lisp/calc/calc-rules.el

   1 ;;; calc-rules.el --- rules for simplifying algebraic expressions in Calc
   2
   3 ;; Copyright (C) 1990-1993, 2001-2014 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 ;; This file is autoloaded from calc-ext.el.
  28
  29 (require 'calc-ext)
  30 (require 'calc-macs)
  31
  32 (defun calc-compile-rule-set (name rules)
  33   (prog2
  34    (message "Preparing rule set %s..." name)
  35    (math-read-plain-expr rules t)
  36    (message "Preparing rule set %s...done" name)))
  37
  38 (defun calc-CommuteRules ()
  39   "CommuteRules"
  40   (calc-compile-rule-set
  41    "CommuteRules" "[
  42 iterations(1),
  43 select(plain(a + b))            :=  select(plain(b + a)),
  44 select(plain(a - b))            :=  select(plain((-b) + a)),
  45 select(plain((1/a) * b))        :=  select(b / a),
  46 select(plain(a * b))            :=  select(b * a),
  47 select((1/a) / b)               :=  select((1/b) / a),
  48 select(a / b)                   :=  select((1/b) * a),
  49 select((a^b) ^ c)               :=  select((a^c) ^ b),
  50 select(log(a, b))               :=  select(1 / log(b, a)),
  51 select(plain(a && b))           :=  select(b && a),
  52 select(plain(a || b))           :=  select(b || a),
  53 select(plain(a = b))            :=  select(b = a),
  54 select(plain(a != b))           :=  select(b != a),
  55 select(a < b)                   :=  select(b > a),
  56 select(a > b)                   :=  select(b < a),
  57 select(a <= b)                  :=  select(b >= a),
  58 select(a >= b)                  :=  select(b <= a) ]"))
  59
  60 (defun calc-JumpRules ()
  61   "JumpRules"
  62   (calc-compile-rule-set
  63    "JumpRules" "[
  64 iterations(1),
  65 plain(select(x) = y)            :=  0 = select(-x) + y,
  66 plain(a + select(x) = y)        :=  a = select(-x) + y,
  67 plain(a - select(x) = y)        :=  a = select(x) + y,
  68 plain(select(x) + a = y)        :=  a = select(-x) + y,
  69 plain(a * select(x) = y)        :=  a = y / select(x),
  70 plain(a / select(x) = y)        :=  a = select(x) * y,
  71 plain(select(x) / a = y)        :=  1/a = y / select(x),
  72 plain(a ^ select(2) = y)        :=  a = select(sqrt(y)),
  73 plain(a ^ select(x) = y)        :=  a = y ^ select(1/x),
  74 plain(select(x) ^ a = y)        :=  a = log(y, select(x)),
  75 plain(log(a, select(x)) = y)    :=  a = select(x) ^ y,
  76 plain(log(select(x), a) = y)    :=  a = select(x) ^ (1/y),
  77 plain(y = select(x))            :=  y - select(x) = 0,
  78 plain(y = a + select(x))        :=  y - select(x) = a,
  79 plain(y = a - select(x))        :=  y + select(x) = a,
  80 plain(y = select(x) + a)        :=  y - select(x) = a,
  81 plain(y = a * select(x))        :=  y / select(x) = a,
  82 plain(y = a / select(x))        :=  y * select(x) = a,
  83 plain(y = select(x) / a)        :=  y / select(x) = 1/a,
  84 plain(y = a ^ select(2))        :=  select(sqrt(y)) = a,
  85 plain(y = a ^ select(x))        :=  y ^ select(1/x) = a,
  86 plain(y = select(x) ^ a)        :=  log(y, select(x)) = a,
  87 plain(y = log(a, select(x)))    :=  select(x) ^ y = a,
  88 plain(y = log(select(x), a))    :=  select(x) ^ (1/y) = a ]"))
  89
  90 (defun calc-DistribRules ()
