-function math-format-bignum-radix "calc-bin" (a))
  70 (declare-function math-compute-max-digits "calc-bin" (w r))
  71 (declare-function math-map-vec "calc-vec" (f a))
  72 (declare-function math-make-frac "calc-frac" (num den))
  73
  74
  75 (defvar math-simplifying nil)
  76 (defvar math-living-dangerously nil)   ; true if unsafe simplifications are okay.
  77 (defvar math-integrating nil)
  78
  79 (defvar math-rewrite-selections nil)
  80
  81 (defvar math-compose-level 0)
  82 (defvar math-comp-selected nil)
  83 (defvar math-comp-tagged nil)
  84 (defvar math-comp-sel-hpos nil)
  85 (defvar math-comp-sel-vpos nil)
  86 (defvar math-comp-sel-cpos nil)
  87 (defvar math-compose-hash-args nil)
  88
  89 (defvar calc-alg-map)
  90 (defvar calc-alg-esc-map)
  91
  92 ;;; The following was made a function so that it could be byte-compiled.
  93 (defun calc-init-extensions ()
  94
  95   (define-key calc-mode-map ":" 'calc-fdiv)
  96   (define-key calc-mode-map "\\" 'calc-idiv)
  97   (define-key calc-mode-map "|" 'calc-concat)
  98   (define-key calc-mode-map "!" 'calc-factorial)
  99   (define-key calc-mode-map "C" 'calc-cos)
 100   (define-key calc-mode-map "E" 'calc-exp)
 101   (define-key calc-mode-map "H" 'calc-hyperbolic)
 102   (define-key calc-mode-map "I" 'calc-inverse)
 103   (define-key calc-mode-map "J" 'calc-conj)
 104   (define-key calc-mode-map "L" 'calc-ln)
 105   (define-key calc-mode-map "N" 'calc-eval-num)
 106   (define-key calc-mode-map "O" 'calc-option)
 107   (define-key calc-mode-map "P" 'calc-pi)
 108   (define-key calc-mode-map "Q" 'calc-sqrt)
 109   (define-key calc-mode-map "R" 'calc-round)
 110   (define-key calc-mode-map "S" 'calc-sin)
 111   (define-key calc-mode-map "T" 'calc-tan)
 112   (define-key calc-mode-map "U" 'calc-undo)
 113   (define-key calc-mode-map "X" 'calc-call-last-kbd-macro)
 114   (define-key calc-mode-map "o" 'calc-realign)
 115   (define-key calc-mode-map "p" 'calc-precision)
 116   (define-key calc-mode-map "w" 'calc-why)
 117   (define-key calc-mode-map "x" 'calc-execute-extended-command)
 118   (define-key calc-mode-map "y" 'calc-copy-to-buffer)
 119
 120   (define-key calc-mode-map "(" 'calc-begin-complex)
 121   (define-key calc-mode-map ")" 'calc-end-complex)
 122   (define-key calc-mode-map "[" 'calc-begin-vector)
 123   (define-key calc-mode-map "]" 'calc-end-vector)
 124   (define-key calc-mode-map "," 'calc-comma)
 125   (define-key calc-mode-map ";" 'calc-semi)
 126   (define-key calc-mode-map "`" 'calc-edit)
 127   (define-key calc-mode-map "=" 'calc-evaluate)
 128   (define-key calc-mode-map "~" 'calc-num-prefix)
 129   (define-key calc-mode-map "<" 'calc-scroll-left)
 130   (define-key calc-mode-map ">" 'calc-scroll-right)
 131   (define-key calc-mode-map "{" 'calc-scroll-down)
 132   (define-key calc-mode-map "}" 'calc-scroll-up)
 133   (define-key calc-mode-map "\C-k" 'calc-kill)
 134   (define-key calc-mode-map "\M-k" 'calc-copy-as-kill)
 135   (define-key calc-mode-map "\C-w" 'calc-kill-region)
 136   (define-key calc-mode-map "\M-w" 'calc-copy-region-as-kill)
 137   (define-key calc-mode-map "\M-\C-w" 'kill-ring-save)
 138   (define-key calc-mode-map "\M-\C-m" 'calc-last-args)
 139
 140   (define-key calc-mode-map "a" nil)
 141   (define-key calc-mode-map "a?" 'calc-a-prefix-help)
 142   (define-key calc-mode-map "aa" 'calc-apart)
 143   (define-key calc-mode-map "ab" 'calc-substitute)
 144   (define-key calc-mode-map "ac" 'calc-collect)
 145   (define-key calc-mode-map "ad" 'calc-derivative)
 146   (define-key calc-mode-map "ae" 'calc-simplify-extended)
 147   (define-key calc-mode-map "af" 'calc-factor)
 148   (define-key calc-mode-map "ag" 'calc-poly-gcd)
 149   (define-key calc-mode-map "ai" 'calc-integral)
 150   (define-key calc-mode-map "am" 'calc-match)
 151   (define-key calc-mode-map "an" 'calc-normalize-rat)
 152   (define-key calc-mode-map "ap" 'calc-poly-interp)
 153   (define-key calc-mode-map "ar" 'calc-rewrite)
 154   (define-key calc-mode-map "as" 'calc-simplify)
 155   (define-key calc-mode-map "at" 'calc-taylor)
 156   (define-key calc-mode-map "av" 'calc-alg-evaluate)
 157   (define-key calc-mode-map "ax" 'calc-expand)
 158   (define-key calc-mode-map "aA" 'calc-abs)
 159   (define-key calc-mode-map "aF" 'calc-curve-fit)
 160   (define-key calc-mode-map "aI" 'calc-num-integral)
 161   (define-key calc-mode-map "aM" 'calc-map-equation)
 162   (define-key calc-mode-map "aN" 'calc-find-minimum)
 163   (define-key calc-mode-map "aP" 'calc-poly-roots)
 164   (define-key calc-mode-map "aS" 'calc-solve-for)
 165   (define-key calc-mode-map "aR" 'calc-find-root)
 166   (define-key calc-mode-map "aT" 'calc-tabulate)
 167   (define-key calc-mode-map "aX" 'calc-find-maximum)
 168   (define-key calc-mode-map "a+" 'calc-summation)
 169   (define-key calc-mode-map "a-" 'calc-alt-summation)
 170   (define-key calc-mode-map "a*" 'calc-product)
 171   (define-key calc-mode-map "a\\" 'calc-poly-div)
 172   (define-key calc-mode-map "a%" 'calc-poly-rem)
 173   (define-key calc-mode-map "a/" 'calc-poly-div-rem)
 174   (define-key calc-mode-map "a=" 'calc-equal-to)
 175   (define-key calc-mode-map "a#" 'calc-not-equal-to)
 176   (define-key calc-mode-map "a<" 'calc-less-than)
 177   (define-key calc-mode-map "a>" 'calc-greater-than)
 178   (define-key calc-mode-map "a[" 'calc-less-equal)
 179   (define-key calc-mode-map "a]" 'calc-greater-equal)
 180   (define-key calc-mode-map "a." 'calc-remove-equal)
 181   (define-key calc-mode-map "a{" 'calc-in-set)
 182   (define-key calc-mode-map "a&" 'calc-logical-and)
 183   (define-key calc-mode-map "a|" 'calc-logical-or)
 184   (define-key calc-mode-map "a!" 'calc-logical-not)
 185   (define-key calc-mode-map "a:" 'calc-logical-if)
 186   (define-key calc-mode-map "a_" 'calc-subscript)
 187   (define-key calc-mode-map "a\"" 'calc-expand-formula)
 188
 189   (define-key calc-mode-map "b" nil)
 190   (define-key calc-mode-map "b?" 'calc-b-prefix-help)
 191   (define-key calc-mode-map "ba" 'calc-and)
 192   (define-key calc-mode-map "bc" 'calc-clip)
 193   (define-key calc-mode-map "bd" 'calc-diff)
 194   (define-key calc-mode-map "bl" 'calc-lshift-binary)
 195   (define-key calc-mode-map "bn" 'calc-not)
 196   (define-key calc-mode-map "bo" 'calc-or)
 197   (define-key calc-mode-map "bp" 'calc-pack-bits)
 198   (define-key calc-mode-map "br" 'calc-rshift-binary)
 199   (define-key calc-mode-map "bt" 'calc-rotate-binary)
 200   (define-key calc-mode-map "bu" 'calc-unpack-bits)
 201   (define-key calc-mode-map "bw" 'calc-word-size)
 202   (define-key calc-mode-map "bx" 'calc-xor)
 203   (define-key calc-mode-map "bB" 'calc-log)
 204   (define-key calc-mode-map "bD" 'calc-fin-ddb)
 205   (define-key calc-mode-map "bF" 'calc-fin-fv)
 206   (define-key calc-mode-map "bI" 'calc-fin-irr)
 207   (define-key calc-mode-map "bL" 'calc-lshift-arith)
 208   (define-key calc-mode-map "bM" 'calc-fin-pmt)
 209   (define-key calc-mode-map "bN" 'calc-fin-npv)
 210   (define-key calc-mode-map "bP" 'calc-fin-pv)
 211   (define-key calc-mode-map "bR" 'calc-rshift-arith)
 212   (define-key calc-mode-map "bS" 'calc-fin-sln)
 213   (define-key calc-mode-map "bT" 'calc-fin-rate)
 214   (define-key calc-mode-map "bY" 'calc-fin-syd)
 215   (define-key calc-mode-map "b#" 'calc-fin-nper)
 216   (define-key calc-mode-map "b%" 'calc-percent-change)
 217
 218   (define-key calc-mode-map "c" nil)
 219   (define-key calc-mode-map "c?" 'calc-c-prefix-help)
 220   (define-key calc-mode-map "cc" 'calc-clean)
 221   (define-key calc-mode-map "cd" 'calc-to-degrees)
 222   (define-key calc-mode-map "cf" 'calc-float)
 223   (define-key calc-mode-map "ch" 'calc-to-hms)
 224   (define-key calc-mode-map "cp" 'calc-polar)
 225   (define-key calc-mode-map "cr" 'calc-to-radians)
 226   (define-key calc-mode-map "cC" 'calc-cos)
 227   (define-key calc-mode-map "cF" 'calc-fraction)
 228   (define-key calc-mode-map "c%" 'calc-convert-percent)
 229
 230   (define-key calc-mode-map "d" nil)
 231   (define-key calc-mode-map "d?" 'calc-d-prefix-help)
 232   (define-key calc-mode-map "d0" 'calc-decimal-radix)
 233   (define-key calc-mode-map "d2" 'calc-binary-radix)
 234   (define-key calc-mode-map "d6" 'calc-hex-radix)
 235   (define-key calc-mode-map "d8" 'calc-octal-radix)
 236   (define-key calc-mode-map "db" 'calc-line-breaking)
 237   (define-key calc-mode-map "dc" 'calc-complex-notation)
 238   (define-key calc-mode-map "dd" 'calc-date-notation)
 239   (define-key calc-mode-map "de" 'calc-eng-notation)
 240   (define-key calc-mode-map "df" 'calc-fix-notation)
 241   (define-key calc-mode-map "dg" 'calc-group-digits)
 242   (define-key calc-mode-map "dh" 'calc-hms-notation)
 243   (define-key calc-mode-map "di" 'calc-i-notation)
 244   (define-key calc-mode-map "dj" 'calc-j-notation)
 245   (define-key calc-mode-map "dl" 'calc-line-numbering)
 246   (define-key calc-mode-map "dn" 'calc-normal-notation)
 247   (define-key calc-mode-map "do" 'calc-over-notation)
 248   (define-key calc-mode-map "dp" 'calc-show-plain)
 249   (define-key calc-mode-map "dr" 'calc-radix)
 250   (define-key calc-mode-map "ds" 'calc-sci-notation)
 251   (define-key calc-mode-map "dt" 'calc-truncate-stack)
 252   (define-key calc-mode-map "dw" 'calc-auto-why)
 253   (define-key calc-mode-map "dz" 'calc-leading-zeros)
 254   (define-key calc-mode-map "dA" 'calc-giac-language)
 255   (define-key calc-mode-map "dB" 'calc-big-language)
 256   (define-key calc-mode-map "dD" 'calc-redo)
 257   (define-key calc-mode-map "dC" 'calc-c-language)
 258   (define-key calc-mode-map "dE" 'calc-eqn-language)
 259   (define-key calc-mode-map "dF" 'calc-fortran-language)
 260   (define-key calc-mode-map "dM" 'calc-mathematica-language)
 261   (define-key calc-mode-map "dN" 'calc-normal-language)
 262   (define-key calc-mode-map "dO" 'calc-flat-language)
 263   (define-key calc-mode-map "dP" 'calc-pascal-language)
 264   (define-key calc-mode-map "dT" 'calc-tex-language)
 265   (define-key calc-mode-map "dL" 'calc-latex-language)
 266   (define-key calc-mode-map "dU" 'calc-unformatted-language)
 267   (define-key calc-mode-map "dW" 'calc-maple-language)
 268   (define-key calc-mode-map "dX" 'calc-maxima-language)
 269   (define-key calc-mode-map "dY" 'calc-yacas-language)
 270   (define-key calc-mode-map "d[" 'calc-truncate-up)
 271   (define-key calc-mode-map "d]" 'calc-truncate-down)
 272   (define-key calc-mode-map "d." 'calc-point-char)
 273   (define-key calc-mode-map "d," 'calc-group-char)
 274   (define-key calc-mode-map "d\"" 'calc-display-strings)
 275   (define-key calc-mode-map "d<" 'calc-left-justify)
 276   (define-key calc-mode-map "d=" 'calc-center-justify)
 277   (define-key calc-mode-map "d>" 'calc-right-justify)
 278   (define-key calc-mode-map "d{" 'calc-left-label)
 279   (define-key calc-mode-map "d}" 'calc-right-label)
 280   (define-key calc-mode-map "d'" 'calc-display-raw)
 281   (define-key calc-mode-map "d " 'calc-refresh)
 282   (define-key calc-mode-map "d\r" 'calc-refresh-top)
 283   (define-key calc-mode-map "d@" 'calc-toggle-banner)
 284
 285   (define-key calc-mode-map "f" nil)
 286   (define-key calc-mode-map "f?" 'calc-f-prefix-help)
 287   (define-key calc-mode-map "fb" 'calc-beta)
 288   (define-key calc-mode-map "fe" 'calc-erf)
 289   (define-key calc-mode-map "fg" 'calc-gamma)
 290   (define-key calc-mode-map "fh" 'calc-hypot)
 291   (define-key calc-mode-map "fi" 'calc-im)
 292   (define-key calc-mode-map "fj" 'calc-bessel-J)
 293   (define-key calc-mode-map "fn" 'calc-min)
 294   (define-key calc-mode-map "fr" 'calc-re)
 295   (define-key calc-mode-map "fs" 'calc-sign)
 296   (define-key calc-mode-map "fx" 'calc-max)
 297   (define-key calc-mode-map "fy" 'calc-bessel-Y)
 298   (define-key calc-mode-map "fA" 'calc-abssqr)
 299   (define-key calc-mode-map "fB" 'calc-inc-beta)
 300   (define-key calc-mode-map "fE" 'calc-expm1)
 301   (define-key calc-mode-map "fF" 'calc-floor)
 302   (define-key calc-mode-map "fG" 'calc-inc-gamma)
 303   (define-key calc-mode-map "fI" 'calc-ilog)
 304   (define-key calc-mode-map "fL" 'calc-lnp1)
 305   (define-key calc-mode-map "fM" 'calc-mant-part)
 306   (define-key calc-mode-map "fQ" 'calc-isqrt)
 307   (define-key calc-mode-map "fS" 'calc-scale-float)
 308   (define-key calc-mode-map "fT" 'calc-arctan2)
 309   (define-key calc-mode-map "fX" 'calc-xpon-part)
 310   (define-key calc-mode-map "f[" 'calc-decrement)
 311   (define-key calc-mode-map "f]" 'calc-increment)
 312
 313   (define-key calc-mode-map "g" nil)
 314   (define-key calc-mode-map "g?" 'calc-g-prefix-help)
 315   (define-key calc-mode-map "ga" 'calc-graph-add)
 316   (define-key calc-mode-map "gb" 'calc-graph-border)
 317   (define-key calc-mode-map "gc" 'calc-graph-clear)
 318   (define-key calc-mode-map "gd" 'calc-graph-delete)
 319   (define-key calc-mode-map "gf" 'calc-graph-fast)
 320   (define-key calc-mode-map "gg" 'calc-graph-grid)
 321   (define-key calc-mode-map "gh" 'calc-graph-header)
 322   (define-key calc-mode-map "gk" 'calc-graph-key)
 323   (define-key calc-mode-map "gj" 'calc-graph-juggle)
 324   (define-key calc-mode-map "gl" 'calc-graph-log-x)
 325   (define-key calc-mode-map "gn" 'calc-graph-name)
 326   (define-key calc-mode-map "gp" 'calc-graph-plot)
 327   (define-key calc-mode-map "gq" 'calc-graph-quit)
 328   (define-key calc-mode-map "gr" 'calc-graph-range-x)
 329   (define-key calc-mode-map "gs" 'calc-graph-line-style)
 330   (define-key calc-mode-map "gt" 'calc-graph-title-x)
 331   (define-key calc-mode-map "gv" 'calc-graph-view-commands)
 332   (define-key calc-mode-map "gx" 'calc-graph-display)
 333   (define-key calc-mode-map "gz" 'calc-graph-zero-x)
 334   (define-key calc-mode-map "gA" 'calc-graph-add-3d)
 335   (define-key calc-mode-map "gC" 'calc-graph-command)
 336   (define-key calc-mode-map "gD" 'calc-graph-device)
 337   (define-key calc-mode-map "gF" 'calc-graph-fast-3d)
 338   (define-key calc-mode-map "gG" 'calc-argument)
 339   (define-key calc-mode-map "gH" 'calc-graph-hide)
 340   (define-key calc-mode-map "gK" 'calc-graph-kill)
 341   (define-key calc-mode-map "gL" 'calc-graph-log-y)
 342   (define-key calc-mode-map "gN" 'calc-graph-num-points)
 343   (define-key calc-mode-map "gO" 'calc-graph-output)
 344   (define-key calc-mode-map "gP" 'calc-graph-print)
 345   (define-key calc-mode-map "gR" 'calc-graph-range-y)
 346   (define-key calc-mode-map "gS" 'calc-graph-point-style)
 347   (define-key calc-mode-map "gT" 'calc-graph-title-y)
 348   (define-key calc-mode-map "gV" 'calc-graph-view-trail)
 349   (define-key calc-mode-map "gX" 'calc-graph-geometry)
 350   (define-key calc-mode-map "gZ" 'calc-graph-zero-y)
 351   (define-key calc-mode-map "g\C-l" 'calc-graph-log-z)
 352   (define-key calc-mode-map "g\C-r" 'calc-graph-range-z)
 353   (define-key calc-mode-map "g\C-t" 'calc-graph-title-z)
 354
 355   (define-key calc-mode-map "h" 'calc-help-prefix)
 356
 357   (define-key calc-mode-map "j" nil)
 358   (define-key calc-mode-map "j?" 'calc-j-prefix-help)
 359   (define-key calc-mode-map "ja" 'calc-select-additional)
 360   (define-key calc-mode-map "jb" 'calc-break-selections)
 361   (define-key calc-mode-map "jc" 'calc-clear-selections)
 362   (define-key calc-mode-map "jd" 'calc-show-selections)
 363   (define-key calc-mode-map "je" 'calc-enable-selections)
 364   (define-key calc-mode-map "jl" 'calc-select-less)
 365   (define-key calc-mode-map "jm" 'calc-select-more)
 366   (define-key calc-mode-map "jn" 'calc-select-next)
 367   (define-key calc-mode-map "jo" 'calc-select-once)
 368   (define-key calc-mode-map "jp" 'calc-select-previous)
 369   (define-key calc-mode-map "jr" 'calc-rewrite-selection)
 370   (define-key calc-mode-map "js" 'calc-select-here)
 371   (define-key calc-mode-map "jv" 'calc-sel-evaluate)
 372   (define-key calc-mode-map "ju" 'calc-unselect)
 373   (define-key calc-mode-map "jC" 'calc-sel-commute)
 374   (define-key calc-mode-map "jD" 'calc-sel-distribute)
 375   (define-key calc-mode-map "jE" 'calc-sel-jump-equals)
 376   (define-key calc-mode-map "jI" 'calc-sel-isolate)
 377   (define-key calc-mode-map "jJ" 'calc-conj)
 378   (define-key calc-mode-map "jL" 'calc-commute-left)
 379   (define-key calc-mode-map "jM" 'calc-sel-merge)
 380   (define-key calc-mode-map "jN" 'calc-sel-negate)
 381   (define-key calc-mode-map "jO" 'calc-select-once-maybe)
 382   (define-key calc-mode-map "jR" 'calc-commute-right)
 383   (define-key calc-mode-map "jS" 'calc-select-here-maybe)
 384   (define-key calc-mode-map "jU" 'calc-sel-unpack)
 385   (define-key calc-mode-map "j&" 'calc-sel-invert)
 386   (define-key calc-mode-map "j\r" 'calc-copy-selection)
 387   (define-key calc-mode-map "j\n" 'calc-copy-selection)
 388   (define-key calc-mode-map "j\010" 'calc-del-selection)
 389   (define-key calc-mode-map "j\177" 'calc-del-selection)
 390   (define-key calc-mode-map "j'" 'calc-enter-selection)
 391   (define-key calc-mode-map "j`" 'calc-edit-selection)
