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