  91   "DistribRules"
  92   (calc-compile-rule-set
  93    "DistribRules" "[
  94 iterations(1),
  95 x * select(a + b)               :=  x*select(a) + x*b,
  96 x * select(sum(a,b,c,d))        :=  sum(x*select(a),b,c,d),
  97 x / select(a + b)               :=  1 / (select(a)/x + b/x),
  98 select(a + b) / x               :=  select(a)/x + b/x,
  99 sum(select(a),b,c,d) / x        :=  sum(select(a)/x,b,c,d),
 100 x ^ select(a + b)               :=  x^select(a) * x^b,
 101 x ^ select(sum(a,b,c,d))        :=  prod(x^select(a),b,c,d),
 102 x ^ select(a * b)               :=  (x^a)^select(b),
 103 x ^ select(a / b)               :=  (x^a)^select(1/b),
 104 select(a + b) ^ n               :=  select(x)
 105                                     :: integer(n) :: n >= 2
 106                                     :: let(x, expandpow(a+b,n))
 107                                     :: quote(matches(x,y+z)),
 108 select(a + b) ^ x               :=  a*select(a+b)^(x-1) + b*select(a+b)^(x-1),
 109 select(a * b) ^ x               :=  a^x * select(b)^x,
 110 select(prod(a,b,c,d)) ^ x       :=  prod(select(a)^x,b,c,d),
 111 select(a / b) ^ x               :=  select(a)^x / b^x,
 112 select(- a) ^ x                 :=  (-1)^x * select(a)^x,
 113 plain(-select(a + b))           :=  select(-a) - b,
 114 plain(-select(sum(a,b,c,d)))    :=  sum(select(-a),b,c,d),
 115 plain(-select(a * b))           :=  select(-a) * b,
 116 plain(-select(a / b))           :=  select(-a) / b,
 117 sqrt(select(a * b))             :=  sqrt(select(a)) * sqrt(b),
 118 sqrt(select(prod(a,b,c,d)))     :=  prod(sqrt(select(a)),b,c,d),
 119 sqrt(select(a / b))             :=  sqrt(select(a)) / sqrt(b),
 120 sqrt(select(- a))               :=  sqrt(-1) sqrt(select(a)),
 121 exp(select(a + b))              :=  exp(select(a)) / exp(-b) :: negative(b),
 122 exp(select(a + b))              :=  exp(select(a)) * exp(b),
 123 exp(select(sum(a,b,c,d)))       :=  prod(exp(select(a)),b,c,d),
 124 exp(select(a * b))              :=  exp(select(a)) ^ b :: constant(b),
 125 exp(select(a * b))              :=  exp(select(a)) ^ b,
 126 exp(select(a / b))              :=  exp(select(a)) ^ (1/b),
 127 ln(select(a * b))               :=  ln(select(a)) + ln(b),
 128 ln(select(prod(a,b,c,d)))       :=  sum(ln(select(a)),b,c,d),
 129 ln(select(a / b))               :=  ln(select(a)) - ln(b),
 130 ln(select(a ^ b))               :=  ln(select(a)) * b,
 131 log10(select(a * b))            :=  log10(select(a)) + log10(b),
 132 log10(select(prod(a,b,c,d)))    :=  sum(log10(select(a)),b,c,d),
 133 log10(select(a / b))            :=  log10(select(a)) - log10(b),
 134 log10(select(a ^ b))            :=  log10(select(a)) * b,
 135 log(select(a * b), x)           :=  log(select(a), x) + log(b,x),
 136 log(select(prod(a,b,c,d)),x)    :=  sum(log(select(a),x),b,c,d),
 137 log(select(a / b), x)           :=  log(select(a), x) - log(b,x),
 138 log(select(a ^ b), x)           :=  log(select(a), x) * b,
 139 log(a, select(b))               :=  ln(a) / select(ln(b)),
 140 sin(select(a + b))              :=  sin(select(a)) cos(b) + cos(a) sin(b),
 141 sin(select(2 a))                :=  2 sin(select(a)) cos(a),
 142 sin(select(n a))                :=  2sin((n-1) select(a)) cos(a) - sin((n-2) a)