 392   (define-key calc-mode-map "j+" 'calc-sel-add-both-sides)
 393   (define-key calc-mode-map "j-" 'calc-sel-sub-both-sides)
 394   (define-key calc-mode-map "j*" 'calc-sel-mult-both-sides)
 395   (define-key calc-mode-map "j/" 'calc-sel-div-both-sides)
 396   (define-key calc-mode-map "j\"" 'calc-sel-expand-formula)
 397
 398   (define-key calc-mode-map "k" nil)
 399   (define-key calc-mode-map "k?" 'calc-k-prefix-help)
 400   (define-key calc-mode-map "ka" 'calc-random-again)
 401   (define-key calc-mode-map "kb" 'calc-bernoulli-number)
 402   (define-key calc-mode-map "kc" 'calc-choose)
 403   (define-key calc-mode-map "kd" 'calc-double-factorial)
 404   (define-key calc-mode-map "ke" 'calc-euler-number)
 405   (define-key calc-mode-map "kf" 'calc-prime-factors)
 406   (define-key calc-mode-map "kg" 'calc-gcd)
 407   (define-key calc-mode-map "kh" 'calc-shuffle)
 408   (define-key calc-mode-map "kl" 'calc-lcm)
 409   (define-key calc-mode-map "km" 'calc-moebius)
 410   (define-key calc-mode-map "kn" 'calc-next-prime)
 411   (define-key calc-mode-map "kp" 'calc-prime-test)
 412   (define-key calc-mode-map "kr" 'calc-random)
 413   (define-key calc-mode-map "ks" 'calc-stirling-number)
 414   (define-key calc-mode-map "kt" 'calc-totient)
 415   (define-key calc-mode-map "kB" 'calc-utpb)
 416   (define-key calc-mode-map "kC" 'calc-utpc)
 417   (define-key calc-mode-map "kE" 'calc-extended-gcd)
 418   (define-key calc-mode-map "kF" 'calc-utpf)
 419   (define-key calc-mode-map "kK" 'calc-keep-args)
 420   (define-key calc-mode-map "kN" 'calc-utpn)
 421   (define-key calc-mode-map "kP" 'calc-utpp)
 422   (define-key calc-mode-map "kT" 'calc-utpt)
 423
 424   (define-key calc-mode-map "l" nil)
 425   (define-key calc-mode-map "lq" 'calc-lu-quant)
 426   (define-key calc-mode-map "ld" 'calc-db)
 427   (define-key calc-mode-map "ln" 'calc-np)
 428   (define-key calc-mode-map "l+" 'calc-lu-plus)
 429   (define-key calc-mode-map "l-" 'calc-lu-minus)
 430   (define-key calc-mode-map "l*" 'calc-lu-times)
 431   (define-key calc-mode-map "l/" 'calc-lu-divide)
 432   (define-key calc-mode-map "ls" 'calc-spn)
 433   (define-key calc-mode-map "lm" 'calc-midi)
 434   (define-key calc-mode-map "lf" 'calc-freq)
 435
 436   (define-key calc-mode-map "l?" 'calc-l-prefix-help)
 437
 438   (define-key calc-mode-map "m" nil)
 439   (define-key calc-mode-map "m?" 'calc-m-prefix-help)
 440   (define-key calc-mode-map "ma" 'calc-algebraic-mode)
 441   (define-key calc-mode-map "md" 'calc-degrees-mode)
 442   (define-key calc-mode-map "me" 'calc-embedded-preserve-modes)
 443   (define-key calc-mode-map "mf" 'calc-frac-mode)
 444   (define-key calc-mode-map "mg" 'calc-get-modes)
 445   (define-key calc-mode-map "mh" 'calc-hms-mode)
 446   (define-key calc-mode-map "mi" 'calc-infinite-mode)
 447   (define-key calc-mode-map "mm" 'calc-save-modes)
 448   (define-key calc-mode-map "mp" 'calc-polar-mode)
 449   (define-key calc-mode-map "mr" 'calc-radians-mode)
 450   (define-key calc-mode-map "ms" 'calc-symbolic-mode)
 451   (define-key calc-mode-map "mt" 'calc-total-algebraic-mode)
 452   (define-key calc-mode-map "\emt" 'calc-total-algebraic-mode)
 453   (define-key calc-mode-map "\em\et" 'calc-total-algebraic-mode)
 454   (define-key calc-mode-map "mv" 'calc-matrix-mode)
 455   (define-key calc-mode-map "mw" 'calc-working)
 456   (define-key calc-mode-map "mx" 'calc-always-load-extensions)
 457   (define-key calc-mode-map "mA" 'calc-alg-simplify-mode)
 458   (define-key calc-mode-map "mB" 'calc-bin-simplify-mode)
 459   (define-key calc-mode-map "mC" 'calc-auto-recompute)
 460   (define-key calc-mode-map "mD" 'calc-default-simplify-mode)
 461   (define-key calc-mode-map "mE" 'calc-ext-simplify-mode)
 462   (define-key calc-mode-map "mF" 'calc-settings-file-name)
 463   (define-key calc-mode-map "mI" 'calc-basic-simplify-mode)
 464   (define-key calc-mode-map "mM" 'calc-more-recursion-depth)
 465   (define-key calc-mode-map "mN" 'calc-num-simplify-mode)
 466   (define-key calc-mode-map "mO" 'calc-no-simplify-mode)
 467   (define-key calc-mode-map "mR" 'calc-mode-record-mode)
 468   (define-key calc-mode-map "mS" 'calc-shift-prefix)
 469   (define-key calc-mode-map "mU" 'calc-units-simplify-mode)
 470   (define-key calc-mode-map "mX" 'calc-load-everything)
 471
 472   (define-key calc-mode-map "r" nil)
 473   (define-key calc-mode-map "ri" 'calc-insert-register)
 474   (define-key calc-mode-map "rs" 'calc-copy-to-register)
 475   (define-key calc-mode-map "r?" 'calc-r-prefix-help)
 476
 477   (define-key calc-mode-map "s" nil)
 478   (define-key calc-mode-map "s?" 'calc-s-prefix-help)
 479   (define-key calc-mode-map "sc" 'calc-copy-variable)
 480   (define-key calc-mode-map "sd" 'calc-declare-variable)
 481   (define-key calc-mode-map "se" 'calc-edit-variable)
 482   (define-key calc-mode-map "si" 'calc-insert-variables)
 483   (define-key calc-mode-map "sk" 'calc-copy-special-constant)
 484   (define-key calc-mode-map "sl" 'calc-let)
 485   (define-key calc-mode-map "sm" 'calc-store-map)
 486   (define-key calc-mode-map "sn" 'calc-store-neg)
 487   (define-key calc-mode-map "sp" 'calc-permanent-variable)
 488   (define-key calc-mode-map "sr" 'calc-recall)
 489   (define-key calc-mode-map "ss" 'calc-store)
 490   (define-key calc-mode-map "st" 'calc-store-into)
 491   (define-key calc-mode-map "su" 'calc-unstore)
 492   (define-key calc-mode-map "sx" 'calc-store-exchange)
 493   (define-key calc-mode-map "sA" 'calc-edit-AlgSimpRules)
 494   (define-key calc-mode-map "sD" 'calc-edit-Decls)
 495   (define-key calc-mode-map "sE" 'calc-edit-EvalRules)
 496   (define-key calc-mode-map "sF" 'calc-edit-FitRules)
 497   (define-key calc-mode-map "sG" 'calc-edit-GenCount)
 498   (define-key calc-mode-map "sH" 'calc-edit-Holidays)
 499   (define-key calc-mode-map "sI" 'calc-edit-IntegLimit)
 500   (define-key calc-mode-map "sL" 'calc-edit-LineStyles)
 501   (define-key calc-mode-map "sP" 'calc-edit-PointStyles)
 502   (define-key calc-mode-map "sR" 'calc-edit-PlotRejects)
 503   (define-key calc-mode-map "sS" 'calc-sin)
 504   (define-key calc-mode-map "sT" 'calc-edit-TimeZone)
 505   (define-key calc-mode-map "sU" 'calc-edit-Units)
 506   (define-key calc-mode-map "sX" 'calc-edit-ExtSimpRules)
 507   (define-key calc-mode-map "s+" 'calc-store-plus)
 508   (define-key calc-mode-map "s-" 'calc-store-minus)
 509   (define-key calc-mode-map "s*" 'calc-store-times)
 510   (define-key calc-mode-map "s/" 'calc-store-div)
 511   (define-key calc-mode-map "s^" 'calc-store-power)
 512   (define-key calc-mode-map "s|" 'calc-store-concat)
 513   (define-key calc-mode-map "s&" 'calc-store-inv)
 514   (define-key calc-mode-map "s[" 'calc-store-decr)
 515   (define-key calc-mode-map "s]" 'calc-store-incr)
 516   (define-key calc-mode-map "s:" 'calc-assign)
 517   (define-key calc-mode-map "s=" 'calc-evalto)
 518
 519   (define-key calc-mode-map "t" nil)
 520   (define-key calc-mode-map "t?" 'calc-t-prefix-help)
 521   (define-key calc-mode-map "tb" 'calc-trail-backward)
 522   (define-key calc-mode-map "td" 'calc-trail-display)
 523   (define-key calc-mode-map "tf" 'calc-trail-forward)
 524   (define-key calc-mode-map "th" 'calc-trail-here)
 525   (define-key calc-mode-map "ti" 'calc-trail-in)
 526   (define-key calc-mode-map "tk" 'calc-trail-kill)
 527   (define-key calc-mode-map "tm" 'calc-trail-marker)
 528   (define-key calc-mode-map "tn" 'calc-trail-next)
 529   (define-key calc-mode-map "to" 'calc-trail-out)
 530   (define-key calc-mode-map "tp" 'calc-trail-previous)
 531   (define-key calc-mode-map "tr" 'calc-trail-isearch-backward)
 532   (define-key calc-mode-map "ts" 'calc-trail-isearch-forward)
 533   (define-key calc-mode-map "ty" 'calc-trail-yank)
 534   (define-key calc-mode-map "t[" 'calc-trail-first)
 535   (define-key calc-mode-map "t]" 'calc-trail-last)
 536   (define-key calc-mode-map "t<" 'calc-trail-scroll-left)
 537   (define-key calc-mode-map "t>" 'calc-trail-scroll-right)
 538   (define-key calc-mode-map "t{" 'calc-trail-backward)
 539   (define-key calc-mode-map "t}" 'calc-trail-forward)
 540   (define-key calc-mode-map "t." 'calc-full-trail-vectors)
 541   (define-key calc-mode-map "tC" 'calc-convert-time-zones)
 542   (define-key calc-mode-map "tD" 'calc-date)
 543   (define-key calc-mode-map "tI" 'calc-inc-month)
 544   (define-key calc-mode-map "tJ" 'calc-julian)
 545   (define-key calc-mode-map "tM" 'calc-new-month)
 546   (define-key calc-mode-map "tN" 'calc-now)
 547   (define-key calc-mode-map "tP" 'calc-date-part)
 548   (define-key calc-mode-map "tT" 'calc-tan)
 549   (define-key calc-mode-map "tU" 'calc-unix-time)
 550   (define-key calc-mode-map "tW" 'calc-new-week)
 551   (define-key calc-mode-map "tY" 'calc-new-year)
 552   (define-key calc-mode-map "tZ" 'calc-time-zone)
 553   (define-key calc-mode-map "t+" 'calc-business-days-plus)
 554   (define-key calc-mode-map "t-" 'calc-business-days-minus)
 555
 556   (define-key calc-mode-map "u" 'nil)
 557   (define-key calc-mode-map "u?" 'calc-u-prefix-help)
 558   (define-key calc-mode-map "ua" 'calc-autorange-units)
 559   (define-key calc-mode-map "ub" 'calc-base-units)
 560   (define-key calc-mode-map "uc" 'calc-convert-units)
 561   (define-key calc-mode-map "ud" 'calc-define-unit)
 562   (define-key calc-mode-map "ue" 'calc-explain-units)
 563   (define-key calc-mode-map "ug" 'calc-get-unit-definition)
 564   (define-key calc-mode-map "un" 'calc-convert-exact-units)
 565   (define-key calc-mode-map "up" 'calc-permanent-units)
 566   (define-key calc-mode-map "ur" 'calc-remove-units)
 567   (define-key calc-mode-map "us" 'calc-simplify-units)
 568   (define-key calc-mode-map "ut" 'calc-convert-temperature)
 569   (define-key calc-mode-map "uu" 'calc-undefine-unit)
 570   (define-key calc-mode-map "uv" 'calc-enter-units-table)
 571   (define-key calc-mode-map "ux" 'calc-extract-units)
 572   (define-key calc-mode-map "uV" 'calc-view-units-table)
 573   (define-key calc-mode-map "uC" 'calc-vector-covariance)
 574   (define-key calc-mode-map "uG" 'calc-vector-geometric-mean)
 575   (define-key calc-mode-map "uM" 'calc-vector-mean)
 576   (define-key calc-mode-map "uN" 'calc-vector-min)
 577   (define-key calc-mode-map "uS" 'calc-vector-sdev)
 578   (define-key calc-mode-map "uU" 'calc-undo)
 579   (define-key calc-mode-map "uX" 'calc-vector-max)
 580   (define-key calc-mode-map "u#" 'calc-vector-count)
 581   (define-key calc-mode-map "u+" 'calc-vector-sum)
 582   (define-key calc-mode-map "u*" 'calc-vector-product)
 583
 584   (define-key calc-mode-map "v" 'nil)
 585   (define-key calc-mode-map "v?" 'calc-v-prefix-help)
 586   (define-key calc-mode-map "va" 'calc-arrange-vector)
 587   (define-key calc-mode-map "vb" 'calc-build-vector)
 588   (define-key calc-mode-map "vc" 'calc-mcol)
 589   (define-key calc-mode-map "vd" 'calc-diag)
 590   (define-key calc-mode-map "ve" 'calc-expand-vector)
 591   (define-key calc-mode-map "vf" 'calc-vector-find)
 592   (define-key calc-mode-map "vh" 'calc-head)
 593   (define-key calc-mode-map "vi" 'calc-ident)
 594   (define-key calc-mode-map "vk" 'calc-cons)
 595   (define-key calc-mode-map "vl" 'calc-vlength)
 596   (define-key calc-mode-map "vm" 'calc-mask-vector)
 597   (define-key calc-mode-map "vn" 'calc-rnorm)
 598   (define-key calc-mode-map "vp" 'calc-pack)
 599   (define-key calc-mode-map "vr" 'calc-mrow)
 600   (define-key calc-mode-map "vs" 'calc-subvector)
 601   (define-key calc-mode-map "vt" 'calc-transpose)
 602   (define-key calc-mode-map "vu" 'calc-unpack)
 603   (define-key calc-mode-map "vv" 'calc-reverse-vector)
 604   (define-key calc-mode-map "vx" 'calc-index)
 605   (define-key calc-mode-map "vA" 'calc-apply)
 606   (define-key calc-mode-map "vC" 'calc-cross)
 607   (define-key calc-mode-map "vK" 'calc-kron)
 608   (define-key calc-mode-map "vD" 'calc-mdet)
 609   (define-key calc-mode-map "vE" 'calc-set-enumerate)
 610   (define-key calc-mode-map "vF" 'calc-set-floor)
 611   (define-key calc-mode-map "vG" 'calc-grade)
 612   (define-key calc-mode-map "vH" 'calc-histogram)
 613   (define-key calc-mode-map "vI" 'calc-inner-product)
 614   (define-key calc-mode-map "vJ" 'calc-conj-transpose)
 615   (define-key calc-mode-map "vL" 'calc-mlud)
 616   (define-key calc-mode-map "vM" 'calc-map)
 617   (define-key calc-mode-map "vN" 'calc-cnorm)
 618   (define-key calc-mode-map "vO" 'calc-outer-product)
 619   (define-key calc-mode-map "vR" 'calc-reduce)
 620   (define-key calc-mode-map "vS" 'calc-sort)
 621   (define-key calc-mode-map "vT" 'calc-mtrace)
 622   (define-key calc-mode-map "vU" 'calc-accumulate)
 623   (define-key calc-mode-map "vV" 'calc-set-union)
 624   (define-key calc-mode-map "vX" 'calc-set-xor)
 625   (define-key calc-mode-map "v^" 'calc-set-intersect)
 626   (define-key calc-mode-map "v-" 'calc-set-difference)
 627   (define-key calc-mode-map "v~" 'calc-set-complement)
 628   (define-key calc-mode-map "v:" 'calc-set-span)
 629   (define-key calc-mode-map "v#" 'calc-set-cardinality)
 630   (define-key calc-mode-map "v+" 'calc-remove-duplicates)
 631   (define-key calc-mode-map "v&" 'calc-inv)
 632   (define-key calc-mode-map "v<" 'calc-matrix-left-justify)
 633   (define-key calc-mode-map "v=" 'calc-matrix-center-justify)
 634   (define-key calc-mode-map "v>" 'calc-matrix-right-justify)
 635   (define-key calc-mode-map "v." 'calc-full-vectors)
 636   (define-key calc-mode-map "v/" 'calc-break-vectors)
 637   (define-key calc-mode-map "v," 'calc-vector-commas)
 638   (define-key calc-mode-map "v[" 'calc-vector-brackets)
 639   (define-key calc-mode-map "v]" 'calc-matrix-brackets)
 640   (define-key calc-mode-map "v{" 'calc-vector-braces)
 641   (define-key calc-mode-map "v}" 'calc-matrix-brackets)
 642   (define-key calc-mode-map "v(" 'calc-vector-parens)
 643   (define-key calc-mode-map "v)" 'calc-matrix-brackets)
 644   ;; We can't rely on the automatic upper->lower conversion because
 645   ;; in the global map V is explicitly bound, so we need to bind it
 646   ;; explicitly as well :-(  --stef
 647   (define-key calc-mode-map "V" (lookup-key calc-mode-map "v"))
 648
 649   (define-key calc-mode-map "z" 'nil)
 650   (define-key calc-mode-map "z?" 'calc-z-prefix-help)
 651
 652   (define-key calc-mode-map "Z" 'nil)
 653   (define-key calc-mode-map "Z?" 'calc-shift-Z-prefix-help)
 654   (define-key calc-mode-map "ZC" 'calc-user-define-composition)
 655   (define-key calc-mode-map "ZD" 'calc-user-define)
 656   (define-key calc-mode-map "ZE" 'calc-user-define-edit)
 657   (define-key calc-mode-map "ZF" 'calc-user-define-formula)
 658   (define-key calc-mode-map "ZG" 'calc-get-user-defn)
 659   (define-key calc-mode-map "ZI" 'calc-user-define-invocation)
 660   (define-key calc-mode-map "ZK" 'calc-user-define-kbd-macro)
 661   (define-key calc-mode-map "ZP" 'calc-user-define-permanent)
 662   (define-key calc-mode-map "ZS" 'calc-edit-user-syntax)
 663   (define-key calc-mode-map "ZT" 'calc-timing)
 664   (define-key calc-mode-map "ZU" 'calc-user-undefine)
 665   (define-key calc-mode-map "Z[" 'calc-kbd-if)
 666   (define-key calc-mode-map "Z:" 'calc-kbd-else)
 667   (define-key calc-mode-map "Z|" 'calc-kbd-else-if)
 668   (define-key calc-mode-map "Z]" 'calc-kbd-end-if)
 669   (define-key calc-mode-map "Z<" 'calc-kbd-repeat)
 670   (define-key calc-mode-map "Z>" 'calc-kbd-end-repeat)
 671   (define-key calc-mode-map "Z(" 'calc-kbd-for)
 672   (define-key calc-mode-map "Z)" 'calc-kbd-end-for)
 673   (define-key calc-mode-map "Z{" 'calc-kbd-loop)
 674   (define-key calc-mode-map "Z}" 'calc-kbd-end-loop)
 675   (define-key calc-mode-map "Z/" 'calc-kbd-break)
 676   (define-key calc-mode-map "Z`" 'calc-kbd-push)
 677   (define-key calc-mode-map "Z'" 'calc-kbd-pop)
 678   (define-key calc-mode-map "Z=" 'calc-kbd-report)
 679   (define-key calc-mode-map "Z#" 'calc-kbd-query)
 680
 681   (calc-init-prefixes)
 682
 683   (mapc (function
 684          (lambda (x)
 685           (define-key calc-mode-map (format "c%c" x) 'calc-clean-num)
 686           (define-key calc-mode-map (format "j%c" x) 'calc-select-part)
 687           (define-key calc-mode-map (format "r%c" x) 'calc-recall-quick)
 688           (define-key calc-mode-map (format "s%c" x) 'calc-store-quick)
 689           (define-key calc-mode-map (format "t%c" x) 'calc-store-into-quick)
 690           (define-key calc-mode-map (format "u%c" x) 'calc-quick-units)))
 691         "0123456789")
 692
 693   (let ((i ?A))
 694     (while (<= i ?z)
 695       (if (eq (car-safe (aref (nth 1 calc-mode-map) i)) 'keymap)
 696           (aset (nth 1 calc-mode-map) i
 697                 (cons 'keymap (cons (cons ?\e (aref (nth 1 calc-mode-map) i))
 698                                     (cdr (aref (nth 1 calc-mode-map) i))))))
 699       (setq i (1+ i))))
 700
 701   (setq calc-alg-map (copy-keymap calc-mode-map)
 702         calc-alg-esc-map (copy-keymap esc-map))
 703   (let ((i 32))
 704     (while (< i 127)
 705       (or (memq i '(?' ?` ?= ??))
 706           (aset (nth 1 calc-alg-map) i 'calc-auto-algebraic-entry))
 707       (or (memq i '(?# ?x ?0 ?1 ?2 ?3 ?4 ?5 ?6 ?7 ?8 ?9))
 708           (aset (nth 1 calc-alg-esc-map) i (aref (nth 1 calc-mode-map) i)))
 709       (setq i (1+ i))))
 710   (define-key calc-alg-map "\e" calc-alg-esc-map)
 711   (define-key calc-alg-map "\e\t" 'calc-roll-up)
 712   (define-key calc-alg-map "\e\C-m" 'calc-last-args-stub)
 713   (define-key calc-alg-map "\e\177" 'calc-pop-above)
 714
 715 ;;;; (Autoloads here)
 716   (mapc (function (lambda (x)
 717     (mapcar (function (lambda (func)
 718       (autoload func (car x)))) (cdr x))))
 719     '(
 720
 721  ("calc-alg" calc-has-rules math-defsimplify
 722 calc-modify-simplify-mode calcFunc-collect calcFunc-esimplify
 723 calcFunc-islin calcFunc-islinnt calcFunc-lin calcFunc-linnt
 724 calcFunc-simplify calcFunc-subst calcFunc-powerexpand math-beforep
 725 math-build-polynomial-expr math-expand-formula math-expr-contains
 726 math-expr-contains-count math-expr-depends math-expr-height
 727 math-expr-subst math-expr-weight math-integer-plus math-is-linear
 728 math-is-multiple math-is-polynomial math-linear-in math-multiple-of
 729 math-poly-depends math-poly-mix math-poly-mul
 730 math-poly-simplify math-poly-zerop math-polynomial-base
 731 math-polynomial-p math-recompile-eval-rules math-simplify
 732 math-simplify-exp math-simplify-extended math-simplify-sqrt
 733 math-to-simple-fraction)
 734
 735  ("calcalg2" calcFunc-asum calcFunc-deriv
 736 calcFunc-ffinv calcFunc-finv calcFunc-fsolve calcFunc-gpoly
 737 calcFunc-integ calcFunc-poly calcFunc-prod calcFunc-roots
 738 calcFunc-solve calcFunc-sum calcFunc-table calcFunc-taylor
 739 calcFunc-tderiv math-expr-calls math-integral-q02 math-integral-q12
 740 math-integral-rational-funcs math-lcm-denoms math-looks-evenp
 741 math-poly-all-roots math-prod-rec math-reject-solution math-solve-eqn
 742 math-solve-for math-sum-rec math-try-integral)
 743
 744  ("calcalg3" calcFunc-efit calcFunc-fit
 745 calcFunc-fitdummy calcFunc-fitparam calcFunc-fitvar
 746 calcFunc-hasfitparams calcFunc-hasfitvars calcFunc-maximize
 747 calcFunc-minimize calcFunc-ninteg calcFunc-polint calcFunc-ratint
 748 calcFunc-root calcFunc-wmaximize calcFunc-wminimize calcFunc-wroot
 749 calcFunc-xfit math-find-minimum math-find-root math-ninteg-evaluate
 750 math-ninteg-midpoint math-ninteg-romberg math-poly-interp)
 751
 752  ("calc-arith" calcFunc-abs calcFunc-abssqr
 753 calcFunc-add calcFunc-ceil calcFunc-decr calcFunc-deven calcFunc-dimag
 754 calcFunc-dint calcFunc-div calcFunc-dnatnum calcFunc-dneg
 755 calcFunc-dnonneg calcFunc-dnonzero calcFunc-dnumint calcFunc-dodd
 756 calcFunc-dpos calcFunc-drange calcFunc-drat calcFunc-dreal
 757 calcFunc-dscalar calcFunc-fceil calcFunc-ffloor calcFunc-float
 758 calcFunc-fround calcFunc-frounde calcFunc-froundu calcFunc-ftrunc
 759 calcFunc-idiv calcFunc-incr calcFunc-ldiv calcFunc-mant calcFunc-max calcFunc-min
 760 calcFunc-mod calcFunc-mul calcFunc-neg calcFunc-percent calcFunc-pow
 761 calcFunc-relch calcFunc-round calcFunc-rounde calcFunc-roundu
 762 calcFunc-scf calcFunc-sub calcFunc-xpon math-abs math-abs-approx
 763 math-add-objects-fancy math-add-or-sub math-add-symb-fancy
 764 math-ceiling math-combine-prod math-combine-sum math-div-by-zero
 765 math-div-objects-fancy math-div-symb-fancy math-div-zero
 766 math-float-fancy math-floor-fancy math-floor-special math-guess-if-neg
 767 math-intv-constp math-known-evenp math-known-imagp math-known-integerp
 768 math-known-matrixp math-known-negp math-known-nonnegp
 769 math-known-nonposp math-known-nonzerop math-known-num-integerp
 770 math-known-oddp math-known-posp math-known-realp math-known-scalarp
 771 math-max math-min math-mod-fancy math-mul-float math-mul-objects-fancy
 772 math-mul-or-div math-mul-symb-fancy math-mul-zero math-neg-fancy
 773 math-neg-float math-okay-neg math-possible-signs math-possible-types
 774 math-pow-fancy math-pow-mod math-pow-of-zero math-pow-zero
 775 math-quarter-integer math-round math-setup-declarations math-sqr
 776 math-sqr-float math-trunc-fancy math-trunc-special)
 777
 778  ("calc-bin" calcFunc-and calcFunc-ash
 779 calcFunc-clip calcFunc-diff calcFunc-lsh calcFunc-not calcFunc-or
 780 calcFunc-rash calcFunc-rot calcFunc-rsh calcFunc-xor math-clip
 781 math-compute-max-digits math-convert-radix-digits math-float-parts
 782 math-format-bignum-binary math-format-bignum-hex
 783 math-format-bignum-octal math-format-bignum-radix math-format-binary
 784 math-format-radix math-format-radix-float math-integer-log2
 785 math-power-of-2 math-radix-float-power)
 786
 787  ("calc-comb"  calc-report-prime-test
 788 calcFunc-choose calcFunc-dfact calcFunc-egcd calcFunc-fact
 789 calcFunc-gcd calcFunc-lcm calcFunc-moebius calcFunc-nextprime
 790 calcFunc-perm calcFunc-prevprime calcFunc-prfac calcFunc-prime
 791 calcFunc-random calcFunc-shuffle calcFunc-stir1 calcFunc-stir2
 792 calcFunc-totient math-init-random-base math-member math-prime-test
 793 math-random-base)
 794
 795  ("calccomp" calcFunc-cascent calcFunc-cdescent
 796 calcFunc-cheight calcFunc-cwidth math-comp-ascent math-comp-descent
 797 math-comp-height math-comp-width math-compose-expr
 798 math-composition-to-string math-stack-value-offset-fancy
 799 math-vector-is-string math-vector-to-string)
 800
 801  ("calc-cplx" calcFunc-arg calcFunc-conj
 802 calcFunc-im calcFunc-polar calcFunc-re calcFunc-rect math-complex
 803 math-fix-circular math-imaginary math-imaginary-i math-normalize-polar
 804 math-polar math-want-polar)
 805
 806  ("calc-embed" calc-do-embedded
 807 calc-do-embedded-activate calc-embedded-evaluate-expr
 808 calc-embedded-modes-change calc-embedded-var-change
 809 calc-embedded-preserve-modes)
 810
 811  ("calc-fin" calc-to-percentage calcFunc-ddb
 812 calcFunc-fv calcFunc-fvb calcFunc-fvl calcFunc-irr calcFunc-irrb
 813 calcFunc-nper calcFunc-nperb calcFunc-nperl calcFunc-npv calcFunc-npvb
 814 calcFunc-pmt calcFunc-pmtb calcFunc-pv calcFunc-pvb calcFunc-pvl
 815 calcFunc-rate calcFunc-rateb calcFunc-ratel calcFunc-sln calcFunc-syd)
 816
 817  ("calc-forms" calcFunc-badd calcFunc-bsub
 818 calcFunc-date calcFunc-day calcFunc-dsadj calcFunc-hms
 819 calcFunc-holiday calcFunc-hour calcFunc-incmonth calcFunc-incyear
 820 calcFunc-intv calcFunc-julian calcFunc-makemod calcFunc-minute
 821 calcFunc-month calcFunc-newmonth calcFunc-newweek calcFunc-newyear
 822 calcFunc-now calcFunc-pwday calcFunc-sdev calcFunc-second
 823 calcFunc-time calcFunc-tzconv calcFunc-tzone calcFunc-unixtime
 824 calcFunc-weekday calcFunc-year calcFunc-yearday math-combine-intervals
 825 math-date-parts math-date-to-dt math-div-mod math-dt-to-date
 826 math-format-date math-from-business-day math-from-hms math-make-intv
 827 math-make-mod math-make-sdev math-mod-intv math-normalize-hms
 828 math-normalize-mod math-parse-date math-read-angle-brackets
 829 math-setup-add-holidays math-setup-holidays math-setup-year-holidays
 830 math-sort-intv math-to-business-day math-to-hms)
 831
 832  ("calc-frac" calc-add-fractions
 833 calc-div-fractions calc-mul-fractions calcFunc-fdiv calcFunc-frac
 834 math-make-frac)
 835
 836  ("calc-funcs" calc-prob-dist calcFunc-bern
 837 calcFunc-besJ calcFunc-besY calcFunc-beta calcFunc-betaB
 838 calcFunc-betaI calcFunc-erf calcFunc-erfc calcFunc-euler
 839 calcFunc-gamma calcFunc-gammaG calcFunc-gammaP calcFunc-gammaQ
 840 calcFunc-gammag calcFunc-ltpb calcFunc-ltpc calcFunc-ltpf
 841 calcFunc-ltpn calcFunc-ltpp calcFunc-ltpt calcFunc-utpb calcFunc-utpc
 842 calcFunc-utpf calcFunc-utpn calcFunc-utpp calcFunc-utpt
 843 math-bernoulli-number math-gammap1-raw)
 844
 845  ("calc-graph" calc-graph-show-tty)
 846
 847  ("calc-incom" calc-digit-dots)
 848
 849  ("calc-keypd" calc-do-keypad
 850 calc-keypad-x-left-click calc-keypad-x-middle-click
 851 calc-keypad-x-right-click)
 852
 853  ("calc-lang" calc-set-language
 854 math-read-big-balance math-read-big-rec)
 855
 856  ("calc-map" calc-get-operator calcFunc-accum
 857 calcFunc-afixp calcFunc-anest calcFunc-apply calcFunc-call
 858 calcFunc-fixp calcFunc-inner calcFunc-map calcFunc-mapa calcFunc-mapc
 859 calcFunc-mapd calcFunc-mapeq calcFunc-mapeqp calcFunc-mapeqr
 860 calcFunc-mapr calcFunc-nest calcFunc-outer calcFunc-raccum
 861 calcFunc-reduce calcFunc-reducea calcFunc-reducec calcFunc-reduced
 862 calcFunc-reducer calcFunc-rreduce calcFunc-rreducea calcFunc-rreducec
 863 calcFunc-rreduced calcFunc-rreducer math-build-call
 864 math-calcFunc-to-var math-multi-subst math-multi-subst-rec
 865 math-var-to-calcFunc)
 866
 867  ("calc-mtx" calcFunc-det calcFunc-lud calcFunc-tr
 868 math-col-matrix math-lud-solve math-matrix-inv-raw math-matrix-lud
 869 math-mul-mat-vec math-mul-mats math-row-matrix)
 870
 871  ("calc-math" calcFunc-alog calcFunc-arccos
 872 calcFunc-arccosh calcFunc-arcsin calcFunc-arcsincos calcFunc-arcsinh
 873 calcFunc-arctan calcFunc-arctan2 calcFunc-arctanh calcFunc-csc
 874 calcFunc-csch calcFunc-cos calcFunc-cosh calcFunc-cot calcFunc-coth
 875 calcFunc-deg calcFunc-exp calcFunc-exp10 calcFunc-expm1
 876 calcFunc-hypot calcFunc-ilog calcFunc-isqrt calcFunc-ln calcFunc-lnp1
 877 calcFunc-log calcFunc-log10 calcFunc-nroot calcFunc-rad calcFunc-sec
 878 calcFunc-sech calcFunc-sin
 879 calcFunc-sincos calcFunc-sinh calcFunc-sqr calcFunc-sqrt calcFunc-tan
 880 calcFunc-tanh math-arccos-raw math-arcsin-raw math-arctan-raw
 881 math-arctan2-raw math-cos-raw math-cot-raw math-csc-raw
 882 math-exp-minus-1-raw math-exp-raw
 883 math-from-radians math-from-radians-2 math-hypot math-infinite-dir
 884 math-isqrt-small math-ln-raw math-nearly-equal math-nearly-equal-float
 885 math-nearly-zerop math-nearly-zerop-float math-nth-root
 886 math-sin-cos-raw math-sin-raw math-sqrt math-sqrt-float math-sqrt-raw
 887 math-tan-raw math-to-radians math-to-radians-2)
 888
 889  ("calc-mode" math-get-modes-vec)
 890
 891  ("calc-poly" calcFunc-apart calcFunc-expand
 892 calcFunc-expandpow calcFunc-factor calcFunc-factors calcFunc-nrat
 893 calcFunc-pcont calcFunc-pdeg calcFunc-pdiv calcFunc-pdivide
 894 calcFunc-pdivrem calcFunc-pgcd calcFunc-plead calcFunc-pprim
 895 calcFunc-prem math-accum-factors math-atomic-factorp
 896 math-div-poly-const math-div-thru math-expand-power math-expand-term
 897 math-factor-contains math-factor-expr math-factor-expr-part
 898 math-factor-expr-try math-factor-finish math-factor-poly-coefs
 899 math-factor-protect math-mul-thru math-padded-polynomial
 900 math-partial-fractions math-poly-degree math-poly-deriv-coefs
 901 math-poly-gcd-frac-list math-poly-modulus-rec math-ratpoly-p
 902 math-to-ratpoly math-to-ratpoly-rec)
 903
 904  ("calc-prog" calc-default-formula-arglist
 905 calc-execute-kbd-macro calc-finish-user-syntax-edit
 906 calc-fix-token-name calc-fix-user-formula calc-read-parse-table
 907 calc-read-parse-table-part calc-subsetp calc-write-parse-table
 908 calc-write-parse-table-part calcFunc-constant calcFunc-eq calcFunc-geq
 909 calcFunc-gt calcFunc-if calcFunc-in calcFunc-integer calcFunc-istrue
 910 calcFunc-land calcFunc-leq calcFunc-lnot calcFunc-lor calcFunc-lt
 911 calcFunc-negative calcFunc-neq calcFunc-nonvar calcFunc-real
 912 calcFunc-refers calcFunc-rmeq calcFunc-typeof calcFunc-variable
 913 math-body-refers-to math-break math-composite-inequalities
 914 math-do-defmath math-handle-for math-handle-foreach
 915 math-normalize-logical-op math-return)
 916
 917  ("calc-rewr" calcFunc-match calcFunc-matches
 918 calcFunc-matchnot calcFunc-rewrite calcFunc-vmatches
 919 math-apply-rewrites math-compile-patterns math-compile-rewrites
 920 math-flatten-lands math-match-patterns math-rewrite
 921 math-rewrite-heads)
 922
 923  ("calc-rules" calc-CommuteRules calc-DistribRules calc-FactorRules
 924 calc-FitRules calc-IntegAfterRules calc-InvertRules calc-JumpRules
 925 calc-MergeRules calc-NegateRules
 926 calc-compile-rule-set)
 927
 928  ("calc-sel" calc-auto-selection
 929 calc-delete-selection calc-encase-atoms calc-find-assoc-parent-formula
 930 calc-find-parent-formula calc-find-sub-formula calc-prepare-selection
 931 calc-preserve-point calc-replace-selections calc-replace-sub-formula
 932 calc-roll-down-with-selections calc-roll-up-with-selections
 933 calc-sel-error)
 934
 935  ("calc-stat" calc-vector-op calcFunc-agmean
 936 calcFunc-vcorr calcFunc-vcount calcFunc-vcov calcFunc-vflat
 937 calcFunc-vgmean calcFunc-vhmean calcFunc-vmax calcFunc-vmean
 938 calcFunc-vmeane calcFunc-vmedian calcFunc-vmin calcFunc-vpcov
 939 calcFunc-vprod calcFunc-vpsdev calcFunc-vpvar calcFunc-vsdev
 940 calcFunc-vsum calcFunc-vvar math-flatten-many-vecs)
 941
 942  ("calc-store" calc-read-var-name
 943 calc-store-value calc-var-name)
 944
 945  ("calc-stuff" calc-explain-why calcFunc-clean
 946 calcFunc-pclean calcFunc-pfloat calcFunc-pfrac)
 947
 948  ("calc-units" calcFunc-usimplify calcFunc-lufadd calcFunc-lupadd
 949 calcFunc-lufsub calcFunc-lupsub calcFunc-lufmul calcFunc-lupmul
 950 calcFunc-lufdiv calcFunc-lupdiv calcFunc-lufquant calcFunc-lupquant
 951 calcFunc-dbfield calcFunc-dbpower calcFunc-npfield
 952 calcFunc-nppower calcFunc-spn calcFunc-midi calcFunc-freq
 953 math-build-units-table math-build-units-table-buffer
 954 math-check-unit-name math-convert-temperature math-convert-units
 955 math-extract-units math-remove-units math-simplify-units
 956 math-single-units-in-expr-p math-to-standard-units
 957 math-units-in-expr-p)
 958
 959  ("calc-vec" calcFunc-append calcFunc-appendrev
 960 calcFunc-arrange calcFunc-cnorm calcFunc-cons calcFunc-cross
 961 calcFunc-kron calcFunc-ctrn calcFunc-cvec calcFunc-diag calcFunc-find
 962 calcFunc-getdiag calcFunc-grade calcFunc-head calcFunc-histogram
 963 calcFunc-idn calcFunc-index calcFunc-mcol calcFunc-mdims
 964 calcFunc-mrcol calcFunc-mrow calcFunc-mrrow calcFunc-pack
 965 calcFunc-rcons calcFunc-rdup calcFunc-rev calcFunc-rgrade
 966 calcFunc-rhead calcFunc-rnorm calcFunc-rsort calcFunc-rsubvec
 967 calcFunc-rtail calcFunc-sort calcFunc-subscr calcFunc-subvec
 968 calcFunc-tail calcFunc-trn calcFunc-unpack calcFunc-unpackt
 969 calcFunc-vcard calcFunc-vcompl calcFunc-vconcat calcFunc-vconcatrev
 970 calcFunc-vdiff calcFunc-vec calcFunc-venum calcFunc-vexp
 971 calcFunc-vfloor calcFunc-vint calcFunc-vlen calcFunc-vmask
 972 calcFunc-vpack calcFunc-vspan calcFunc-vunion calcFunc-vunpack
 973 calcFunc-vxor math-check-for-commas math-clean-set math-copy-matrix
 974 math-dimension-error math-dot-product math-flatten-vector math-map-vec
 975 math-map-vec-2 math-mat-col math-mimic-ident math-prepare-set
 976 math-read-brackets math-reduce-cols math-reduce-vec math-transpose)
 977
 978  ("calc-yank" calc-alg-edit calc-clean-newlines
 979 calc-do-grab-rectangle calc-do-grab-region calc-finish-stack-edit
 980 calc-copy-to-register calc-insert-register
 981 calc-append-to-register calc-prepend-to-register
 982 calc-force-refresh calc-locate-cursor-element calc-show-edit-buffer)
 983
 984 ))
 985
 986   (mapcar (function (lambda (x)
 987     (mapcar (function (lambda (cmd)
 988       (autoload cmd (car x) nil t))) (cdr x))))
 989     '(
 990
 991  ("calc-alg" calc-alg-evaluate calc-apart calc-collect calc-expand
 992 calc-expand-formula calc-factor calc-normalize-rat calc-poly-div
 993 calc-poly-div-rem calc-poly-gcd calc-poly-rem calc-simplify
 994 calc-simplify-extended calc-substitute calc-powerexpand)
 995
 996  ("calcalg2" calc-alt-summation calc-derivative
 997 calc-dump-integral-cache calc-integral calc-num-integral
 998 calc-poly-roots calc-product calc-solve-for calc-summation
 999 calc-tabulate calc-taylor)
1000
1001  ("calcalg3" calc-curve-fit calc-find-maximum calc-find-minimum
1002 calc-find-root calc-poly-interp)
1003
1004  ("calc-arith" calc-abs calc-abssqr calc-ceiling calc-decrement
1005 calc-floor calc-idiv calc-increment calc-mant-part calc-max calc-min
1006 calc-round calc-scale-float calc-sign calc-trunc calc-xpon-part)
1007
1008  ("calc-bin" calc-and calc-binary-radix calc-clip calc-twos-complement-mode
1009 calc-decimal-radix calc-diff calc-hex-radix calc-leading-zeros
1010 calc-lshift-arith calc-lshift-binary calc-not calc-octal-radix calc-or calc-radix
1011 calc-rotate-binary calc-rshift-arith calc-rshift-binary calc-word-size
1012 calc-xor)
1013
1014  ("calc-comb" calc-choose calc-double-factorial calc-extended-gcd
1015 calc-factorial calc-gamma calc-gcd calc-lcm calc-moebius
1016 calc-next-prime calc-perm calc-prev-prime calc-prime-factors
1017 calc-prime-test calc-random calc-random-again calc-rrandom
1018 calc-shuffle calc-totient)
1019
1020  ("calc-cplx" calc-argument calc-complex-notation calc-i-notation
1021 calc-im calc-j-notation calc-polar calc-polar-mode calc-re)
1022
1023  ("calc-embed" calc-embedded-copy-formula-as-kill
1024 calc-embedded-duplicate calc-embedded-edit calc-embedded-forget
1025 calc-embedded-kill-formula calc-embedded-mark-formula
1026 calc-embedded-new-formula calc-embedded-next calc-embedded-previous
1027 calc-embedded-select calc-embedded-update-formula calc-embedded-word
1028 calc-find-globals calc-show-plain)
1029
1030  ("calc-fin" calc-convert-percent calc-fin-ddb calc-fin-fv
1031 calc-fin-irr calc-fin-nper calc-fin-npv calc-fin-pmt calc-fin-pv
1032 calc-fin-rate calc-fin-sln calc-fin-syd calc-percent-change)
1033
1034  ("calc-forms" calc-business-days-minus calc-business-days-plus
1035 calc-convert-time-zones calc-date calc-date-notation calc-date-part
1036 calc-from-hms calc-hms-mode calc-hms-notation calc-inc-month
1037 calc-julian calc-new-month calc-new-week calc-new-year calc-now
1038 calc-time calc-time-zone calc-to-hms calc-unix-time)
1039
1040  ("calc-frac" calc-fdiv calc-frac-mode calc-fraction
1041 calc-over-notation calc-slash-notation)
1042
1043  ("calc-funcs" calc-bernoulli-number calc-bessel-J calc-bessel-Y
1044 calc-beta calc-erf calc-erfc calc-euler-number calc-inc-beta
1045 calc-inc-gamma calc-stirling-number calc-utpb calc-utpc calc-utpf
1046 calc-utpn calc-utpp calc-utpt)
1047
1048  ("calc-graph" calc-graph-add calc-graph-add-3d calc-graph-border
1049 calc-graph-clear calc-graph-command calc-graph-delete
1050 calc-graph-device calc-graph-display calc-graph-fast
1051 calc-graph-fast-3d calc-graph-geometry calc-graph-grid
1052 calc-graph-header calc-graph-hide calc-graph-juggle calc-graph-key
1053 calc-graph-kill calc-graph-line-style calc-graph-log-x
1054 calc-graph-log-y calc-graph-log-z calc-graph-name
1055 calc-graph-num-points calc-graph-output calc-graph-plot
1056 calc-graph-point-style calc-graph-print calc-graph-quit
1057 calc-graph-range-x calc-graph-range-y calc-graph-range-z
1058 calc-graph-show-dumb calc-graph-title-x calc-graph-title-y
1059 calc-graph-title-z calc-graph-view-commands calc-graph-view-trail
1060 calc-graph-zero-x calc-graph-zero-y)
1061
1062  ("calc-help" calc-a-prefix-help calc-b-prefix-help calc-c-prefix-help
1063 calc-d-prefix-help calc-describe-function calc-describe-key
1064 calc-describe-key-briefly calc-describe-variable calc-f-prefix-help
1065 calc-full-help calc-g-prefix-help calc-help-prefix
1066 calc-hyperbolic-prefix-help calc-inv-hyp-prefix-help calc-option-prefix-help
1067 calc-inverse-prefix-help calc-j-prefix-help calc-k-prefix-help
1068 calc-m-prefix-help calc-r-prefix-help calc-s-prefix-help
1069 calc-t-prefix-help calc-u-prefix-help calc-l-prefix-help