 143                                     :: integer(n) :: n > 2,
 144 cos(select(a + b))              :=  cos(select(a)) cos(b) - sin(a) sin(b),
 145 cos(select(2 a))                :=  2 cos(select(a))^2 - 1,
 146 cos(select(n a))                :=  2cos((n-1) select(a)) cos(a) - cos((n-2) a)
 147                                     :: integer(n) :: n > 2,
 148 tan(select(a + b))              :=  (tan(select(a)) + tan(b)) /
 149                                     (1 - tan(a) tan(b)),
 150 tan(select(2 a))                :=  2 tan(select(a)) / (1 - tan(a)^2),
 151 tan(select(n a))                :=  (tan((n-1) select(a)) + tan(a)) /
 152                                     (1 - tan((n-1) a) tan(a))
 153                                     :: integer(n) :: n > 2,
 154 cot(select(a + b))              :=  (cot(select(a)) cot(b) - 1) /
 155                                     (cot(a) + cot(b)),
 156 sinh(select(a + b))             :=  sinh(select(a)) cosh(b) + cosh(a) sinh(b),
 157 cosh(select(a + b))             :=  cosh(select(a)) cosh(b) + sinh(a) sinh(b),
 158 tanh(select(a + b))             :=  (tanh(select(a)) + tanh(b)) /
 159                                     (1 + tanh(a) tanh(b)),
 160 coth(select(a + b))             :=  (coth(select(a)) coth(b) + 1) /
 161                                     (coth(a) + coth(b)),
 162 x && select(a || b)             :=  (x && select(a)) || (x && b),
 163 select(a || b) && x             :=  (select(a) && x) || (b && x),
 164 ! select(a && b)                :=  (!a) || (!b),
 165 ! select(a || b)                :=  (!a) && (!b) ]"))
 166
 167 (defun calc-MergeRules ()
 168   "MergeRules"
 169   (calc-compile-rule-set
 170    "MergeRules" "[
 171 iterations(1),
 172  (x*opt(a)) + select(x*b)       :=  x * (a + select(b)),
 173  (x*opt(a)) - select(x*b)       :=  x * (a - select(b)),
 174 sum(select(x)*a,b,c,d)          :=  x * sum(select(a),b,c,d),
 175  (a/x) + select(b/x)            :=  (a + select(b)) / x,
 176  (a/x) - select(b/x)            :=  (a - select(b)) / x,
 177 sum(a/select(x),b,c,d)          :=  sum(select(a),b,c,d) / x,
 178  (a/opt(b)) + select(c/d)       :=  ((select(a)*d) + (b*c)) / (b*d),
 179  (a/opt(b)) - select(c/d)       :=  ((select(a)*d) - (b*c)) / (b*d),
 180  (x^opt(a)) * select(x^b)       :=  x ^ (a + select(b)),
 181  (x^opt(a)) / select(x^b)       :=  x ^ (a - select(b)),
 182 select(x^a) / (x^opt(b))        :=  x ^ (select(a) - b),
 183 prod(select(x)^a,b,c,d)         :=  x ^ sum(select(a),b,c,d),
 184 select(x^a) / (x^opt(b))        :=  x ^ (select(a) - b),
 185  (a^x) * select(b^x)            :=  select((a * b) ^x),
 186  (a^x) / select(b^x)            :=  select((b / b) ^ x),
 187 select(a^x) / (b^x)             :=  select((a / b) ^ x),
 188 prod(a^select(x),b,c,d)         :=  select(prod(a,b,c,d) ^ x),
 189  (a^x) * select(b^y)            :=  select((a * b^(y-x)) ^x),
 190  (a^x) / select(b^y)            :=  select((b / b^(y-x)) ^ x),
 191 select(a^x) / (b^y)             :=  select((a / b^(y-x)) ^ x),
 192 select(x^a) ^ b                 :=  x ^ select(a * b),
 193  (x^a) ^ select(b)              :=  x ^ select(a * b),
 194 select(sqrt(a)) ^ b             :=  select(a ^ (b / 2)),
 195 sqrt(a) ^ select(b)             :=  select(a ^ (b / 2)),
 196 sqrt(select(a) ^ b)             :=  select(a ^ (b / 2)),
 197 sqrt(a ^ select(b))             :=  select(a ^ (b / 2)),
 198 sqrt(a) * select(sqrt(b))       :=  select(sqrt(a * b)),
 199 sqrt(a) / select(sqrt(b))       :=  select(sqrt(a / b)),
 200 select(sqrt(a)) / sqrt(b)       :=  select(sqrt(a / b)),
 201 prod(select(sqrt(a)),b,c,d)     :=  select(sqrt(prod(a,b,c,d))),
 202 exp(a) * select(exp(b))         :=  select(exp(a + b)),
 203 exp(a) / select(exp(b))         :=  select(exp(a - b)),
 204 select(exp(a)) / exp(b)         :=  select(exp(a - b)),
 205 prod(select(exp(a)),b,c,d)      :=  select(exp(sum(a,b,c,d))),
 206 select(exp(a)) ^ b              :=  select(exp(a * b)),
 207 exp(a) ^ select(b)              :=  select(exp(a * b)),
 208 ln(a) + select(ln(b))           :=  select(ln(a * b)),
 209 ln(a) - select(ln(b))           :=  select(ln(a / b)),
 210 select(ln(a)) - ln(b)           :=  select(ln(a / b)),
 211 sum(select(ln(a)),b,c,d)        :=  select(ln(prod(a,b,c,d))),
 212 b * select(ln(a))               :=  select(ln(a ^ b)),
 213 select(b) * ln(a)               :=  select(ln(a ^ b)),
 214 select(ln(a)) / ln(b)           :=  select(log(a, b)),
 215 ln(a) / select(ln(b))           :=  select(log(a, b)),
 216 select(ln(a)) / b               :=  select(ln(a ^ (1/b))),
 217 ln(a) / select(b)               :=  select(ln(a ^ (1/b))),
 218 log10(a) + select(log10(b))     :=  select(log10(a * b)),
 219 log10(a) - select(log10(b))     :=  select(log10(a / b)),
 220 select(log10(a)) - log10(b)     :=  select(log10(a / b)),
 221 sum(select(log10(a)),b,c,d)     :=  select(log10(prod(a,b,c,d))),
 222 b * select(log10(a))            :=  select(log10(a ^ b)),
 223 select(b) * log10(a)            :=  select(log10(a ^ b)),
 224 select(log10(a)) / log10(b)     :=  select(log(a, b)),
 225 log10(a) / select(log10(b))     :=  select(log(a, b)),
 226 select(log10(a)) / b            :=  select(log10(a ^ (1/b))),
 227 log10(a) / select(b)            :=  select(log10(a ^ (1/b))),
 228 log(a,x) + select(log(b,x))     :=  select(log(a * b,x)),
 229 log(a,x) - select(log(b,x))     :=  select(log(a / b,x)),
 230 select(log(a,x)) - log(b,x)     :=  select(log(a / b,x)),
 231 sum(select(log(a,x)),b,c,d)     :=  select(log(prod(a,b,c,d),x)),
 232 b * select(log(a,x))            :=  select(log(a ^ b,x)),
 233 select(b) * log(a,x)            :=  select(log(a ^ b,x)),
 234 select(log(a,x)) / log(b,x)     :=  select(log(a, b)),
 235 log(a,x) / select(log(b,x))     :=  select(log(a, b)),
 236 select(log(a,x)) / b            :=  select(log(a ^ (1/b),x)),
 237 log(a,x) / select(b)            :=  select(log(a ^ (1/b),x)),
 238 select(x && a) || (x && opt(b)) :=  x && (select(a) || b) ]"))
 239
 240 (defun calc-NegateRules ()
 241   "NegateRules"
 242   (calc-compile-rule-set
 243    "NegateRules" "[
 244 iterations(1),
 245 a + select(x)                   :=  a - select(-x),
 246 a - select(x)                   :=  a + select(-x),
 247 sum(select(x),b,c,d)            :=  -sum(select(-x),b,c,d),
 248 a * select(x)                   :=  -a * select(-x),
 249 a / select(x)                   :=  -a / select(-x),
 250 select(x) / a                   :=  -select(-x) / a,