1070 calc-v-prefix-help)
1071
1072  ("calc-incom" calc-begin-complex calc-begin-vector calc-comma
1073 calc-dots calc-end-complex calc-end-vector calc-semi)
1074
1075  ("calc-keypd" calc-keypad-menu calc-keypad-menu-back
1076 calc-keypad-press)
1077
1078  ("calc-lang" calc-big-language calc-c-language calc-eqn-language
1079 calc-flat-language calc-fortran-language calc-maple-language
1080 calc-yacas-language calc-maxima-language calc-giac-language
1081 calc-mathematica-language calc-normal-language calc-pascal-language
1082 calc-tex-language calc-latex-language calc-unformatted-language)
1083
1084  ("calc-map" calc-accumulate calc-apply calc-inner-product calc-map
1085 calc-map-equation calc-map-stack calc-outer-product calc-reduce)
1086
1087  ("calc-mtx" calc-mdet calc-mlud calc-mtrace)
1088
1089  ("calc-math" calc-arccos calc-arccosh calc-arcsin calc-arcsinh
1090 calc-arctan calc-arctan2 calc-arctanh calc-conj calc-cos calc-cosh
1091 calc-cot calc-coth calc-csc calc-csch
1092 calc-degrees-mode calc-exp calc-expm1 calc-hypot calc-ilog
1093 calc-imaginary calc-isqrt calc-ln calc-lnp1 calc-log calc-log10
1094 calc-pi calc-radians-mode calc-sec calc-sech
1095 calc-sin calc-sincos calc-sinh calc-sqrt
1096 calc-tan calc-tanh calc-to-degrees calc-to-radians)
1097
1098  ("calc-mode" calc-alg-simplify-mode calc-algebraic-mode
1099 calc-always-load-extensions calc-auto-recompute calc-auto-why
1100 calc-basic-simplify-mode calc-bin-simplify-mode calc-break-vectors
1101 calc-center-justify calc-default-simplify-mode calc-display-raw
1102 calc-eng-notation calc-ext-simplify-mode calc-fix-notation
1103 calc-full-trail-vectors calc-full-vectors calc-get-modes calc-group-char
1104 calc-group-digits calc-infinite-mode calc-left-justify calc-left-label
1105 calc-line-breaking calc-line-numbering calc-matrix-brackets
1106 calc-matrix-center-justify calc-matrix-left-justify calc-matrix-mode
1107 calc-matrix-right-justify calc-mode-record-mode calc-no-simplify-mode
1108 calc-normal-notation calc-num-simplify-mode calc-point-char
1109 calc-right-justify calc-right-label calc-save-modes calc-sci-notation
1110 calc-settings-file-name calc-shift-prefix calc-symbolic-mode
1111 calc-total-algebraic-mode calc-truncate-down calc-truncate-stack
1112 calc-truncate-up calc-units-simplify-mode calc-vector-braces
1113 calc-vector-brackets calc-vector-commas calc-vector-parens
1114 calc-working)
1115
1116  ("calc-prog" calc-call-last-kbd-macro calc-edit-user-syntax
1117 calc-equal-to calc-get-user-defn calc-greater-equal calc-greater-than
1118 calc-in-set calc-kbd-break calc-kbd-else calc-kbd-else-if
1119 calc-kbd-end-for calc-kbd-end-if calc-kbd-end-loop calc-kbd-end-repeat
1120 calc-kbd-for calc-kbd-if calc-kbd-loop calc-kbd-pop calc-kbd-push
1121 calc-kbd-query calc-kbd-repeat calc-kbd-report calc-less-equal
1122 calc-less-than calc-logical-and calc-logical-if calc-logical-not
1123 calc-logical-or calc-not-equal-to calc-pass-errors calc-remove-equal
1124 calc-timing calc-user-define calc-user-define-composition
1125 calc-user-define-edit calc-user-define-formula
1126 calc-user-define-invocation calc-user-define-kbd-macro
1127 calc-user-define-permanent calc-user-undefine)
1128
1129  ("calc-rewr" calc-match calc-rewrite calc-rewrite-selection)
1130
1131  ("calc-sel" calc-break-selections calc-clear-selections
1132 calc-copy-selection calc-del-selection calc-edit-selection
1133 calc-enable-selections calc-enter-selection calc-sel-add-both-sides
1134 calc-sel-div-both-sides calc-sel-evaluate calc-sel-expand-formula
1135 calc-sel-mult-both-sides calc-sel-sub-both-sides
1136 calc-select-additional calc-select-here calc-select-here-maybe
1137 calc-select-less calc-select-more calc-select-next calc-select-once
1138 calc-select-once-maybe calc-select-part calc-select-previous
1139 calc-show-selections calc-unselect)
1140
1141  ("calcsel2" calc-commute-left calc-commute-right calc-sel-commute
1142 calc-sel-distribute calc-sel-invert calc-sel-isolate
1143 calc-sel-jump-equals calc-sel-merge calc-sel-negate calc-sel-unpack)
1144
1145  ("calc-stat" calc-vector-correlation calc-vector-count
1146 calc-vector-covariance calc-vector-geometric-mean
1147 calc-vector-harmonic-mean calc-vector-max calc-vector-mean
1148 calc-vector-mean-error calc-vector-median calc-vector-min
1149 calc-vector-pop-covariance calc-vector-pop-sdev
1150 calc-vector-pop-variance calc-vector-product calc-vector-sdev
1151 calc-vector-sum calc-vector-variance)
1152
1153  ("calc-store" calc-assign calc-copy-special-constant
1154 calc-copy-variable calc-declare-variable
1155 calc-edit-AlgSimpRules calc-edit-Decls calc-edit-EvalRules
1156 calc-edit-ExtSimpRules calc-edit-FitRules calc-edit-GenCount
1157 calc-edit-Holidays calc-edit-IntegLimit calc-edit-LineStyles
1158 calc-edit-PlotRejects calc-edit-PointStyles calc-edit-TimeZone
1159 calc-edit-Units calc-edit-variable calc-evalto calc-insert-variables
1160 calc-let calc-permanent-variable calc-recall calc-recall-quick
1161 calc-store calc-store-concat calc-store-decr calc-store-div
1162 calc-store-exchange calc-store-incr calc-store-into
1163 calc-store-into-quick calc-store-inv calc-store-map calc-store-minus
1164 calc-store-neg calc-store-plus calc-store-power calc-store-quick
1165 calc-store-times calc-subscript calc-unstore)
1166
1167  ("calc-stuff" calc-clean calc-clean-num calc-flush-caches
1168 calc-less-recursion-depth calc-more-recursion-depth calc-num-prefix
1169 calc-why)
1170
1171  ("calc-trail" calc-trail-backward calc-trail-first calc-trail-forward
1172 calc-trail-in calc-trail-isearch-backward calc-trail-isearch-forward
1173 calc-trail-kill calc-trail-last calc-trail-marker calc-trail-next
1174 calc-trail-out calc-trail-previous calc-trail-scroll-left
1175 calc-trail-scroll-right calc-trail-yank)
1176
1177  ("calc-undo" calc-last-args calc-redo)
1178
1179  ("calc-units" calc-autorange-units calc-base-units
1180 calc-convert-temperature calc-convert-units
1181 calc-convert-exact-units calc-define-unit
1182 calc-enter-units-table calc-explain-units calc-extract-units
1183 calc-get-unit-definition calc-permanent-units calc-quick-units
1184 calc-remove-units calc-simplify-units calc-undefine-unit
1185 calc-view-units-table calc-lu-quant calc-db
1186 calc-np calc-lu-plus calc-lu-minus
1187 calc-lu-times calc-lu-divide calc-spn calc-midi
1188 calc-freq)
1189
1190  ("calc-vec" calc-arrange-vector calc-build-vector calc-cnorm
1191 calc-conj-transpose calc-cons calc-cross calc-kron calc-diag
1192 calc-display-strings calc-expand-vector calc-grade calc-head
1193 calc-histogram calc-ident calc-index calc-mask-vector calc-mcol
1194 calc-mrow calc-pack calc-pack-bits calc-remove-duplicates
1195 calc-reverse-vector calc-rnorm calc-set-cardinality
1196 calc-set-complement calc-set-difference calc-set-enumerate
1197 calc-set-floor calc-set-intersect calc-set-span calc-set-union
1198 calc-set-xor calc-sort calc-subvector calc-tail calc-transpose
1199 calc-unpack calc-unpack-bits calc-vector-find calc-vlength)
1200
1201  ("calc-yank" calc-copy-as-kill calc-copy-region-as-kill
1202 calc-copy-to-buffer calc-edit calc-edit-cancel calc-edit-mode
1203 calc-kill calc-kill-region calc-yank))))
1204
1205 (defun calc-init-prefixes ()
1206   (if calc-shift-prefix
1207       (progn
1208         (define-key calc-mode-map "A" (lookup-key calc-mode-map "a"))
1209         (define-key calc-mode-map "B" (lookup-key calc-mode-map "b"))
1210         (define-key calc-mode-map "C" (lookup-key calc-mode-map "c"))
1211         (define-key calc-mode-map "D" (lookup-key calc-mode-map "d"))
1212         (define-key calc-mode-map "F" (lookup-key calc-mode-map "f"))
1213         (define-key calc-mode-map "G" (lookup-key calc-mode-map "g"))
1214         (define-key calc-mode-map "J" (lookup-key calc-mode-map "j"))
1215         (define-key calc-mode-map "K" (lookup-key calc-mode-map "k"))
1216         (define-key calc-mode-map "M" (lookup-key calc-mode-map "m"))
1217         (define-key calc-mode-map "S" (lookup-key calc-mode-map "s"))
1218         (define-key calc-mode-map "T" (lookup-key calc-mode-map "t"))
1219         (define-key calc-mode-map "U" (lookup-key calc-mode-map "u")))
1220     (define-key calc-mode-map "A" 'calc-abs)
1221     (define-key calc-mode-map "B" 'calc-log)
1222     (define-key calc-mode-map "C" 'calc-cos)
1223     (define-key calc-mode-map "D" 'calc-redo)
1224     (define-key calc-mode-map "F" 'calc-floor)
1225     (define-key calc-mode-map "G" 'calc-argument)
1226     (define-key calc-mode-map "J" 'calc-conj)
1227     (define-key calc-mode-map "K" 'calc-keep-args)
1228     (define-key calc-mode-map "M" 'calc-more-recursion-depth)
1229     (define-key calc-mode-map "S" 'calc-sin)
1230     (define-key calc-mode-map "T" 'calc-tan)
1231     (define-key calc-mode-map "U" 'calc-undo)))
1232
1233 (calc-init-extensions)
1234
1235
1236
1237
1238 ;;;; Miscellaneous.
1239
1240 ;; calc-command-flags is declared in calc.el
1241 (defvar calc-command-flags)
1242
1243 (defun calc-clear-command-flag (f)
1244   (setq calc-command-flags (delq f calc-command-flags)))
1245
1246
1247 (defun calc-record-message (tag &rest args)
1248   (let ((msg (apply 'format args)))
1249     (message "%s" msg)
1250     (calc-record msg tag))
1251   (calc-clear-command-flag 'clear-message))
1252
1253
1254 (defun calc-normalize-fancy (val)
1255   (let ((simp (if (consp calc-simplify-mode)
1256                   (car calc-simplify-mode)
1257                 calc-simplify-mode)))
1258     (cond ((eq simp 'binary)
1259            (let ((s (math-normalize val)))
1260              (if (math-realp s)
1261                  (math-clip (math-round s))
1262                s)))
1263           ((eq simp 'alg)
1264            (math-simplify val))
1265           ((eq simp 'ext)
1266            (math-simplify-extended val))
1267           ((eq simp 'units)
1268            (math-simplify-units val))
1269           (t  ; nil, none, num
1270            (math-normalize val)))))
1271
1272
1273 (defvar calc-help-map nil)
1274
1275 (if calc-help-map
1276     nil
1277   (setq calc-help-map (make-keymap))
1278   (define-key calc-help-map "b" 'calc-describe-bindings)
1279   (define-key calc-help-map "c" 'calc-describe-key-briefly)
1280   (define-key calc-help-map "f" 'calc-describe-function)
1281   (define-key calc-help-map "h" 'calc-full-help)
1282   (define-key calc-help-map "i" 'calc-info)
1283   (define-key calc-help-map "k" 'calc-describe-key)
1284   (define-key calc-help-map "n" 'calc-view-news)
1285   (define-key calc-help-map "s" 'calc-info-summary)
1286   (define-key calc-help-map "t" 'calc-tutorial)
1287   (define-key calc-help-map "v" 'calc-describe-variable)
1288   (define-key calc-help-map "\C-c" 'calc-describe-copying)
1289   (define-key calc-help-map "\C-d" 'calc-describe-distribution)
1290   (define-key calc-help-map "\C-n" 'calc-view-news)
1291   (define-key calc-help-map "\C-w" 'calc-describe-no-warranty)
1292   (define-key calc-help-map "?" 'calc-help-for-help)
1293   (define-key calc-help-map "\C-h" 'calc-help-for-help))
1294
1295 (defvar calc-prefix-help-phase 0)
1296 (defun calc-do-prefix-help (msgs group key)
1297   (if calc-full-help-flag
1298       (list msgs group key)
1299     (if (cdr msgs)
1300         (progn
1301           (setq calc-prefix-help-phase
1302                 (if (eq this-command last-command)
1303                     (% (1+ calc-prefix-help-phase) (1+ (length msgs)))
1304                   0))
1305           (let ((msg (nth calc-prefix-help-phase msgs)))
1306             (message "%s" (if msg
1307                               (concat group ": " msg ":"
1308                                       (make-string
1309                                        (- (apply 'max (mapcar 'length msgs))
1310                                           (length msg)) 32)
1311                                       "  [MORE]"
1312                                       (if key
1313                                           (concat "  " (char-to-string key)
1314                                                   "-")
1315                                         ""))
1316                             (if key (format "%c-" key) "")))))
1317       (setq calc-prefix-help-phase 0)
1318       (if key
1319           (if msgs
1320               (message "%s: %s: %c-" group (car msgs) key)
1321             (message "%s: (none)  %c-" group key))
1322         (message "%s: %s" group (car msgs))))
1323     (and key (calc-unread-command key))))
1324
1325 ;;;; Commands.
1326
1327
1328 ;;; General.
1329
1330 (defun calc-reset (arg)
1331   (interactive "P")
1332   (setq arg (if arg (prefix-numeric-value arg) nil))
1333   (cond
1334    ((and
1335      calc-embedded-info
1336      (equal (aref calc-embedded-info 0) (current-buffer))
1337      (<= (point) (aref calc-embedded-info 5))
1338      (>= (point) (aref calc-embedded-info 4)))
1339     (let ((cbuf (aref calc-embedded-info 1))
1340           (calc-embedded-quiet t))
1341       (save-window-excursion
1342         (calc-embedded nil)
1343         (set-buffer cbuf)
1344         (calc-reset arg))
1345       (calc-embedded nil)))
1346    ((eq major-mode 'calc-mode)
1347     (save-excursion
1348       (unless (and arg (> (abs arg) 0))
1349         (setq calc-stack nil))
1350       (setq calc-undo-list nil
1351             calc-redo-list nil)
1352       (let (calc-stack calc-user-parse-tables calc-standard-date-formats
1353                        calc-invocation-macro)
1354         (mapc (function (lambda (v) (set v nil))) calc-local-var-list)
1355         (if (and arg (<= arg 0))
1356             (calc-mode-var-list-restore-default-values)
1357           (calc-mode-var-list-restore-saved-values)))
1358       (calc-set-language nil nil t)
1359       (calc-mode)
1360       (calc-flush-caches t)
1361       (run-hooks 'calc-reset-hook))
1362     (calc-wrapper
1363      (let ((win (get-buffer-window (current-buffer))))
1364        (calc-realign 0)
1365        ;; Adjust the window height if the window is visible, but doesn't
1366        ;; take up the whole height of the frame.
1367        (if (and
1368             win
1369             (not (window-full-height-p)))
1370            (let ((height (- (window-height win) 2)))
1371              (set-window-point win (point))
1372              (or (= height calc-window-height)
1373                  (let ((swin (selected-window)))
1374                    (select-window win)
1375                    (enlarge-window (- calc-window-height height))
1376                    (select-window swin)))))))
1377     (message "(Calculator reset)"))
1378    (t
1379     (message "(Not inside a Calc buffer)"))))
1380
1381 ;; What a pain; scroll-left behaves differently when called non-interactively.
1382 (defun calc-scroll-left (n)
1383   (interactive "P")
1384   (setq prefix-arg (or n (/ (window-width) 2)))
1385   (call-interactively #'scroll-left))
1386
1387 (defun calc-scroll-right (n)
1388   (interactive "P")
1389   (setq prefix-arg (or n (/ (window-width) 2)))
1390   (call-interactively #'scroll-right))
1391
1392 (defun calc-scroll-up (n)
1393   (interactive "P")
1394   (condition-case err
1395       (scroll-up (or n (/ (window-height) 2)))
1396     (error nil))
1397   (if (pos-visible-in-window-p (max 1 (- (point-max) 2)))
1398       (if (eq major-mode 'calc-mode)
1399           (calc-realign)
1400         (goto-char (point-max))
1401         (set-window-start (selected-window)
1402                           (save-excursion
1403                             (forward-line (- (1- (window-height))))
1404                             (point)))
1405         (forward-line -1))))
1406
1407 (defun calc-scroll-down (n)
1408   (interactive "P")
1409   (or (pos-visible-in-window-p 1)
1410       (scroll-down (or n (/ (window-height) 2)))))
1411
1412
1413 (defun calc-precision (n)
1414   (interactive "NPrecision: ")
1415   (calc-wrapper
1416    (if (< (prefix-numeric-value n) 3)
1417        (error "Precision must be at least 3 digits")
1418      (calc-change-mode 'calc-internal-prec (prefix-numeric-value n)
1419                        (and (memq (car calc-float-format) '(float sci eng))
1420                             (< (nth 1 calc-float-format)
1421                                 (if (= calc-number-radix 10) 0 1))))
1422      (calc-record calc-internal-prec "prec"))
1423    (message "Floating-point precision is %d digits" calc-internal-prec)))
1424
1425
1426 (defun calc-inverse (&optional n)
1427   (interactive "P")
1428   (let* ((hyp-flag (if (or
1429                         (eq major-mode 'calc-keypad-mode)
1430                         (eq major-mode 'calc-trail-mode))
1431                        (with-current-buffer calc-main-buffer
1432                          calc-hyperbolic-flag)
1433                      calc-hyperbolic-flag))
1434          (opt-flag (if (or
1435                         (eq major-mode 'calc-keypad-mode)
1436                         (eq major-mode 'calc-trail-mode))
1437                        (with-current-buffer calc-main-buffer
1438                          calc-option-flag)
1439                      calc-option-flag))
1440          (msg
1441           (cond
1442            ((and opt-flag hyp-flag) "Option Inverse Hyperbolic...")
1443            (hyp-flag "Inverse Hyperbolic...")
1444            (opt-flag "Option Inverse...")
1445            (t "Inverse..."))))
1446     (calc-fancy-prefix 'calc-inverse-flag msg n)))
1447
1448 (defconst calc-fancy-prefix-map
1449   (let ((map (make-sparse-keymap)))
1450     (define-key map [t] 'calc-fancy-prefix-other-key)
1451     (define-key map (vector meta-prefix-char t) 'calc-fancy-prefix-other-key)
1452     (define-key map [switch-frame] nil)
1453     (define-key map [?\C-u] 'universal-argument)
1454     (define-key map [?0] 'digit-argument)
1455     (define-key map [?1] 'digit-argument)
1456     (define-key map [?2] 'digit-argument)
1457     (define-key map [?3] 'digit-argument)
1458     (define-key map [?4] 'digit-argument)
1459     (define-key map [?5] 'digit-argument)
1460     (define-key map [?6] 'digit-argument)
1461     (define-key map [?7] 'digit-argument)
1462     (define-key map [?8] 'digit-argument)
1463     (define-key map [?9] 'digit-argument)
1464     map)
1465   "Keymap used while processing calc-fancy-prefix.")
1466
1467 (defvar calc-is-keypad-press nil)
1468 (defun calc-fancy-prefix (flag msg n)
1469   (let (prefix)
1470     (calc-wrapper
1471      (calc-set-command-flag 'keep-flags)
1472      (calc-set-command-flag 'no-align)
1473      (setq prefix (set flag (not (symbol-value flag)))
1474            prefix-arg n)
1475      (message "%s" (if prefix msg "")))
1476     (and prefix
1477          (not calc-is-keypad-press)
1478          (if (boundp 'overriding-terminal-local-map)
1479              (setq overriding-terminal-local-map calc-fancy-prefix-map)
1480            (let ((event (calc-read-key t)))
1481              (if (eq (setq last-command-event (car event)) ?\C-u)
1482                  (universal-argument)
1483                (if (or (not (integerp last-command-event))
1484                        (and (>= last-command-event 0) (< last-command-event ? )
1485                             (not (memq last-command-event '(?\e)))))
1486                    (calc-wrapper))  ; clear flags if not a Calc command.
1487                (setq last-command-event (cdr event))
1488                (if (or (not (integerp last-command-event))
1489                        (eq last-command-event ?-))
1490                    (calc-unread-command)
1491                  (digit-argument n))))))))
1492
1493 (defun calc-fancy-prefix-other-key (arg)
1494   (interactive "P")
1495   (if (and
1496        (not (eq last-command-event 'tab))
1497        (not (eq last-command-event 'M-tab))
1498        (or (not (integerp last-command-event))
1499            (and (>= last-command-event 0) (< last-command-event ? )
1500                 (not (eq last-command-event meta-prefix-char)))))
1501      (calc-wrapper))  ; clear flags if not a Calc command.
1502   (setq prefix-arg arg)
1503   (calc-unread-command)
1504   (setq overriding-terminal-local-map nil))
1505
1506 (defun calc-invert-func ()
1507   (save-excursion
1508     (calc-select-buffer)
1509     (setq calc-inverse-flag (not (calc-is-inverse))
1510           calc-hyperbolic-flag (calc-is-hyperbolic)
1511           current-prefix-arg nil)))
1512
1513 (defun calc-is-inverse ()
1514   calc-inverse-flag)
1515
1516 (defun calc-hyperbolic (&optional n)
1517   (interactive "P")
1518   (let* ((inv-flag (if (or
1519                         (eq major-mode 'calc-keypad-mode)
1520                         (eq major-mode 'calc-trail-mode))
1521                        (with-current-buffer calc-main-buffer
1522                          calc-inverse-flag)
1523                      calc-inverse-flag))
1524          (opt-flag (if (or
1525                         (eq major-mode 'calc-keypad-mode)
1526                         (eq major-mode 'calc-trail-mode))
1527                        (with-current-buffer calc-main-buffer
1528                          calc-option-flag)
1529                      calc-option-flag))
1530          (msg
1531           (cond
1532            ((and opt-flag inv-flag) "Option Inverse Hyperbolic...")
1533            (opt-flag "Option Hyperbolic...")
1534            (inv-flag "Inverse Hyperbolic...")
1535            (t "Hyperbolic..."))))
1536     (calc-fancy-prefix 'calc-hyperbolic-flag msg n)))
1537
1538 (defun calc-hyperbolic-func ()
1539   (save-excursion
1540     (calc-select-buffer)
1541     (setq calc-inverse-flag (calc-is-inverse)
1542           calc-hyperbolic-flag (not (calc-is-hyperbolic))
1543           current-prefix-arg nil)))
1544
1545 (defun calc-is-hyperbolic ()
1546   calc-hyperbolic-flag)
1547
1548 (defun calc-option (&optional n)
1549   (interactive "P")
1550   (let* ((inv-flag (if (or
1551                         (eq major-mode 'calc-keypad-mode)
1552                         (eq major-mode 'calc-trail-mode))
1553                        (with-current-buffer calc-main-buffer
1554                          calc-inverse-flag)
1555                      calc-inverse-flag))
1556          (hyp-flag (if (or
1557                         (eq major-mode 'calc-keypad-mode)
1558                         (eq major-mode 'calc-trail-mode))
1559                        (with-current-buffer calc-main-buffer
1560                          calc-hyperbolic-flag)
1561                      calc-hyperbolic-flag))
1562          (msg
1563           (cond
1564            ((and hyp-flag inv-flag) "Option Inverse Hyperbolic...")
1565            (hyp-flag "Option Hyperbolic...")
1566            (inv-flag "Option Inverse...")
1567            (t "Option..."))))
1568     (calc-fancy-prefix 'calc-option-flag msg n)))
1569
1570 (defun calc-is-option ()
1571   calc-option-flag)
1572
1573 (defun calc-keep-args (&optional n)
1574   (interactive "P")
1575   (calc-fancy-prefix 'calc-keep-args-flag "Keep args..." n))
1576
1577
1578 (defun calc-change-mode (var value &optional refresh option)
1579   (if option
1580       (setq value (if value
1581                       (> (prefix-numeric-value value) 0)
1582                     (not (symbol-value var)))))
1583   (or (consp var) (setq var (list var) value (list value)))
1584   (if calc-inverse-flag
1585       (let ((old nil))
1586         (or refresh (error "Not a display-mode command"))
1587         (calc-check-stack 1)
1588         (unwind-protect
1589             (let ((v var))
1590               (while v
1591                 (setq old (cons (symbol-value (car v)) old))
1592                 (set (car v) (car value))
1593                 (setq v (cdr v)
1594                       value (cdr value)))
1595               (calc-refresh-top 1)
1596               (calc-refresh-evaltos)
1597               (symbol-value (car var)))
1598           (let ((v var))
1599             (setq old (nreverse old))
1600             (while v
1601               (set (car v) (car old))
1602               (setq v (cdr v)
1603                     old (cdr old)))
1604             (if (eq (car var) 'calc-language)
1605                 (calc-set-language calc-language calc-language-option t)))))
1606     (let ((chg nil)
1607           (v var))
1608       (while v
1609         (or (equal (symbol-value (car v)) (car value))
1610             (progn
1611               (set (car v) (car value))
1612               (if (eq (car v) 'calc-float-format)
1613                   (setq calc-full-float-format
1614                         (list (if (eq (car (car value)) 'fix)
1615                                   'float
1616                                 (car (car value)))
1617                               0)))
1618               (setq chg t)))
1619         (setq v (cdr v)
1620               value (cdr value)))
1621       (if chg
1622           (progn
1623             (or (and refresh (calc-do-refresh))
1624                 (calc-refresh-evaltos))
1625             (and (eq calc-mode-save-mode 'save)
1626                  (not (equal var '(calc-mode-save-mode)))
1627                  (calc-save-modes))))
1628       (if calc-embedded-info (calc-embedded-modes-change var))
1629       (symbol-value (car var)))))
1630
1631 (defun calc-toggle-banner ()
1632   "Toggle display of the friendly greeting calc normally shows above the stack."
1633   (interactive)
1634   (setq calc-show-banner (not calc-show-banner))
1635   (calc-refresh))
1636
1637 (defun calc-refresh-top (n)
1638   (interactive "p")
1639   (calc-wrapper
1640    (cond ((< n 0)
1641           (setq n (- n))
1642           (let ((entry (calc-top n 'entry))
1643                 (calc-undo-list nil) (calc-redo-list nil))
1644             (calc-pop-stack 1 n t)
1645             (calc-push-list (list (car entry)) n (list (nth 2 entry)))))
1646          ((= n 0)
1647           (calc-refresh))
1648          (t
1649           (let ((entries (calc-top-list n 1 'entry))
1650                 (calc-undo-list nil) (calc-redo-list nil))
1651             (calc-pop-stack n 1 t)
1652             (calc-push-list (mapcar 'car entries)
1653                             1
1654                             (mapcar (function (lambda (x) (nth 2 x)))
1655                                     entries)))))))
1656
1657 (defvar calc-refreshing-evaltos nil)
1658 (defvar calc-no-refresh-evaltos nil)
1659 (defun calc-refresh-evaltos (&optional which-var)
1660   (and calc-any-evaltos calc-auto-recompute (not calc-no-refresh-evaltos)
1661        (let ((calc-refreshing-evaltos t)
1662              (num (calc-stack-size))
1663              (calc-undo-list nil) (calc-redo-list nil)
1664              value new-val)
1665          (while (> num 0)
1666            (setq value (calc-top num 'entry))
1667            (if (and (not (nth 2 value))
1668                     (setq value (car value))
1669                     (or (eq (car-safe value) 'calcFunc-evalto)
1670                         (and (eq (car-safe value) 'vec)
1671                              (eq (car-safe (nth 1 value)) 'calcFunc-evalto))))
1672                (progn
1673                  (setq new-val (math-normalize value))
1674                  (or (equal new-val value)
1675                      (progn
1676                        (calc-push-list (list new-val) num)
1677                        (calc-pop-stack 1 (1+ num) t)))))
1678            (setq num (1- num)))))
1679   (and calc-embedded-active which-var
1680        (calc-embedded-var-change which-var)))
1681
1682 (defun calc-push (&rest vals)
1683   (calc-push-list vals))
1684
1685 (defun calc-pop-push (n &rest vals)
1686   (calc-pop-push-list n vals))
1687
1688 (defun calc-pop-push-record (n prefix &rest vals)
1689   (calc-pop-push-record-list n prefix vals))
1690
1691
1692 (defun calc-evaluate (n)
1693   (interactive "p")
1694   (calc-slow-wrapper
1695    (if (= n 0)
1696        (setq n (calc-stack-size)))
1697    (calc-with-default-simplification
1698     (if (< n 0)
1699         (calc-pop-push-record-list 1 "eval"
1700                                    (math-evaluate-expr (calc-top (- n)))
1701                                    (- n))
1702       (calc-pop-push-record-list n "eval" (mapcar 'math-evaluate-expr
1703                                                   (calc-top-list n)))))
1704    (calc-handle-whys)))
1705
1706
1707 (defun calc-eval-num (n)
1708   (interactive "P")
1709   (calc-slow-wrapper
1710    (let* ((nn (prefix-numeric-value n))
1711           (calc-internal-prec (cond ((>= nn 3) nn)
1712                                     ((< nn 0) (max (+ calc-internal-prec nn)
1713                                                    3))
1714                                     (t calc-internal-prec)))
1715           (calc-symbolic-mode nil))
1716      (calc-with-default-simplification
1717       (calc-pop-push-record 1 "num" (math-evaluate-expr (calc-top 1)))))
1718    (calc-handle-whys)))
1719
1720
1721 (defvar calc-extended-command-history nil
1722   "The history list for calc-execute-extended-command.")
1723
1724 (defun calc-execute-extended-command (n)
1725   (interactive "P")
1726   (let* ((prompt (concat (calc-num-prefix-name n) "M-x "))
1727          (cmd (intern
1728                (completing-read prompt obarray 'commandp t "calc-"
1729                                 'calc-extended-command-history))))
1730     (setq prefix-arg n)
1731     (command-execute cmd)))
1732
1733
1734 (defun calc-realign (&optional num)
1735   (interactive "P")
1736   (if (and num (eq major-mode 'calc-mode))
1737       (progn
1738         (calc-check-stack num)
1739         (calc-cursor-stack-index num)
1740         (and calc-line-numbering
1741              (forward-char 4)))
1742     (if (and calc-embedded-info
1743              (eq (current-buffer) (aref calc-embedded-info 0)))
1744         (progn
1745           (goto-char (aref calc-embedded-info 2))
1746           (if (with-current-buffer (aref calc-embedded-info 1)
1747                 calc-show-plain)
1748               (forward-line 1)))
1749       (calc-wrapper
1750        (if (get-buffer-window (current-buffer))
1751            (set-window-hscroll (get-buffer-window (current-buffer)) 0))))))
1752
1753 (defvar math-cache-list nil)
1754
1755 (defun calc-var-value (v)
1756   (and (symbolp v)
1757        (boundp v)
1758        (symbol-value v)
1759        (if (symbolp (symbol-value v))
1760            (set v (funcall (symbol-value v)))
1761          (if (stringp (symbol-value v))
1762              (let ((val (math-read-expr (symbol-value v))))
1763                (if (eq (car-safe val) 'error)
1764                    (error "Bad format in variable contents: %s" (nth 2 val))
1765                  (set v val)))
1766            (symbol-value v)))))
1767
1768 ;;; In the following table, ( OP LOPS ROPS ) means that if an OP
1769 ;;; term appears as the first argument to any LOPS term, or as the
1770 ;;; second argument to any ROPS term, then they should be treated
1771 ;;; as one large term for purposes of associative selection.
1772 (defconst calc-assoc-ops '( ( + ( + - ) ( + ) )
1773                             ( - ( + - ) ( + ) )
1774                             ( * ( * )   ( * ) )
1775                             ( / ( / )   (   ) )
1776                             ( | ( | )   ( | ) )
1777                             ( calcFunc-land ( calcFunc-land )
1778                                             ( calcFunc-land ) )
1779                             ( calcFunc-lor ( calcFunc-lor )
1780                                            ( calcFunc-lor ) ) ))
1781
1782
1783 (defvar var-CommuteRules 'calc-CommuteRules)
1784 (defvar var-JumpRules    'calc-JumpRules)
1785 (defvar var-DistribRules 'calc-DistribRules)
1786 (defvar var-MergeRules   'calc-MergeRules)
1787 (defvar var-NegateRules  'calc-NegateRules)
1788 (defvar var-InvertRules  'calc-InvertRules)
1789
1790
1791 (defconst calc-tweak-eqn-table '( ( calcFunc-eq  calcFunc-eq  calcFunc-neq )
1792                                   ( calcFunc-neq calcFunc-neq calcFunc-eq  )
1793                                   ( calcFunc-lt  calcFunc-gt  calcFunc-geq )
1794                                   ( calcFunc-gt  calcFunc-lt  calcFunc-leq )
1795                                   ( calcFunc-leq calcFunc-geq calcFunc-gt  )
1796                                   ( calcFunc-geq calcFunc-leq calcFunc-lt  ) ))
1797
1798
1799
1800
1801 (defun calc-float (arg)
1802   (interactive "P")
1803   (calc-slow-wrapper
1804    (calc-unary-op "flt"
1805                   (if (calc-is-hyperbolic) 'calcFunc-float 'calcFunc-pfloat)
1806                   arg)))
1807
1808
1809 (defvar calc-gnuplot-process nil)
1810 (defvar calc-gnuplot-input)
1811 (defvar calc-gnuplot-buffer)
1812
1813 (defun calc-gnuplot-alive ()
1814   (and calc-gnuplot-process
1815        calc-gnuplot-buffer
1816        (buffer-name calc-gnuplot-buffer)
1817        calc-gnuplot-input
1818        (buffer-name calc-gnuplot-input)
1819        (memq (process-status calc-gnuplot-process) '(run stop))))
1820
1821
1822
1823
1824
1825 (defun calc-load-everything ()
1826   (interactive)
1827   (require 'calc-aent)
1828   (require 'calc-alg)
1829   (require 'calc-arith)
1830   (require 'calc-bin)
1831   (require 'calc-comb)
1832   (require 'calc-cplx)
1833   (require 'calc-embed)
1834   (require 'calc-fin)
1835   (require 'calc-forms)
1836   (require 'calc-frac)
1837   (require 'calc-funcs)
1838   (require 'calc-graph)
1839   (require 'calc-help)
1840   (require 'calc-incom)
1841   (require 'calc-keypd)
1842   (require 'calc-lang)
1843   (require 'calc-macs)
1844   (require 'calc-map)
1845   (require 'calc-math)
1846   (require 'calc-misc)
1847   (require 'calc-mode)
1848   (require 'calc-mtx)
1849   (require 'calc-poly)
1850   (require 'calc-prog)
1851   (require 'calc-rewr)
1852   (require 'calc-rules)
1853   (require 'calc-sel)
1854   (require 'calc-stat)
1855   (require 'calc-store)
1856   (require 'calc-stuff)
1857   (require 'calc-trail)
1858   (require 'calc-undo)
1859   (require 'calc-units)
1860   (require 'calc-vec)
1861   (require 'calc-yank)
1862   (require 'calcalg2)
1863   (require 'calcalg3)
1864   (require 'calccomp)
1865   (require 'calcsel2)
1866
1867   (message "All parts of Calc are now loaded"))
1868
1869
1870 ;;; Vector commands.
1871
1872 (defun calc-concat (arg)
1873   (interactive "P")
1874   (calc-wrapper
1875    (if (calc-is-inverse)
1876        (if (calc-is-hyperbolic)
1877            (calc-enter-result 2 "apnd" (list 'calcFunc-append
1878                                           (calc-top 1) (calc-top 2)))
1879          (calc-enter-result 2 "|" (list 'calcFunc-vconcat
1880                                         (calc-top 1) (calc-top 2))))
1881      (if (calc-is-hyperbolic)
1882          (calc-binary-op "apnd" 'calcFunc-append arg '(vec))
1883        (calc-binary-op "|" 'calcFunc-vconcat arg '(vec) nil '|)))))
1884
1885 (defun calc-append (arg)
1886   (interactive "P")
1887   (calc-hyperbolic-func)
1888   (calc-concat arg))
1889
1890
1891 (defconst calc-arg-values '( ( var ArgA var-ArgA ) ( var ArgB var-ArgB )
1892                              ( var ArgC var-ArgC ) ( var ArgD var-ArgD )
1893                              ( var ArgE var-ArgE ) ( var ArgF var-ArgF )
1894                              ( var ArgG var-ArgG ) ( var ArgH var-ArgH )
1895                              ( var ArgI var-ArgI ) ( var ArgJ var-ArgJ )
1896 ))
1897
1898 (defun calc-invent-args (n)
1899   (nreverse (nthcdr (- (length calc-arg-values) n) (reverse calc-arg-values))))
1900
1901
1902
1903
1904 ;;; User menu.
1905
1906 (defun calc-user-key-map ()
1907   (if (featurep 'xemacs)
1908       (error "User-defined keys are not supported in XEmacs"))
1909   (let ((res (cdr (lookup-key calc-mode-map "z"))))
1910     (if (eq (car (car res)) 27)
1911         (cdr res)
1912       res)))
1913
1914 (defvar calc-z-prefix-buf nil)
1915 (defvar calc-z-prefix-msgs nil)
1916
1917 (defun calc-z-prefix-help ()
1918   (interactive)
1919   (let* ((calc-z-prefix-msgs nil)
1920          (calc-z-prefix-buf "")
1921          (kmap (sort (copy-sequence (calc-user-key-map))
1922                      (function (lambda (x y) (< (car x) (car y))))))
1923          (flags (apply 'logior
1924                        (mapcar (function
1925                                 (lambda (k)
1926                                   (calc-user-function-classify (car k))))
1927                                kmap))))
1928     (if (= (logand flags 8) 0)
1929         (calc-user-function-list kmap 7)
1930       (calc-user-function-list kmap 1)
1931       (setq calc-z-prefix-msgs (cons calc-z-prefix-buf calc-z-prefix-msgs)
1932             calc-z-prefix-buf "")
1933       (calc-user-function-list kmap 6))
1934     (if (/= flags 0)
1935         (setq calc-z-prefix-msgs (cons calc-z-prefix-buf calc-z-prefix-msgs)))
1936     (calc-do-prefix-help (nreverse calc-z-prefix-msgs) "user" ?z)))
1937
1938 (defun calc-user-function-classify (key)
1939   (cond ((/= key (downcase key))    ; upper-case
1940          (if (assq (downcase key) (calc-user-key-map)) 9 1))
1941         ((/= key (upcase key)) 2)   ; lower-case
1942         ((= key ??) 0)
1943         (t 4)))   ; other
1944
1945 (defun calc-user-function-list (map flags)
1946   (and map
1947        (let* ((key (car (car map)))
1948               (kind (calc-user-function-classify key))
1949               (func (cdr (car map))))
1950          (if (or (= (logand kind flags) 0)
1951                  (not (symbolp func)))
1952              ()
1953            (let* ((name (symbol-name func))
1954                   (name (if (string-match "\\`calc-" name)
1955                             (substring name 5) name))
1956                   (pos (string-match (char-to-string key) name))
1957                   (desc
1958                    (if (symbolp func)
1959                        (if (= (logand kind 3) 0)
1960                            (format "`%c' = %s" key name)
1961                          (if pos
1962                              (format "%s%c%s"
1963                                      (downcase (substring name 0 pos))
1964                                      (upcase key)
1965                                      (downcase (substring name (1+ pos))))
1966                            (format "%c = %s"
1967                                    (upcase key)
1968                                    (downcase name))))
1969                      (char-to-string (upcase key)))))
1970              (if (= (length calc-z-prefix-buf) 0)
1971                  (setq calc-z-prefix-buf (concat (if (= flags 1) "SHIFT + " "")
1972                                    desc))
1973                (if (> (+ (length calc-z-prefix-buf) (length desc)) 58)
1974                    (setq calc-z-prefix-msgs
1975                          (cons calc-z-prefix-buf calc-z-prefix-msgs)
1976                          calc-z-prefix-buf (concat (if (= flags 1) "SHIFT + " "")
1977                                      desc))
1978                  (setq calc-z-prefix-buf (concat calc-z-prefix-buf ", " desc))))))
1979          (calc-user-function-list (cdr map) flags))))
1980
1981
1982
1983 (defun calc-shift-Z-prefix-help ()
1984   (interactive)
1985   (calc-do-prefix-help
1986    '("Define, Undefine, Formula, Kbd-macro, Edit, Get-defn"
1987      "Composition, Syntax; Invocation; Permanent; Timing"
1988      "kbd-macros: [ (if), : (else), | (else-if), ] (end-if)"
1989      "kbd-macros: < > (repeat), ( ) (for), { } (loop)"
1990      "kbd-macros: / (break)"
1991      "kbd-macros: ` (save), ' (restore)")
1992    "user" ?Z))
1993
1994
1995 ;;;; Caches.
1996
1997 (defmacro math-defcache (name init form)
1998   (let ((cache-prec (intern (concat (symbol-name name) "-cache-prec")))
1999         (cache-val (intern (concat (symbol-name name) "-cache")))
2000         (last-prec (intern (concat (symbol-name name) "-last-prec")))
2001         (last-val (intern (concat (symbol-name name) "-last"))))
2002     `(progn
2003 ;      (defvar ,cache-prec ,(if init (math-numdigs (nth 1 init)) -100))
2004        (defvar ,cache-prec (cond
2005                             ((consp ,init) (math-numdigs (nth 1 ,init)))
2006                             (,init
2007                              (nth 1 (math-numdigs (eval ,init))))
2008                             (t
2009                              -100)))
2010        (defvar ,cache-val (cond ((consp ,init) ,init)
2011                                 (,init (eval ,init))
2012                                 (t ,init)))
2013        (defvar ,last-prec -100)
2014        (defvar ,last-val nil)
2015        (setq math-cache-list
2016              (cons ',cache-prec
2017                    (cons ',last-prec
2018                          math-cache-list)))
2019        (defun ,name ()
2020          (or (= ,last-prec calc-internal-prec)
2021              (setq ,last-val
2022                    (math-normalize
2023                     (progn (or (>= ,cache-prec calc-internal-prec)
2024                                (setq ,cache-val
2025                                      (let ((calc-internal-prec
2026                                             (+ calc-internal-prec 4)))
2027                                        ,form)
2028                                      ,cache-prec (+ calc-internal-prec 2)))
2029                            ,cache-val))
2030                    ,last-prec calc-internal-prec))
2031          ,last-val))))
2032 (put 'math-defcache 'lisp-indent-hook 2)
2033
2034 ;;; Betcha didn't know that pi = 16 atan(1/5) - 4 atan(1/239).   [F] [Public]
2035 (defconst math-approx-pi
2036   (math-read-number-simple "3.141592653589793238463")
2037   "An approximation for pi.")