 251 prod(select(x),b,c,d)           :=  (-1)^(d-c+1) * prod(select(-x),b,c,d),
 252 select(x) ^ n                   :=  select(-x) ^ a :: integer(n) :: n%2 = 0,
 253 select(x) ^ n                   :=  -(select(-x) ^ a) :: integer(n) :: n%2 = 1,
 254 select(x) ^ a                   :=  (-select(-x)) ^ a,
 255 a ^ select(x)                   :=  (1 / a)^select(-x),
 256 abs(select(x))                  :=  abs(select(-x)),
 257 i sqrt(select(x))               :=  -sqrt(select(-x)),
 258 sqrt(select(x))                 :=  i sqrt(select(-x)),
 259 re(select(x))                   :=  -re(select(-x)),
 260 im(select(x))                   :=  -im(select(-x)),
 261 conj(select(x))                 :=  -conj(select(-x)),
 262 trunc(select(x))                :=  -trunc(select(-x)),
 263 round(select(x))                :=  -round(select(-x)),
 264 floor(select(x))                :=  -ceil(select(-x)),
 265 ceil(select(x))                 :=  -floor(select(-x)),
 266 ftrunc(select(x))               :=  -ftrunc(select(-x)),
 267 fround(select(x))               :=  -fround(select(-x)),
 268 ffloor(select(x))               :=  -fceil(select(-x)),
 269 fceil(select(x))                :=  -ffloor(select(-x)),
 270 exp(select(x))                  :=  1 / exp(select(-x)),
 271 sin(select(x))                  :=  -sin(select(-x)),
 272 cos(select(x))                  :=  cos(select(-x)),
 273 tan(select(x))                  :=  -tan(select(-x)),
 274 sec(select(x))                  :=  sec(select(-x)),
 275 csc(select(x))                  :=  -csc(select(-x)),
 276 cot(select(x))                  :=  -cot(select(-x)),
 277 arcsin(select(x))               :=  -arcsin(select(-x)),
 278 arccos(select(x))               :=  4 arctan(1) - arccos(select(-x)),
 279 arctan(select(x))               :=  -arctan(select(-x)),
 280 sinh(select(x))                 :=  -sinh(select(-x)),
 281 cosh(select(x))                 :=  cosh(select(-x)),
 282 tanh(select(x))                 :=  -tanh(select(-x)),
 283 sech(select(x))                 :=  sech(select(-x)),
 284 csch(select(x))                 :=  -csch(select(-x)),
 285 coth(select(x))                 :=  -coth(select(-x)),
 286 arcsinh(select(x))              :=  -arcsinh(select(-x)),
 287 arctanh(select(x))              :=  -arctanh(select(-x)),
 288 select(x) = a                   :=  select(-x) = -a,
 289 select(x) != a                  :=  select(-x) != -a,
 290 select(x) < a                   :=  select(-x) > -a,
 291 select(x) > a                   :=  select(-x) < -a,
 292 select(x) <= a                  :=  select(-x) >= -a,
 293 select(x) >= a                  :=  select(-x) <= -a,
 294 a < select(x)                   :=  -a > select(-x),
 295 a > select(x)                   :=  -a < select(-x),
 296 a <= select(x)                  :=  -a >= select(-x),
 297 a >= select(x)                  :=  -a <= select(-x),
 298 select(x)                       :=  -select(-x) ]"))
 299
 300 (defun calc-InvertRules ()
 301   "InvertRules"
 302   (calc-compile-rule-set
 303    "InvertRules" "[
 304 iterations(1),
 305 a * select(x)                   :=  a / select(1/x),
 306 a / select(x)                   :=  a * select(1/x),