2038
2039 (math-defcache math-pi math-approx-pi
2040   (math-add-float (math-mul-float '(float 16 0)
2041                                   (math-arctan-raw '(float 2 -1)))
2042                   (math-mul-float '(float -4 0)
2043                                   (math-arctan-raw
2044                                    (math-float '(frac 1 239))))))
2045
2046 (math-defcache math-two-pi nil
2047   (math-mul-float (math-pi) '(float 2 0)))
2048
2049 (math-defcache math-pi-over-2 nil
2050   (math-mul-float (math-pi) '(float 5 -1)))
2051
2052 (math-defcache math-pi-over-4 nil
2053   (math-mul-float (math-pi) '(float 25 -2)))
2054
2055 (math-defcache math-pi-over-180 nil
2056   (math-div-float (math-pi) '(float 18 1)))
2057
2058 (math-defcache math-sqrt-pi nil
2059   (math-sqrt-float (math-pi)))
2060
2061 (math-defcache math-sqrt-2 nil
2062   (math-sqrt-float '(float 2 0)))
2063
2064 (math-defcache math-sqrt-12 nil
2065   (math-sqrt-float '(float 12 0)))
2066
2067 (math-defcache math-sqrt-two-pi nil
2068   (math-sqrt-float (math-two-pi)))
2069
2070 (defconst math-approx-sqrt-e
2071   (math-read-number-simple "1.648721270700128146849")
2072   "An approximation for sqrt(3).")
2073
2074 (math-defcache math-sqrt-e math-approx-sqrt-e
2075   (math-add-float '(float 1 0) (math-exp-minus-1-raw '(float 5 -1))))
2076
2077 (math-defcache math-e nil
2078   (math-pow (math-sqrt-e) 2))
2079
2080 (math-defcache math-phi nil
2081   (math-mul-float (math-add-float (math-sqrt-raw '(float 5 0)) '(float 1 0))
2082                   '(float 5 -1)))
2083
2084 (defconst math-approx-gamma-const
2085   (math-read-number-simple
2086    "0.5772156649015328606065120900824024310421593359399235988057672348848677267776646709369470632917467495")
2087   "An approximation for gamma.")
2088
2089 (math-defcache math-gamma-const nil
2090   math-approx-gamma-const)
2091
2092 (defun math-half-circle (symb)
2093   (if (eq calc-angle-mode 'rad)
2094       (if symb
2095           '(var pi var-pi)
2096         (math-pi))
2097     180))
2098
2099 (defun math-full-circle (symb)
2100   (math-mul 2 (math-half-circle symb)))
2101
2102 (defun math-quarter-circle (symb)
2103   (math-div (math-half-circle symb) 2))
2104
2105 (defvar math-expand-formulas nil)
2106
2107 ;;;; Miscellaneous math routines.
2108
2109 ;;; True if A is an odd integer.  [P R R] [Public]
2110 (defun math-oddp (a)
2111   (if (consp a)
2112       (and (memq (car a) '(bigpos bigneg))
2113            (= (% (nth 1 a) 2) 1))
2114     (/= (% a 2) 0)))
2115
2116 ;;; True if A is a small or big integer.  [P x] [Public]
2117 (defun math-integerp (a)
2118   (or (integerp a)
2119       (memq (car-safe a) '(bigpos bigneg))))
2120
2121 ;;; True if A is (numerically) a non-negative integer.  [P N] [Public]
2122 (defun math-natnump (a)
2123   (or (natnump a)
2124       (eq (car-safe a) 'bigpos)))
2125
2126 ;;; True if A is a rational (or integer).  [P x] [Public]
2127 (defun math-ratp (a)
2128   (or (integerp a)
2129       (memq (car-safe a) '(bigpos bigneg frac))))
2130
2131 ;;; True if A is a real (or rational).  [P x] [Public]
2132 (defun math-realp (a)
2133   (or (integerp a)
2134       (memq (car-safe a) '(bigpos bigneg frac float))))
2135
2136 ;;; True if A is a real or HMS form.  [P x] [Public]
2137 (defun math-anglep (a)
2138   (or (integerp a)
2139       (memq (car-safe a) '(bigpos bigneg frac float hms))))
2140
2141 ;;; True if A is a number of any kind.  [P x] [Public]
2142 (defun math-numberp (a)
2143   (or (integerp a)
2144       (memq (car-safe a) '(bigpos bigneg frac float cplx polar))))
2145
2146 ;;; True if A is a complex number or angle.  [P x] [Public]
2147 (defun math-scalarp (a)
2148   (or (integerp a)
2149       (memq (car-safe a) '(bigpos bigneg frac float cplx polar hms))))
2150
2151 ;;; True if A is a vector.  [P x] [Public]
2152 (defun math-vectorp (a)
2153   (eq (car-safe a) 'vec))
2154
2155 ;;; True if A is any vector or scalar data object.  [P x]
2156 (defun math-objvecp (a)    ;  [Public]
2157   (or (integerp a)
2158       (memq (car-safe a) '(bigpos bigneg frac float cplx polar
2159                                   hms date sdev intv mod vec incomplete))))
2160
2161 ;;; True if A is an object not composed of sub-formulas .  [P x] [Public]
2162 (defun math-primp (a)
2163   (or (integerp a)
2164       (memq (car-safe a) '(bigpos bigneg frac float cplx polar
2165                                   hms date mod var))))
2166
2167 ;;; True if A is numerically (but not literally) an integer.  [P x] [Public]
2168 (defun math-messy-integerp (a)
2169   (cond
2170    ((eq (car-safe a) 'float) (>= (nth 2 a) 0))
2171    ((eq (car-safe a) 'frac) (Math-integerp (math-normalize a)))))
2172
2173 ;;; True if A is numerically an integer.  [P x] [Public]
2174 (defun math-num-integerp (a)
2175   (or (Math-integerp a)
2176       (Math-messy-integerp a)))
2177
2178 ;;; True if A is (numerically) a non-negative integer.  [P N] [Public]
2179 (defun math-num-natnump (a)
2180   (or (natnump a)
2181       (eq (car-safe a) 'bigpos)
2182       (and (eq (car-safe a) 'float)
2183            (Math-natnump (nth 1 a))
2184            (>= (nth 2 a) 0))))
2185
2186 ;;; True if A is an integer or will evaluate to an integer.  [P x] [Public]
2187 (defun math-provably-integerp (a)
2188   (or (Math-integerp a)
2189       (and (memq (car-safe a) '(calcFunc-trunc
2190                                 calcFunc-round
2191                                 calcFunc-rounde
2192                                 calcFunc-roundu
2193                                 calcFunc-floor
2194                                 calcFunc-ceil))
2195            (= (length a) 2))))
2196
2197 ;;; True if A is a real or will evaluate to a real.  [P x] [Public]
2198 (defun math-provably-realp (a)
2199   (or (Math-realp a)
2200       (math-provably-integerp a)
2201       (memq (car-safe a) '(abs arg))))
2202
2203 ;;; True if A is a non-real, complex number.  [P x] [Public]
2204 (defun math-complexp (a)
2205   (memq (car-safe a) '(cplx polar)))
2206
2207 ;;; True if A is a non-real, rectangular complex number.  [P x] [Public]
2208 (defun math-rect-complexp (a)
2209   (eq (car-safe a) 'cplx))
2210
2211 ;;; True if A is a non-real, polar complex number.  [P x] [Public]
2212 (defun math-polar-complexp (a)
2213   (eq (car-safe a) 'polar))
2214
2215 ;;; True if A is a matrix.  [P x] [Public]
2216 (defun math-matrixp (a)
2217   (and (Math-vectorp a)
2218        (Math-vectorp (nth 1 a))
2219        (cdr (nth 1 a))
2220        (let ((len (length (nth 1 a))))
2221          (setq a (cdr a))
2222          (while (and (setq a (cdr a))
2223                      (Math-vectorp (car a))
2224                      (= (length (car a)) len)))
2225          (null a))))
2226
2227 (defun math-matrixp-step (a len)   ; [P L]
2228   (or (null a)
2229       (and (Math-vectorp (car a))
2230            (= (length (car a)) len)
2231            (math-matrixp-step (cdr a) len))))
2232
2233 ;;; True if A is a square matrix.  [P V] [Public]
2234 (defun math-square-matrixp (a)
2235   (let ((dims (math-mat-dimens a)))
2236     (and (cdr dims)
2237          (= (car dims) (nth 1 dims)))))
2238
2239 ;;; True if MAT is an identity matrix.
2240 (defun math-identity-matrix-p (mat &optional mul)
2241   (if (math-square-matrixp mat)
2242       (let ((a (if mul
2243                    (nth 1 (nth 1 mat))
2244                  1))
2245             (n (1- (length mat)))
2246             (i 1))
2247         (while (and (<= i n)
2248                     (math-ident-row-p (nth i mat) i a))
2249           (setq i (1+ i)))
2250         (if (> i n)
2251             a
2252           nil))))
2253
2254 (defun math-ident-row-p (row n &optional a)
2255   (unless a
2256     (setq a 1))
2257   (and
2258    (not (memq nil (mapcar
2259                    (lambda (x) (eq x 0))
2260                    (nthcdr (1+ n) row))))
2261    (not (memq nil (mapcar
2262                    (lambda (x) (eq x 0))
2263                    (butlast
2264                     (cdr row)
2265                     (- (length row) n)))))
2266    (eq (elt row n) a)))
2267
2268 ;;; True if A is any scalar data object.  [P x]
2269 (defun math-objectp (a)    ;  [Public]
2270   (or (integerp a)
2271       (memq (car-safe a) '(bigpos bigneg frac float cplx
2272                                   polar hms date sdev intv mod))))
2273
2274 ;;; Verify that A is an integer and return A in integer form.  [I N; - x]
2275 (defun math-check-integer (a)   ;  [Public]
2276   (cond ((integerp a) a)  ; for speed
2277         ((math-integerp a) a)
2278         ((math-messy-integerp a)
2279          (math-trunc a))
2280         (t (math-reject-arg a 'integerp))))
2281
2282 ;;; Verify that A is a small integer and return A in integer form.  [S N; - x]
2283 (defun math-check-fixnum (a &optional allow-inf)   ;  [Public]
2284   (cond ((integerp a) a)  ; for speed
2285         ((Math-num-integerp a)
2286          (let ((a (math-trunc a)))
2287            (if (integerp a)
2288                a
2289              (if (or (Math-lessp (lsh -1 -1) a)
2290                      (Math-lessp a (- (lsh -1 -1))))
2291                  (math-reject-arg a 'fixnump)
2292                (math-fixnum a)))))
2293         ((and allow-inf (equal a '(var inf var-inf)))
2294          (lsh -1 -1))
2295         ((and allow-inf (equal a '(neg (var inf var-inf))))
2296          (- (lsh -1 -1)))
2297         (t (math-reject-arg a 'fixnump))))
2298
2299 ;;; Verify that A is an integer >= 0 and return A in integer form.  [I N; - x]
2300 (defun math-check-natnum (a)    ;  [Public]
2301   (cond ((natnump a) a)
2302         ((and (not (math-negp a))
2303               (Math-num-integerp a))
2304          (math-trunc a))
2305         (t (math-reject-arg a 'natnump))))
2306
2307 ;;; Verify that A is in floating-point form, or force it to be a float.  [F N]
2308 (defun math-check-float (a)    ; [Public]
2309   (cond ((eq (car-safe a) 'float) a)
2310         ((Math-vectorp a) (math-map-vec 'math-check-float a))
2311         ((Math-objectp a) (math-float a))
2312         (t a)))
2313
2314 ;;; Verify that A is a constant.
2315 (defun math-check-const (a &optional exp-ok)
2316   (if (or (math-constp a)
2317           (and exp-ok math-expand-formulas))
2318       a
2319     (math-reject-arg a 'constp)))
2320
2321 ;;; Some functions for working with error forms.
2322 (defun math-get-value (x)
2323   "Get the mean value of the error form X.
2324 If X is not an error form, return X."
2325   (if (eq (car-safe x) 'sdev)
2326       (nth 1 x)
2327     x))
2328
2329 (defun math-get-sdev (x &optional one)
2330   "Get the standard deviation of the error form X.
2331 If X is not an error form, return 1."
2332   (if (eq (car-safe x) 'sdev)
2333       (nth 2 x)
2334     (if one 1 0)))
2335
2336 (defun math-contains-sdev-p (ls)
2337   "Non-nil if the list LS contains an error form."
2338   (let ((ls (if (eq (car-safe ls) 'vec) (cdr ls) ls)))
2339     (memq t (mapcar (lambda (x) (eq (car-safe x) 'sdev)) ls))))
2340
2341 ;;; Coerce integer A to be a small integer.  [S I]
2342 (defun math-fixnum (a)
2343   (if (consp a)
2344       (if (cdr a)
2345           (if (eq (car a) 'bigneg)
2346               (- (math-fixnum-big (cdr a)))
2347             (math-fixnum-big (cdr a)))
2348         0)
2349     a))
2350
2351 (defun math-fixnum-big (a)
2352   (if (cdr a)
2353       (+ (car a) (* (math-fixnum-big (cdr a)) math-bignum-digit-size))
2354     (car a)))
2355
2356 (defvar math-simplify-only nil)
2357
2358 (defun math-normalize-fancy (a)
2359   (cond ((eq (car a) 'frac)
2360          (math-make-frac (math-normalize (nth 1 a))
2361                          (math-normalize (nth 2 a))))
2362         ((eq (car a) 'cplx)
2363          (let ((real (math-normalize (nth 1 a)))
2364                (imag (math-normalize (nth 2 a))))
2365            (if (and (math-zerop imag)
2366                     (not math-simplify-only))   ; oh, what a kludge!
2367                real
2368              (list 'cplx real imag))))
2369         ((eq (car a) 'polar)
2370          (math-normalize-polar a))
2371         ((eq (car a) 'hms)
2372          (math-normalize-hms a))
2373         ((eq (car a) 'date)
2374          (list 'date (math-normalize (nth 1 a))))
2375         ((eq (car a) 'mod)
2376          (math-normalize-mod a))
2377         ((eq (car a) 'sdev)
2378          (let ((x (math-normalize (nth 1 a)))
2379                (s (math-normalize (nth 2 a))))
2380            (if (or (and (Math-objectp x) (not (Math-scalarp x)))
2381                    (and (Math-objectp s) (not (Math-scalarp s))))
2382                (list 'calcFunc-sdev x s)
2383              (math-make-sdev x s))))
2384         ((eq (car a) 'intv)
2385          (let ((mask (math-normalize (nth 1 a)))
2386                (lo (math-normalize (nth 2 a)))
2387                (hi (math-normalize (nth 3 a))))
2388            (if (if (eq (car-safe lo) 'date)
2389                    (not (eq (car-safe hi) 'date))
2390                  (or (and (Math-objectp lo) (not (Math-anglep lo)))
2391                      (and (Math-objectp hi) (not (Math-anglep hi)))))
2392                (list 'calcFunc-intv mask lo hi)
2393              (math-make-intv mask lo hi))))
2394         ((eq (car a) 'vec)
2395          (cons 'vec (mapcar 'math-normalize (cdr a))))
2396         ((eq (car a) 'quote)
2397          (math-normalize (nth 1 a)))
2398         ((eq (car a) 'special-const)
2399          (calc-with-default-simplification
2400           (math-normalize (nth 1 a))))
2401         ((eq (car a) 'var)
2402          (cons 'var (cdr a)))   ; need to re-cons for selection routines
2403         ((eq (car a) 'calcFunc-if)
2404          (math-normalize-logical-op a))
2405         ((memq (car a) '(calcFunc-lambda calcFunc-quote calcFunc-condition))
2406          (let ((calc-simplify-mode 'none))
2407            (cons (car a) (mapcar 'math-normalize (cdr a)))))
2408         ((eq (car a) 'calcFunc-evalto)
2409          (setq a (or (nth 1 a) 0))
2410          (or calc-refreshing-evaltos
2411              (setq a (let ((calc-simplify-mode 'none)) (math-normalize a))))
2412          (let ((b (if (and (eq (car-safe a) 'calcFunc-assign)
2413                            (= (length a) 3))
2414                       (nth 2 a)
2415                     a)))
2416            (list 'calcFunc-evalto
2417                  a
2418                  (if (eq calc-simplify-mode 'none)
2419                      (math-normalize b)
2420                    (calc-with-default-simplification
2421                     (math-evaluate-expr b))))))
2422         ((or (integerp (car a)) (consp (car a)))
2423          (if (null (cdr a))
2424              (math-normalize (car a))
2425            (error "Can't use multi-valued function in an expression")))))
2426
2427 ;; The variable math-normalize-a is local to math-normalize in calc.el,
2428 ;; but is used by math-normalize-nonstandard, which is called by
2429 ;; math-normalize.
2430 (defvar math-normalize-a)
2431
2432 (defun math-normalize-nonstandard ()
2433   (if (consp calc-simplify-mode)
2434       (progn
2435         (setq calc-simplify-mode 'none
2436               math-simplify-only (car-safe (cdr-safe math-normalize-a)))
2437         nil)
2438     (and (symbolp (car math-normalize-a))
2439          (or (eq calc-simplify-mode 'none)
2440              (and (eq calc-simplify-mode 'num)
2441                   (let ((aptr (setq math-normalize-a
2442                                     (cons
2443                                      (car math-normalize-a)
2444                                      (mapcar 'math-normalize
2445                                              (cdr math-normalize-a))))))
2446                     (while (and aptr (math-constp (car aptr)))
2447                       (setq aptr (cdr aptr)))
2448                     aptr)))
2449          (cons (car math-normalize-a)
2450                (mapcar 'math-normalize (cdr math-normalize-a))))))
2451
2452
2453 ;;; Normalize a bignum digit list by trimming high-end zeros.  [L l]
2454 (defun math-norm-bignum (a)
2455   (let ((digs a) (last nil))
2456     (while digs
2457       (or (eq (car digs) 0) (setq last digs))
2458       (setq digs (cdr digs)))
2459     (and last
2460          (progn
2461            (setcdr last nil)
2462            a))))
2463
2464 (defun math-bignum-test (a)   ; [B N; B s; b b]
2465   (if (consp a)
2466       a
2467     (math-bignum a)))
2468
2469
2470 ;;; Return 0 for zero, -1 for negative, 1 for positive.  [S n] [Public]
2471 (defun calcFunc-sign (a &optional x)
2472   (let ((signs (math-possible-signs a)))
2473     (cond ((eq signs 4) (or x 1))
2474           ((eq signs 2) 0)
2475           ((eq signs 1) (if x (math-neg x) -1))
2476           ((math-looks-negp a) (math-neg (calcFunc-sign (math-neg a))))
2477           (t (calc-record-why 'realp a)
2478              (if x
2479                  (list 'calcFunc-sign a x)
2480                (list 'calcFunc-sign a))))))
2481
2482 ;;; Return 0 if A is numerically equal to B, <0 if less, >0 if more.
2483 ;;; Arguments must be normalized!  [S N N]
2484 (defun math-compare (a b)
2485   (cond ((equal a b)
2486          (if (and (consp a)
2487                   (memq (car a) '(var neg * /))
2488                   (math-infinitep a))
2489              2
2490            0))
2491         ((and (integerp a) (Math-integerp b))
2492          (if (consp b)
2493              (if (eq (car b) 'bigpos) -1 1)
2494            (if (< a b) -1 1)))
2495         ((and (eq (car-safe a) 'bigpos) (Math-integerp b))
2496          (if (eq (car-safe b) 'bigpos)
2497              (math-compare-bignum (cdr a) (cdr b))
2498            1))
2499         ((and (eq (car-safe a) 'bigneg) (Math-integerp b))
2500          (if (eq (car-safe b) 'bigneg)
2501              (math-compare-bignum (cdr b) (cdr a))
2502            -1))
2503         ((eq (car-safe a) 'frac)
2504          (if (eq (car-safe b) 'frac)
2505              (math-compare (math-mul (nth 1 a) (nth 2 b))
2506                            (math-mul (nth 1 b) (nth 2 a)))
2507            (math-compare (nth 1 a) (math-mul b (nth 2 a)))))
2508         ((eq (car-safe b) 'frac)
2509          (math-compare (math-mul a (nth 2 b)) (nth 1 b)))
2510         ((and (eq (car-safe a) 'float) (eq (car-safe b) 'float))
2511          (if (math-lessp-float a b) -1 1))
2512         ((and (eq (car-safe a) 'date) (eq (car-safe b) 'date))
2513          (math-compare (nth 1 a) (nth 1 b)))
2514         ((and (or (Math-anglep a)
2515                   (and (eq (car a) 'cplx) (eq (nth 2 a) 0)))
2516               (or (Math-anglep b)
2517                   (and (eq (car b) 'cplx) (eq (nth 2 b) 0))))
2518          (calcFunc-sign (math-add a (math-neg b))))
2519         ((and (eq (car-safe a) 'intv)
2520               (or (Math-anglep b) (eq (car-safe b) 'date)))
2521          (let ((res (math-compare (nth 2 a) b)))
2522            (cond ((eq res 1) 1)
2523                  ((and (eq res 0) (memq (nth 1 a) '(0 1))) 1)
2524                  ((eq (setq res (math-compare (nth 3 a) b)) -1) -1)
2525                  ((and (eq res 0) (memq (nth 1 a) '(0 2))) -1)
2526                  (t 2))))
2527         ((and (eq (car-safe b) 'intv)
2528               (or (Math-anglep a) (eq (car-safe a) 'date)))
2529          (let ((res (math-compare a (nth 2 b))))
2530            (cond ((eq res -1) -1)
2531                  ((and (eq res 0) (memq (nth 1 b) '(0 1))) -1)
2532                  ((eq (setq res (math-compare a (nth 3 b))) 1) 1)
2533                  ((and (eq res 0) (memq (nth 1 b) '(0 2))) 1)
2534                  (t 2))))
2535         ((and (eq (car-safe a) 'intv) (eq (car-safe b) 'intv))
2536          (let ((res (math-compare (nth 3 a) (nth 2 b))))
2537            (cond ((eq res -1) -1)
2538                  ((and (eq res 0) (or (memq (nth 1 a) '(0 2))
2539                                       (memq (nth 1 b) '(0 1)))) -1)
2540                  ((eq (setq res (math-compare (nth 2 a) (nth 3 b))) 1) 1)
2541                  ((and (eq res 0) (or (memq (nth 1 a) '(0 1))
2542                                       (memq (nth 1 b) '(0 2)))) 1)
2543                  (t 2))))
2544         ((math-infinitep a)
2545          (if (or (equal a '(var uinf var-uinf))
2546                  (equal a '(var nan var-nan)))
2547              2
2548            (let ((dira (math-infinite-dir a)))
2549              (if (math-infinitep b)
2550                  (if (or (equal b '(var uinf var-uinf))
2551                          (equal b '(var nan var-nan)))
2552                      2
2553                    (let ((dirb (math-infinite-dir b)))
2554                      (cond ((and (eq dira 1) (eq dirb -1)) 1)
2555                            ((and (eq dira -1) (eq dirb 1)) -1)
2556                            (t 2))))
2557                (cond ((eq dira 1) 1)
2558                      ((eq dira -1) -1)
2559                      (t 2))))))
2560         ((math-infinitep b)
2561          (if (or (equal b '(var uinf var-uinf))
2562                  (equal b '(var nan var-nan)))
2563              2
2564            (let ((dirb (math-infinite-dir b)))
2565              (cond ((eq dirb 1) -1)
2566                    ((eq dirb -1) 1)
2567                    (t 2)))))
2568         ((and (eq (car-safe a) 'calcFunc-exp)
2569               (eq (car-safe b) '^)
2570               (equal (nth 1 b) '(var e var-e)))
2571          (math-compare (nth 1 a) (nth 2 b)))
2572         ((and (eq (car-safe b) 'calcFunc-exp)
2573               (eq (car-safe a) '^)
2574               (equal (nth 1 a) '(var e var-e)))
2575          (math-compare (nth 2 a) (nth 1 b)))
2576         ((or (and (eq (car-safe a) 'calcFunc-sqrt)
2577                   (eq (car-safe b) '^)
2578                   (or (equal (nth 2 b) '(frac 1 2))
2579                       (equal (nth 2 b) '(float 5 -1))))
2580              (and (eq (car-safe b) 'calcFunc-sqrt)
2581                   (eq (car-safe a) '^)
2582                   (or (equal (nth 2 a) '(frac 1 2))
2583                       (equal (nth 2 a) '(float 5 -1)))))
2584          (math-compare (nth 1 a) (nth 1 b)))
2585         ((eq (car-safe a) 'var)
2586          2)
2587         (t
2588          (if (and (consp a) (consp b)
2589                   (eq (car a) (car b))
2590                   (math-compare-lists (cdr a) (cdr b)))
2591              0
2592            2))))
2593
2594 ;;; Compare two bignum digit lists, return -1 for A<B, 0 for A=B, 1 for A>B.
2595 (defun math-compare-bignum (a b)   ; [S l l]
2596   (let ((res 0))
2597     (while (and a b)
2598       (if (< (car a) (car b))
2599           (setq res -1)
2600         (if (> (car a) (car b))
2601             (setq res 1)))
2602       (setq a (cdr a)
2603             b (cdr b)))
2604     (if a
2605         (progn
2606           (while (eq (car a) 0) (setq a (cdr a)))
2607           (if a 1 res))
2608       (while (eq (car b) 0) (setq b (cdr b)))
2609       (if b -1 res))))
2610
2611 (defun math-compare-lists (a b)
2612   (cond ((null a) (null b))
2613         ((null b) nil)
2614         (t (and (Math-equal (car a) (car b))
2615                 (math-compare-lists (cdr a) (cdr b))))))
2616
2617 (defun math-lessp-float (a b)   ; [P F F]
2618   (let ((ediff (- (nth 2 a) (nth 2 b))))
2619     (if (>= ediff 0)
2620         (if (>= ediff (+ calc-internal-prec calc-internal-prec))
2621             (if (eq (nth 1 a) 0)
2622                 (Math-integer-posp (nth 1 b))
2623               (Math-integer-negp (nth 1 a)))
2624           (Math-lessp (math-scale-int (nth 1 a) ediff)
2625                       (nth 1 b)))
2626       (if (>= (setq ediff (- ediff))
2627               (+ calc-internal-prec calc-internal-prec))
2628           (if (eq (nth 1 b) 0)
2629               (Math-integer-negp (nth 1 a))
2630             (Math-integer-posp (nth 1 b)))
2631         (Math-lessp (nth 1 a)
2632                     (math-scale-int (nth 1 b) ediff))))))
2633
2634 ;;; True if A is numerically equal to B.  [P N N] [Public]
2635 (defun math-equal (a b)
2636   (= (math-compare a b) 0))
2637
2638 ;;; True if A is numerically less than B.  [P R R] [Public]
2639 (defun math-lessp (a b)
2640   (= (math-compare a b) -1))
2641
2642 ;;; True if A is numerically equal to the integer B.  [P N S] [Public]
2643 ;;; B must not be a multiple of 10.
2644 (defun math-equal-int (a b)
2645   (or (eq a b)
2646       (and (eq (car-safe a) 'float)
2647            (eq (nth 1 a) b)
2648            (= (nth 2 a) 0))))
2649
2650
2651
2652
2653 ;;; Return the dimensions of a matrix as a list.  [l x] [Public]
2654 (defun math-mat-dimens (m)
2655   (if (math-vectorp m)
2656       (if (math-matrixp m)
2657           (cons (1- (length m))
2658                 (math-mat-dimens (nth 1 m)))
2659         (list (1- (length m))))
2660     nil))
2661
2662
2663
2664 (defun calc-binary-op-fancy (name func arg ident unary)
2665   (let ((n (prefix-numeric-value arg)))
2666     (cond ((> n 1)
2667            (calc-enter-result n
2668                               name
2669                               (list 'calcFunc-reduce
2670                                     (math-calcFunc-to-var func)
2671                                     (cons 'vec (calc-top-list-n n)))))
2672           ((= n 1)
2673            (if unary
2674                (calc-enter-result 1 name (list unary (calc-top-n 1)))))
2675           ((= n 0)
2676            (if ident
2677                (calc-enter-result 0 name ident)
2678              (error "Argument must be nonzero")))
2679           (t
2680            (let ((rhs (calc-top-n 1)))
2681              (calc-enter-result (- 1 n)
2682                                 name
2683                                 (mapcar (function
2684                                          (lambda (x)
2685                                            (list func x rhs)))
2686                                         (calc-top-list-n (- n) 2))))))))
2687
2688 (defun calc-unary-op-fancy (name func arg)
2689   (let ((n (prefix-numeric-value arg)))
2690     (if (= n 0) (setq n (calc-stack-size)))
2691     (cond ((> n 0)
2692            (calc-enter-result n
2693                               name
2694                               (mapcar (function
2695                                        (lambda (x)
2696                                          (list func x)))
2697                                       (calc-top-list-n n))))
2698           ((< n 0)
2699            (calc-enter-result 1
2700                               name
2701                               (list func (calc-top-n (- n)))
2702                               (- n))))))
2703
2704 (defvar var-Holidays '(vec (var sat var-sat) (var sun var-sun)))
2705 (defvar var-Decls (list 'vec))
2706
2707
2708 (defun math-inexact-result ()
2709   (and calc-symbolic-mode
2710        (signal 'inexact-result nil)))
2711
2712 (defun math-overflow (&optional exp)
2713   (if (and exp (math-negp exp))
2714       (math-underflow)
2715     (signal 'math-overflow nil)))
2716
2717 (defun math-underflow ()
2718   (signal 'math-underflow nil))
2719
2720 ;;; Compute the greatest common divisor of A and B.   [I I I] [Public]
2721 (defun math-gcd (a b)
2722   (cond ((not (or (consp a) (consp b)))
2723          (if (< a 0) (setq a (- a)))
2724          (if (< b 0) (setq b (- b)))
2725          (let (c)
2726            (if (< a b)
2727                (setq c b b a a c))
2728            (while (> b 0)
2729              (setq c b
2730                    b (% a b)
2731                    a c))
2732            a))
2733         ((eq a 0) b)
2734         ((eq b 0) a)
2735         (t
2736          (if (Math-integer-negp a) (setq a (math-neg a)))
2737          (if (Math-integer-negp b) (setq b (math-neg b)))
2738          (let (c)
2739            (if (Math-natnum-lessp a b)
2740                (setq c b b a a c))
2741            (while (and (consp a) (not (eq b 0)))
2742              (setq c b
2743                    b (math-imod a b)
2744                    a c))
2745            (while (> b 0)
2746              (setq c b
2747                    b (% a b)
2748                    a c))
2749            a))))
2750
2751
2752 ;;;; Algebra.
2753
2754 ;;; Evaluate variables in an expression.
2755 (defun math-evaluate-expr (x)  ; [Public]
2756   (if calc-embedded-info
2757       (calc-embedded-evaluate-expr x)
2758     (calc-normalize (math-evaluate-expr-rec x))))
2759
2760 (defalias 'calcFunc-evalv 'math-evaluate-expr)
2761
2762 (defun calcFunc-evalvn (x &optional prec)
2763   (if prec
2764       (progn
2765         (or (math-num-integerp prec)
2766             (if (and (math-vectorp prec)
2767                      (= (length prec) 2)
2768                      (math-num-integerp (nth 1 prec)))
2769                 (setq prec (math-add (nth 1 prec) calc-internal-prec))
2770               (math-reject-arg prec 'integerp)))
2771         (setq prec (math-trunc prec))
2772         (if (< prec 3) (setq prec 3))
2773         (if (> prec calc-internal-prec)
2774             (math-normalize
2775              (let ((calc-internal-prec prec))
2776                (calcFunc-evalvn x)))
2777           (let ((calc-internal-prec prec))
2778             (calcFunc-evalvn x))))
2779     (let ((calc-symbolic-mode nil))
2780       (math-evaluate-expr x))))
2781
2782 (defun math-evaluate-expr-rec (x)
2783   (if (consp x)
2784       (if (memq (car x) '(calcFunc-quote calcFunc-condition
2785                                          calcFunc-evalto calcFunc-assign))
2786           (if (and (eq (car x) 'calcFunc-assign)
2787                    (= (length x) 3))
2788               (list (car x) (nth 1 x) (math-evaluate-expr-rec (nth 2 x)))
2789             x)
2790         (if (eq (car x) 'var)
2791             (if (and (calc-var-value (nth 2 x))
2792                      (not (eq (car-safe (symbol-value (nth 2 x)))
2793                               'incomplete)))
2794                 (let ((val (symbol-value (nth 2 x))))
2795                   (if (eq (car-safe val) 'special-const)
2796                       (if calc-symbolic-mode
2797                           x
2798                         val)
2799                     val))
2800               x)
2801           (if (Math-primp x)
2802               x
2803             (cons (car x) (mapcar 'math-evaluate-expr-rec (cdr x))))))
2804     x))
2805
2806 (defun math-any-floats (expr)
2807   (if (Math-primp expr)
2808       (math-floatp expr)
2809     (while (and (setq expr (cdr expr)) (not (math-any-floats (car expr)))))
2810     expr))
2811
2812 (defvar var-FactorRules 'calc-FactorRules)
2813
2814 (defvar math-mt-many nil)
2815 (defvar math-mt-func nil)
2816
2817 (defun math-map-tree (math-mt-func mmt-expr &optional math-mt-many)
2818   (or math-mt-many (setq math-mt-many 1000000))
2819   (math-map-tree-rec mmt-expr))
2820
2821 (defun math-map-tree-rec (mmt-expr)
2822   (or (= math-mt-many 0)
2823       (let ((mmt-done nil)
2824             mmt-nextval)
2825         (while (not mmt-done)
2826           (while (and (/= math-mt-many 0)
2827                       (setq mmt-nextval (funcall math-mt-func mmt-expr))
2828                       (not (equal mmt-expr mmt-nextval)))
2829             (setq mmt-expr mmt-nextval
2830                   math-mt-many (if (> math-mt-many 0)
2831                                    (1- math-mt-many)
2832                                  (1+ math-mt-many))))
2833           (if (or (Math-primp mmt-expr)
2834                   (<= math-mt-many 0))
2835               (setq mmt-done t)
2836             (setq mmt-nextval (cons (car mmt-expr)
2837                                     (mapcar 'math-map-tree-rec
2838                                             (cdr mmt-expr))))
2839             (if (equal mmt-nextval mmt-expr)
2840                 (setq mmt-done t)
2841               (setq mmt-expr mmt-nextval))))))
2842   mmt-expr)
2843
2844 (defun math-is-true (expr)
2845   (if (Math-numberp expr)
2846       (not (Math-zerop expr))
2847     (math-known-nonzerop expr)))
2848
2849 (defun math-const-var (expr)
2850   (and (consp expr)
2851        (eq (car expr) 'var)
2852        (or (and (symbolp (nth 2 expr))
2853                 (boundp (nth 2 expr))
2854                 (eq (car-safe (symbol-value (nth 2 expr))) 'special-const))
2855            (memq (nth 2 expr) '(var-inf var-uinf var-nan)))))
2856
2857 ;; The variable math-integral-cache is originally declared in calcalg2.el,
2858 ;; but is set by math-defintegral and math-defintegral-2.
2859 (defvar math-integral-cache)
2860
2861 (defmacro math-defintegral (funcs &rest code)
2862   (setq math-integral-cache nil)
2863   (cons 'progn
2864         (mapcar #'(lambda (func)
2865                     `(put ',func 'math-integral
2866                           (nconc
2867                            (get ',func 'math-integral)
2868                            (list
2869                             #'(lambda (u) ,@code)))))
2870                 (if (symbolp funcs) (list funcs) funcs))))
2871 (put 'math-defintegral 'lisp-indent-hook 1)
2872
2873 (defmacro math-defintegral-2 (funcs &rest code)
2874   (setq math-integral-cache nil)
2875   (cons 'progn
2876         (mapcar #'(lambda (func)
2877                     `(put ',func 'math-integral-2
2878                           (nconc
2879                             (get ',func 'math-integral-2)
2880                             (list #'(lambda (u v) ,@code)))))
2881                 (if (symbolp funcs) (list funcs) funcs))))
2882 (put 'math-defintegral-2 'lisp-indent-hook 1)
2883
2884 (defvar var-IntegAfterRules 'calc-IntegAfterRules)
2885
2886 (defvar var-FitRules 'calc-FitRules)
2887
2888 (defvar math-poly-base-variable nil)
2889 (defvar math-poly-neg-powers nil)
2890 (defvar math-poly-mult-powers 1)
2891 (defvar math-poly-frac-powers nil)
2892 (defvar math-poly-exp-base nil)
2893
2894 (defun math-build-var-name (name)
2895   (if (stringp name)
2896       (setq name (intern name)))
2897   (if (string-match "\\`var-." (symbol-name name))
2898       (list 'var (intern (substring (symbol-name name) 4)) name)
2899     (list 'var name (intern (concat "var-" (symbol-name name))))))
2900
2901 (defvar math-simplifying-units nil)
2902 (defvar math-combining-units t)
2903
2904 ;;; Nontrivial number parsing.
2905
2906 (defun math-read-number-fancy (s)
2907   (cond
2908
2909    ;; Integer+fractions
2910    ((string-match "^\\([0-9]*\\)[:/]\\([0-9]*\\)[:/]\\([0-9]*\\)$" s)
2911     (let ((int (math-match-substring s 1))
2912           (num (math-match-substring s 2))
2913           (den (math-match-substring s 3)))
2914       (let ((int (if (> (length int) 0) (math-read-number int) 0))
2915             (num (if (> (length num) 0) (math-read-number num) 1))
2916             (den (if (> (length num) 0) (math-read-number den) 1)))
2917         (and int num den
2918              (math-integerp int) (math-integerp num) (math-integerp den)
2919              (not (math-zerop den))
2920              (list 'frac (math-add num (math-mul int den)) den)))))
2921
2922    ;; Fractions
2923    ((string-match "^\\([0-9]*\\)[:/]\\([0-9]*\\)$" s)
2924     (let ((num (math-match-substring s 1))
2925           (den (math-match-substring s 2)))
2926       (let ((num (if (> (length num) 0) (math-read-number num) 1))
2927             (den (if (> (length num) 0) (math-read-number den) 1)))
2928         (and num den (math-integerp num) (math-integerp den)
2929              (not (math-zerop den))
2930              (list 'frac num den)))))
2931
2932    ;; Modulo forms
2933    ((string-match "^\\(.*\\) *mod *\\(.*\\)$" s)
2934     (let* ((n (math-match-substring s 1))
2935            (m (math-match-substring s 2))
2936            (n (math-read-number n))
2937            (m (math-read-number m)))
2938       (and n m (math-anglep n) (math-anglep m)
2939            (list 'mod n m))))
2940
2941    ;; Error forms
2942    ((string-match "^\\(.*\\) *\\+/- *\\(.*\\)$" s)
2943     (let* ((x (math-match-substring s 1))
2944            (sigma (math-match-substring s 2))
2945            (x (math-read-number x))
2946            (sigma (math-read-number sigma)))
2947       (and x sigma (math-scalarp x) (math-anglep sigma)
2948            (list 'sdev x sigma))))
2949
2950    ;; Integer+fraction with explicit radix
2951    ((string-match "^\\([0-9]+\\)\\(#\\|\\^\\^\\)\\([0-9a-zA-Z]*\\)[:/]\\([0-9a-zA-Z]*\\)[:/]\\([0-9a-zA-Z]\\)$" s)
2952     (let ((radix (string-to-number (math-match-substring s 1)))
2953           (int (math-match-substring s 3))
2954           (num (math-match-substring s 4))
2955           (den (math-match-substring s 5)))
2956       (let ((int (if (> (length int) 0) (math-read-radix int radix) 0))
2957             (num (if (> (length num) 0) (math-read-radix num radix) 1))
2958             (den (if (> (length den) 0) (math-read-radix den radix) 1)))
2959         (and int num den (not (math-zerop den))
2960              (list 'frac
2961                    (math-add num (math-mul int den))
2962                    den)))))
2963
2964    ;; Fraction with explicit radix
2965    ((string-match "^\\([0-9]+\\)\\(#\\|\\^\\^\\)\\([0-9a-zA-Z]*\\)[:/]\\([0-9a-zA-Z]*\\)$" s)
2966     (let ((radix (string-to-number (math-match-substring s 1)))
2967           (num (math-match-substring s 3))
2968           (den (math-match-substring s 4)))
2969       (let ((num (if (> (length num) 0) (math-read-radix num radix) 1))
2970             (den (if (> (length den) 0) (math-read-radix den radix) 1)))
2971         (and num den (not (math-zerop den)) (list 'frac num den)))))
2972
2973    ;; Float with explicit radix and exponent
2974    ((or (string-match "^0*\\(\\([2-9]\\|1[0-4]\\)\\(#\\|\\^\\^\\)[0-9a-dA-D.]+\\)[eE]\\([-+]?[0-9]+\\)$" s)
2975         (string-match "^\\(\\([0-9]+\\)\\(#\\|\\^\\^\\)[0-9a-zA-Z.]+\\) *\\* *\\2\\.? *\\^ *\\([-+]?[0-9]+\\)$" s))
2976     (let ((radix (string-to-number (math-match-substring s 2)))
2977           (mant (math-match-substring s 1))
2978           (exp (math-match-substring s 4)))
2979       (let ((mant (math-read-number mant))
2980             (exp (math-read-number exp)))
2981         (and mant exp
2982              (math-mul mant (math-pow (math-float radix) exp))))))
2983
2984    ;; Float with explicit radix, no exponent
2985    ((string-match "^\\([0-9]+\\)\\(#\\|\\^\\^\\)\\([0-9a-zA-Z]*\\)\\.\\([0-9a-zA-Z]*\\)$" s)
2986     (let ((radix (string-to-number (math-match-substring s 1)))
2987           (int (math-match-substring s 3))
2988           (fracs (math-match-substring s 4)))
2989       (let ((int (if (> (length int) 0) (math-read-radix int radix) 0))
2990             (frac (if (> (length fracs) 0) (math-read-radix fracs radix) 0))
2991             (calc-prefer-frac nil))
2992         (and int frac
2993              (math-add int (math-div frac (math-pow radix (length fracs))))))))
2994
2995    ;; Integer with explicit radix
2996    ((string-match "^\\([0-9]+\\)\\(#&?\\|\\^\\^\\)\\([0-9a-zA-Z]+\\)$" s)
2997     (math-read-radix (math-match-substring s 3)
2998                      (string-to-number (math-match-substring s 1))))
2999
3000    ;; Two's complement with explicit radix
3001    ((string-match "^\\([0-9]+\\)\\(##\\)\\([0-9a-zA-Z]+\\)$" s)
3002     (let ((num (math-read-radix (math-match-substring s 3)
3003                                 (string-to-number (math-match-substring s 1)))))
3004       (if (and
3005            (Math-lessp num math-2-word-size)
3006            (<= (math-compare math-half-2-word-size num) 0))
3007           (math-sub num math-2-word-size)
3008         num)))
3009
3010    ;; C language hexadecimal notation
3011    ((and (eq calc-language 'c)
3012          (string-match "^0[xX]\\([0-9a-fA-F]+\\)$" s))
3013     (let ((digs (math-match-substring s 1)))
3014       (math-read-radix digs 16)))
3015
3016    ;; Pascal language hexadecimal notation
3017    ((and (eq calc-language 'pascal)
3018          (string-match "^\\$\\([0-9a-fA-F]+\\)$" s))
3019     (let ((digs (math-match-substring s 1)))
3020       (math-read-radix digs 16)))
3021
3022    ;; Hours (or degrees)
3023    ((or (string-match "^\\([^#^]+\\)[@oOhH]\\(.*\\)$" s)
3024         (string-match "^\\([^#^]+\\)[dD][eE]?[gG]?\\(.*\\)$" s))
3025     (let* ((hours (math-match-substring s 1))
3026            (minsec (math-match-substring s 2))
3027            (hours (math-read-number hours))
3028            (minsec (if (> (length minsec) 0) (math-read-number minsec) 0)))
3029       (and hours minsec
3030            (math-num-integerp hours)
3031            (not (math-negp hours)) (not (math-negp minsec))
3032            (cond ((math-num-integerp minsec)
3033                   (and (Math-lessp minsec 60)
3034                        (list 'hms hours minsec 0)))
3035                  ((and (eq (car-safe minsec) 'hms)
3036                        (math-zerop (nth 1 minsec)))
3037                   (math-add (list 'hms hours 0 0) minsec))
3038                  (t nil)))))
3039
3040    ;; Minutes
3041    ((string-match "^\\([^'#^]+\\)[mM']\\(.*\\)$" s)
3042     (let* ((minutes (math-match-substring s 1))
3043            (seconds (math-match-substring s 2))
3044            (minutes (math-read-number minutes))
3045            (seconds (if (> (length seconds) 0) (math-read-number seconds) 0)))
3046       (and minutes seconds
3047            (math-num-integerp minutes)
3048            (not (math-negp minutes)) (not (math-negp seconds))
3049            (cond ((math-realp seconds)
3050                   (and (Math-lessp minutes 60)
3051                        (list 'hms 0 minutes seconds)))
3052                  ((and (eq (car-safe seconds) 'hms)
3053                        (math-zerop (nth 1 seconds))
3054                        (math-zerop (nth 2 seconds)))
3055                   (math-add (list 'hms 0 minutes 0) seconds))
3056                  (t nil)))))
3057
3058    ;; Seconds
3059    ((string-match "^\\([^\"#^]+\\)[sS\"]$" s)
3060     (let ((seconds (math-read-number (math-match-substring s 1))))
3061       (and seconds (math-realp seconds)
3062            (not (math-negp seconds))
3063            (Math-lessp seconds 60)
3064            (list 'hms 0 0 seconds))))
3065
3066    ;; Fraction using "/" instead of ":"
3067    ((string-match "^\\([0-9]+\\)/\\([0-9/]+\\)$" s)
3068     (math-read-number (concat (math-match-substring s 1) ":"
3069                               (math-match-substring s 2))))
3070
3071    ;; Syntax error!