 307 select(x) / a                   :=  1 / (select(1/x) a),
 308 prod(select(x),b,c,d)           :=  1 / prod(select(1/x),b,c,d),
 309 abs(select(x))                  :=  1 / abs(select(1/x)),
 310 sqrt(select(x))                 :=  1 / sqrt(select(1/x)),
 311 ln(select(x))                   :=  -ln(select(1/x)),
 312 log10(select(x))                :=  -log10(select(1/x)),
 313 log(select(x), a)               :=  -log(select(1/x), a),
 314 log(a, select(x))               :=  -log(a, select(1/x)),
 315 arctan(select(x))               :=  simplify(2 arctan(1))-arctan(select(1/x)),
 316 select(x) = a                   :=  select(1/x) = 1/a,
 317 select(x) != a                  :=  select(1/x) != 1/a,
 318 select(x) < a                   :=  select(1/x) > 1/a,
 319 select(x) > a                   :=  select(1/x) < 1/a,
 320 select(x) <= a                  :=  select(1/x) >= 1/a,
 321 select(x) >= a                  :=  select(1/x) <= 1/a,
 322 a < select(x)                   :=  1/a > select(1/x),
 323 a > select(x)                   :=  1/a < select(1/x),
 324 a <= select(x)                  :=  1/a >= select(1/x),
 325 a >= select(x)                  :=  1/a <= select(1/x),
 326 select(x)                       :=  1 / select(1/x) ]"))
 327
 328
 329 (defun calc-FactorRules ()
 330   "FactorRules"
 331   (calc-compile-rule-set
 332    "FactorRules" "[
 333 thecoefs(x, [z, a+b, c]) := thefactors(x, [d x + d a/c, (c/d) x + (b/d)])
 334         :: z = a b/c :: let(d := pgcd(pcont(c), pcont(b))),
 335 thecoefs(x, [z, a, c]) := thefactors(x, [(r x + a/(2 r))^2])
 336         :: z = (a/2)^2/c :: let(r := esimplify(sqrt(c)))
 337         :: !matches(r, sqrt(rr)),
 338 thecoefs(x, [z, 0, c]) := thefactors(x, [rc x + rz, rc x - rz])
 339         :: negative(z)
 340         :: let(rz := esimplify(sqrt(-z))) :: !matches(rz, sqrt(rzz))
 341         :: let(rc := esimplify(sqrt(c))) :: !matches(rc, sqrt(rcc)),
 342 thecoefs(x, [z, 0, c]) := thefactors(x, [rz + rc x, rz - rc x])
 343         :: negative(c)
 344         :: let(rz := esimplify(sqrt(z))) :: !matches(rz, sqrt(rzz))
 345         :: let(rc := esimplify(sqrt(-c))) :: !matches(rc, sqrt(rcc))
 346  ]"))
 347 ;;(setq var-FactorRules 'calc-FactorRules)
 348
 349
 350 (defun calc-IntegAfterRules ()
 351   "IntegAfterRules"
 352   (calc-compile-rule-set
 353    "IntegAfterRules" "[
 354  opt(a) ln(x) + opt(b) ln(y) := 2 a esimplify(arctanh(x-1))
 355      :: a + b = 0 :: nrat(x + y) = 2 || nrat(x - y) = 2,
 356  a * (b + c) := a b + a c :: constant(a)
 357  ]"))
 358
 359 ;;(setq var-IntegAfterRules 'calc-IntegAfterRules)
 360
 361
 362 (defun calc-FitRules ()
 363   "FitRules"
 364   (calc-compile-rule-set
 365    "FitRules" "[
 366
 367 schedule(1,2,3,4),
 368 iterations(inf),
 369
 370 phase(1),
 371 e^x             :=  exp(x),
 372 x^y             :=  exp(y ln(x))  :: !istrue(constant(y)),
 373 x/y             :=  x fitinv(y),
 374 fitinv(x y)     :=  fitinv(x) fitinv(y),
 375 exp(a) exp(b)   :=  exp(a + b),
 376 a exp(b)        :=  exp(ln(a) + b)  :: !hasfitvars(a),
 377 fitinv(exp(a))  :=  exp(-a),
 378 ln(a b)         :=  ln(a) + ln(b),
 379 ln(fitinv(a))   :=  -ln(a),
 380 log10(a b)      :=  log10(a) + log10(b),
 381 log10(fitinv(a)) := -log10(a),