3072    (t nil)))
3073
3074 (defun math-read-radix (s r)   ; [I X D]
3075   (setq s (upcase s))
3076   (let ((i 0)
3077         (res 0)
3078         dig)
3079     (while (and (< i (length s))
3080                 (setq dig (math-read-radix-digit (elt s i)))
3081                 (< dig r))
3082       (setq res (math-add (math-mul res r) dig)
3083             i (1+ i)))
3084     (and (= i (length s))
3085          res)))
3086
3087
3088
3089 ;;; Expression parsing.
3090
3091 (defvar math-expr-data)
3092
3093 (defun math-read-expr (math-exp-str)
3094   (let ((math-exp-pos 0)
3095         (math-exp-old-pos 0)
3096         (math-exp-keep-spaces nil)
3097         math-exp-token math-expr-data)
3098     (setq math-exp-str (math-read-preprocess-string math-exp-str))
3099     (while (setq math-exp-token (string-match "\\.\\.\\([^.]\\|.[^.]\\)" math-exp-str))
3100       (setq math-exp-str (concat (substring math-exp-str 0 math-exp-token) "\\dots"
3101                             (substring math-exp-str (+ math-exp-token 2)))))
3102     (math-build-parse-table)
3103     (math-read-token)
3104     (let ((val (catch 'syntax (math-read-expr-level 0))))
3105       (if (stringp val)
3106           (list 'error math-exp-old-pos val)
3107         (if (equal math-exp-token 'end)
3108             val
3109           (list 'error math-exp-old-pos "Syntax error"))))))
3110
3111 (defun math-read-plain-expr (exp-str &optional error-check)
3112   (let* ((calc-language nil)
3113          (math-expr-opers (math-standard-ops))
3114          (val (math-read-expr exp-str)))
3115     (and error-check
3116          (eq (car-safe val) 'error)
3117          (error "%s: %s" (nth 2 val) exp-str))
3118     val))
3119
3120
3121 (defun math-read-string ()
3122   (let ((str (read-from-string (concat math-expr-data "\""))))
3123     (or (and (= (cdr str) (1+ (length math-expr-data)))
3124              (stringp (car str)))
3125         (throw 'syntax "Error in string constant"))
3126     (math-read-token)
3127     (append '(vec) (car str) nil)))
3128
3129
3130
3131 ;;; They said it couldn't be done...
3132
3133 (defun math-read-big-expr (str)
3134   (and (> (length calc-left-label) 0)
3135        (string-match (concat "^" (regexp-quote calc-left-label)) str)
3136        (setq str (concat (substring str 0 (match-beginning 0))
3137                          (substring str (match-end 0)))))
3138   (and (> (length calc-right-label) 0)
3139        (string-match (concat (regexp-quote calc-right-label) " *$") str)
3140        (setq str (concat (substring str 0 (match-beginning 0))
3141                          (substring str (match-end 0)))))
3142   (if (string-match "\\\\[^ \n|]" str)
3143       (if (eq calc-language 'latex)
3144           (math-read-expr str)
3145         (let ((calc-language 'latex)
3146               (calc-language-option nil)
3147               (math-expr-opers (get 'latex 'math-oper-table))
3148               (math-expr-function-mapping (get 'latex 'math-function-table))
3149               (math-expr-variable-mapping (get 'latex 'math-variable-table)))
3150           (math-read-expr str)))
3151     (let ((math-read-big-lines nil)
3152           (pos 0)
3153           (width 0)
3154           (math-read-big-err-msg nil)
3155           math-read-big-baseline math-read-big-h2
3156           new-pos p)
3157       (while (setq new-pos (string-match "\n" str pos))
3158         (setq math-read-big-lines
3159               (cons (substring str pos new-pos) math-read-big-lines)
3160               pos (1+ new-pos)))
3161       (setq math-read-big-lines
3162             (nreverse (cons (substring str pos) math-read-big-lines))
3163             p math-read-big-lines)
3164       (while p
3165         (setq width (max width (length (car p)))
3166               p (cdr p)))
3167       (if (math-read-big-bigp math-read-big-lines)
3168           (or (catch 'syntax
3169                 (math-read-big-rec 0 0 width (length math-read-big-lines)))
3170               math-read-big-err-msg
3171               '(error 0 "Syntax error"))
3172         (math-read-expr str)))))
3173
3174 (defun math-read-big-bigp (math-read-big-lines)
3175   (and (cdr math-read-big-lines)
3176        (let ((matrix nil)
3177              (v 0)
3178              (height (if (> (length (car math-read-big-lines)) 0) 1 0)))
3179          (while (and (cdr math-read-big-lines)
3180                      (let* ((i 0)
3181                             j
3182                             (l1 (car math-read-big-lines))
3183                             (l2 (nth 1 math-read-big-lines))
3184                             (len (min (length l1) (length l2))))
3185                        (if (> (length l2) 0)
3186                            (setq height (1+ height)))
3187                        (while (and (< i len)
3188                                    (or (memq (aref l1 i) '(?\  ?\- ?\_))
3189                                        (memq (aref l2 i) '(?\  ?\-))
3190                                        (and (memq (aref l1 i) '(?\| ?\,))
3191                                             (= (aref l2 i) (aref l1 i)))
3192                                        (and (eq (aref l1 i) ?\[)
3193                                             (eq (aref l2 i) ?\[)
3194                                             (let ((math-rb-h2 (length l1)))
3195                                               (setq j (math-read-big-balance
3196                                                        (1+ i) v "[")))
3197                                             (setq i (1- j)))))
3198                          (setq i (1+ i)))
3199                        (or (= i len)
3200                            (and (eq (aref l1 i) ?\[)
3201                                 (eq (aref l2 i) ?\[)
3202                                 (setq matrix t)
3203                                 nil))))
3204            (setq math-read-big-lines (cdr math-read-big-lines)
3205                  v (1+ v)))
3206          (or (and (> height 1)
3207                   (not (cdr math-read-big-lines)))
3208              matrix))))
3209
3210 ;;; Nontrivial "flat" formatting.
3211
3212 (defvar math-format-hash-args nil)
3213 (defvar calc-can-abbrev-vectors nil)
3214
3215 (defun math-format-flat-expr-fancy (a prec)
3216   (cond
3217    ((eq (car a) 'incomplete)
3218     (format "<incomplete %s>" (nth 1 a)))
3219    ((eq (car a) 'vec)
3220     (if (or calc-full-trail-vectors (not calc-can-abbrev-vectors)
3221             (< (length a) 7))
3222         (concat "[" (math-format-flat-vector (cdr a) ", "
3223                                              (if (cdr (cdr a)) 0 1000)) "]")
3224       (concat "["
3225               (math-format-flat-expr (nth 1 a) 0) ", "
3226               (math-format-flat-expr (nth 2 a) 0) ", "
3227               (math-format-flat-expr (nth 3 a) 0) ", ..., "
3228               (math-format-flat-expr (nth (1- (length a)) a) 0) "]")))
3229    ((eq (car a) 'intv)
3230     (concat (if (memq (nth 1 a) '(0 1)) "(" "[")
3231             (math-format-flat-expr (nth 2 a) 1000)
3232             " .. "
3233             (math-format-flat-expr (nth 3 a) 1000)
3234             (if (memq (nth 1 a) '(0 2)) ")" "]")))
3235    ((eq (car a) 'date)
3236     (concat "<" (math-format-date a) ">"))
3237    ((and (eq (car a) 'calcFunc-lambda) (> (length a) 2))
3238     (let ((p (cdr a))
3239           (ap calc-arg-values)
3240           (math-format-hash-args (if (= (length a) 3) 1 t)))
3241       (while (and (cdr p) (equal (car p) (car ap)))
3242         (setq p (cdr p) ap (cdr ap)))
3243       (concat "<"
3244               (if (cdr p)
3245                   (concat (math-format-flat-vector
3246                            (nreverse (cdr (reverse (cdr a)))) ", " 0)
3247                           " : ")
3248                 "")
3249               (math-format-flat-expr (nth (1- (length a)) a) 0)
3250               ">")))
3251    ((eq (car a) 'var)
3252     (or (and math-format-hash-args
3253              (let ((p calc-arg-values) (v 1))
3254                (while (and p (not (equal (car p) a)))
3255                  (setq p (and (eq math-format-hash-args t) (cdr p))
3256                        v (1+ v)))
3257                (and p
3258                     (if (eq math-format-hash-args 1)
3259                         "#"
3260                       (format "#%d" v)))))
3261         (symbol-name (nth 1 a))))
3262    ((and (memq (car a) '(calcFunc-string calcFunc-bstring))
3263          (= (length a) 2)
3264          (math-vectorp (nth 1 a))
3265          (math-vector-is-string (nth 1 a)))
3266     (concat (substring (symbol-name (car a)) 9)
3267             "(" (math-vector-to-string (nth 1 a) t) ")"))
3268    (t
3269     (let ((op (math-assq2 (car a) (math-standard-ops))))
3270       (cond ((and op (= (length a) 3))
3271              (if (> prec (min (nth 2 op) (nth 3 op)))
3272                  (concat "(" (math-format-flat-expr a 0) ")")
3273                (let ((lhs (math-format-flat-expr (nth 1 a) (nth 2 op)))
3274                      (rhs (math-format-flat-expr (nth 2 a) (nth 3 op))))
3275                  (setq op (car op))
3276                  (if (or (equal op "^") (equal op "_"))
3277                      (if (= (aref lhs 0) ?-)
3278                          (setq lhs (concat "(" lhs ")")))
3279                    (setq op (concat " " op " ")))
3280                  (concat lhs op rhs))))
3281             ((eq (car a) 'neg)
3282              (concat "-" (math-format-flat-expr (nth 1 a) 1000)))
3283             (t
3284              (concat (math-remove-dashes
3285                       (if (string-match "\\`calcFunc-\\([a-zA-Zα-ωΑ-Ω0-9']+\\)\\'"
3286                                         (symbol-name (car a)))
3287                           (math-match-substring (symbol-name (car a)) 1)
3288                         (symbol-name (car a))))
3289                      "("
3290                      (math-format-flat-vector (cdr a) ", " 0)
3291                      ")")))))))
3292
3293 (defun math-format-flat-vector (vec sep prec)
3294   (if vec
3295       (let ((buf (math-format-flat-expr (car vec) prec)))
3296         (while (setq vec (cdr vec))
3297           (setq buf (concat buf sep (math-format-flat-expr (car vec) prec))))
3298         buf)
3299     ""))
3300
3301 (defun math-format-nice-expr (x w)
3302   (cond ((and (eq (car-safe x) 'vec)
3303               (cdr (cdr x))
3304               (let ((ops '(vec calcFunc-assign calcFunc-condition
3305                                calcFunc-schedule calcFunc-iterations
3306                                calcFunc-phase)))
3307                 (or (memq (car-safe (nth 1 x)) ops)
3308                     (memq (car-safe (nth 2 x)) ops)
3309                     (memq (car-safe (nth 3 x)) ops)
3310                     calc-break-vectors)))
3311          (concat "[ " (math-format-flat-vector (cdr x) ",\n  " 0) " ]"))
3312         (t
3313          (let ((str (math-format-flat-expr x 0))
3314                (pos 0) p)
3315            (or (string-match "\"" str)
3316                (while (<= (setq p (+ pos w)) (length str))
3317                  (while (and (> (setq p (1- p)) pos)
3318                              (not (= (aref str p) ? ))))
3319                  (if (> p (+ pos 5))
3320                      (setq str (concat (substring str 0 p)
3321                                        "\n "
3322                                        (substring str p))
3323                            pos (1+ p))
3324                    (setq pos (+ pos w)))))
3325            str))))
3326
3327 (defun math-assq2 (v a)
3328   (while (and a (not (eq v (nth 1 (car a)))))
3329     (setq a (cdr a)))
3330   (car a))
3331
3332 (defun math-format-number-fancy (a prec)
3333   (cond
3334    ((eq (car a) 'float)    ; non-decimal radix
3335     (if (Math-integer-negp (nth 1 a))
3336         (concat "-" (math-format-number (math-neg a)))
3337       (let ((str (if (and calc-radix-formatter
3338                           (not (memq calc-language '(c pascal))))
3339                      (funcall calc-radix-formatter
3340                               calc-number-radix
3341                               (math-format-radix-float a prec))
3342                    (format "%d#%s" calc-number-radix
3343                            (math-format-radix-float a prec)))))
3344         (if (and prec (> prec 191) (string-match "\\*" str))
3345             (concat "(" str ")")
3346           str))))
3347    ((eq (car a) 'frac)
3348     (setq a (math-adjust-fraction a))
3349     (if (> (length (car calc-frac-format)) 1)
3350         (if (Math-integer-negp (nth 1 a))
3351             (concat "-" (math-format-number (math-neg a)))
3352           (let ((q (math-idivmod (nth 1 a) (nth 2 a))))
3353             (concat (let ((calc-frac-format nil))
3354                       (math-format-number (car q)))
3355                     (substring (car calc-frac-format) 0 1)
3356                     (let ((math-radix-explicit-format nil)
3357                           (calc-frac-format nil))
3358                       (math-format-number (cdr q)))
3359                     (substring (car calc-frac-format) 1 2)
3360                     (let ((math-radix-explicit-format nil)
3361                           (calc-frac-format nil))
3362                       (math-format-number (nth 2 a))))))
3363       (concat (let ((calc-frac-format nil))
3364                 (math-format-number (nth 1 a)))
3365               (car calc-frac-format)
3366               (let ((math-radix-explicit-format nil)
3367                     (calc-frac-format nil))
3368                 (math-format-number (nth 2 a))))))
3369    ((eq (car a) 'cplx)
3370     (if (math-zerop (nth 2 a))
3371         (math-format-number (nth 1 a))
3372       (if (null calc-complex-format)
3373           (concat "(" (math-format-number (nth 1 a))
3374                   ", " (math-format-number (nth 2 a)) ")")
3375         (if (math-zerop (nth 1 a))
3376             (if (math-equal-int (nth 2 a) 1)
3377                 (symbol-name calc-complex-format)
3378               (if (math-equal-int (nth 2 a) -1)
3379                   (concat "-" (symbol-name calc-complex-format))
3380                 (if prec
3381                     (math-compose-expr (list '* (nth 2 a) '(cplx 0 1)) prec)
3382                   (concat (math-format-number (nth 2 a)) " "
3383                           (symbol-name calc-complex-format)))))
3384           (if prec
3385               (math-compose-expr (list (if (math-negp (nth 2 a)) '- '+)
3386                                        (nth 1 a)
3387                                        (list 'cplx 0 (math-abs (nth 2 a))))
3388                                  prec)
3389             (concat (math-format-number (nth 1 a))
3390                     (if (math-negp (nth 2 a)) " - " " + ")
3391                     (math-format-number
3392                      (list 'cplx 0 (math-abs (nth 2 a))))))))))
3393    ((eq (car a) 'polar)
3394     (concat "(" (math-format-number (nth 1 a))
3395             "; " (math-format-number (nth 2 a)) ")"))
3396    ((eq (car a) 'hms)
3397     (if (math-negp a)
3398         (concat "-" (math-format-number (math-neg a)))
3399       (let ((calc-number-radix 10)
3400             (calc-twos-complement-mode nil)
3401             (calc-leading-zeros nil)
3402             (calc-group-digits nil))
3403         (format calc-hms-format
3404                 (let ((calc-frac-format '(":" nil)))
3405                   (math-format-number (nth 1 a)))
3406                 (let ((calc-frac-format '(":" nil)))
3407                   (math-format-number (nth 2 a)))
3408                 (math-format-number (nth 3 a))))))
3409    ((eq (car a) 'intv)
3410     (concat (if (memq (nth 1 a) '(0 1)) "(" "[")
3411             (math-format-number (nth 2 a))
3412             " .. "
3413             (math-format-number (nth 3 a))
3414             (if (memq (nth 1 a) '(0 2)) ")" "]")))
3415    ((eq (car a) 'sdev)
3416     (concat (math-format-number (nth 1 a))
3417             " +/- "
3418             (math-format-number (nth 2 a))))
3419    ((eq (car a) 'vec)
3420     (math-format-flat-expr a 0))
3421    (t (format "%s" a))))
3422
3423 (defun math-adjust-fraction (a)
3424   (if (nth 1 calc-frac-format)
3425       (progn
3426         (if (Math-integerp a) (setq a (list 'frac a 1)))
3427         (let ((g (math-quotient (nth 1 calc-frac-format)
3428                                 (math-gcd (nth 2 a)
3429                                           (nth 1 calc-frac-format)))))
3430           (list 'frac (math-mul (nth 1 a) g) (math-mul (nth 2 a) g))))
3431     a))
3432
3433 (defun math-format-bignum-fancy (a)   ; [X L]
3434   (let ((str (cond ((= calc-number-radix 10)
3435                     (math-format-bignum-decimal a))
3436                    ((= calc-number-radix 2)
3437                     (math-format-bignum-binary a))
3438                    ((= calc-number-radix 8)
3439                     (math-format-bignum-octal a))
3440                    ((= calc-number-radix 16)
3441                     (math-format-bignum-hex a))
3442                    (t (math-format-bignum-radix a)))))
3443     (if calc-leading-zeros
3444         (let* ((calc-internal-prec 6)
3445                (digs (math-compute-max-digits (math-abs calc-word-size)
3446                                               calc-number-radix))
3447                (len (length str)))
3448           (if (< len digs)
3449               (setq str (concat (make-string (- digs len) ?0) str)))))
3450     (if calc-group-digits
3451         (let ((i (length str))
3452               (g (if (integerp calc-group-digits)
3453                      (math-abs calc-group-digits)
3454                    (if (memq calc-number-radix '(2 16)) 4 3))))
3455           (while (> i g)
3456             (setq i (- i g)
3457                   str (concat (substring str 0 i)
3458                               calc-group-char
3459                               (substring str i))))
3460           str))
3461     (if (and (/= calc-number-radix 10)
3462              math-radix-explicit-format)
3463         (if calc-radix-formatter
3464             (funcall calc-radix-formatter calc-number-radix str)
3465           (format "%d#%s" calc-number-radix str))
3466       str)))
3467
3468
3469 (defun math-group-float (str)   ; [X X]
3470   (let* ((pt (or (string-match "[^0-9a-zA-Z]" str) (length str)))
3471          (g (if (integerp calc-group-digits) (math-abs calc-group-digits)
3472               (if (memq calc-number-radix '(2 16)) 4 3)))
3473          (i pt))
3474     (if (and (integerp calc-group-digits) (< calc-group-digits 0))
3475         (while (< (setq i (+ (1+ i) g)) (length str))
3476           (setq str (concat (substring str 0 i)
3477                             calc-group-char
3478                             (substring str i))
3479                 i (+ i (1- (length calc-group-char))))))
3480     (setq i pt)
3481     (while (> i g)
3482       (setq i (- i g)
3483             str (concat (substring str 0 i)
3484                         calc-group-char
3485                         (substring str i))))
3486     str))
3487
3488 ;;; Users can redefine this in their init files.
3489 (defvar calc-keypad-user-menu nil
3490   "If non-nil, this describes an additional menu for calc-keypad.
3491 It should contain a list of three rows.
3492 Each row should be a list of six keys.
3493 Each key should be a list of a label string, plus a Calc command name spec.
3494 A command spec is a command name symbol, a keyboard macro string, a
3495 list containing a numeric entry string, or nil.
3496 A key may contain additional specs for Inverse, Hyperbolic, and Inv+Hyp.")
3497
3498 (run-hooks 'calc-ext-load-hook)
3499
3500 (provide 'calc-ext)
3501
3502 ;; Local variables:
3503 ;; coding: utf-8
3504 ;; End:
3505
3506 ;;; calc-ext.el ends here