 382 log(a,b)        :=  ln(a)/ln(b),
 383 ln(exp(a))      :=  a,
 384 a*(b+c)         :=  a*b + a*c,
 385 (a+b)^n         :=  x  :: integer(n) :: n >= 2
 386                        :: let(x, expandpow(a+b,n))
 387                        :: quote(matches(x,y+z)),
 388
 389 phase(1,2),
 390 fitmodel(y = x)   :=  fitmodel(0, y - x),
 391 fitmodel(y, x+c)  :=  fitmodel(y-c, x)  :: !hasfitparams(c),
 392 fitmodel(y, x c)  :=  fitmodel(y/c, x)  :: !hasfitparams(c),
 393 fitmodel(y, x/(c opt(d)))  :=  fitmodel(y c, x/d)  :: !hasfitparams(c),
 394 fitmodel(y, apply(f,[x]))  :=  fitmodel(yy, x)
 395                                :: hasfitparams(x)
 396                                :: let(FTemp() = yy,
 397                                       solve(apply(f,[FTemp()]) = y,
 398                                             FTemp())),
 399 fitmodel(y, apply(f,[x,c]))  :=  fitmodel(yy, x)
 400                                  :: !hasfitparams(c)
 401                                  :: let(FTemp() = yy,
 402                                         solve(apply(f,[FTemp(),c]) = y,
 403                                               FTemp())),
 404 fitmodel(y, apply(f,[c,x]))  :=  fitmodel(yy, x)
 405                                  :: !hasfitparams(c)
 406                                  :: let(FTemp() = yy,
 407                                         solve(apply(f,[c,FTemp()]) = y,
 408                                               FTemp())),
 409
 410 phase(2,3),
 411 fitmodel(y, x)              :=  fitsystem(y, [], [], fitpart(1,1,x)),
 412 fitpart(a,b,plain(x + y))   :=  fitpart(a,b,x) + fitpart(a,b,y),
 413 fitpart(a,b,plain(x - y))   :=  fitpart(a,b,x) + fitpart(-a,b,y),
 414 fitpart(a,b,plain(-x))      :=  fitpart(-a,b,x),
 415 fitpart(a,b,x opt(c))       :=  fitpart(a,x b,c)  :: !hasfitvars(x),
 416 fitpart(a,x opt(b),c)       :=  fitpart(x a,b,c)  :: !hasfitparams(x),
 417 fitpart(a,x y + x opt(z),c) :=  fitpart(a,x*(y+z),c),
 418 fitpart(a,b,c)              :=  fitpart2(a,b,c),
 419
 420 phase(3),
 421 fitpart2(a1,b1,x) + fitpart2(a2,b2,x)  :=  fitpart(1, a1 b1 + a2 b2, x),
 422 fitpart2(a1,x,c1) + fitpart2(a2,x,c2)  :=  fitpart2(1, x, a1 c1 + a2 c2),
 423
 424 phase(4),
 425 fitinv(x)       :=  1 / x,
 426 exp(x + ln(y))  :=  y exp(x),
 427 exp(x ln(y))    :=  y^x,
 428 ln(x) + ln(y)   :=  ln(x y),
 429 ln(x) - ln(y)   :=  ln(x/y),
 430 x*y + x*z       :=  x*(y+z),
 431 fitsystem(y, xv, pv, fitpart2(a,fitparam(b),c) + opt(d))
 432                 :=  fitsystem(y, rcons(xv, a c),
 433                               rcons(pv, fitdummy(b) = fitparam(b)), d)
 434                     :: b = vlen(pv)+1,
 435 fitsystem(y, xv, pv, fitpart2(a,b,c) + opt(d))
 436                 :=  fitsystem(y, rcons(xv, a c),
 437                               rcons(pv, fitdummy(vlen(pv)+1) = b), d),
 438 fitsystem(y, xv, pv, 0)  :=  fitsystem(y, xv, cons(fvh,fvt))
 439                              :: !hasfitparams(xv)
 440                              :: let(cons(fvh,fvt),
 441                                     solve(pv, table(fitparam(j), j, 1,
 442                                                     hasfitparams(pv)))),
 443 fitparam(n) = x  :=  x ]"))
 444
 445 (provide 'calc-rules)
 446
 447 ;;; calc-rules.el ends here