lisp/calc/calc-rules.el

   1 ;;; calc-rules.el --- rules for simplifying algebraic expressions in Calc
   2
   3 ;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2005 Free Software Foundation, Inc.
   4
   5 ;; Author: David Gillespie <daveg@synaptics.com>
   6 ;; Maintainer: Jay Belanger <belanger@truman.edu>
   7
   8 ;; This file is part of GNU Emacs.
   9
  10 ;; GNU Emacs is distributed in the hope that it will be useful,
  11 ;; but WITHOUT ANY WARRANTY.  No author or distributor
  12 ;; accepts responsibility to anyone for the consequences of using it
  13 ;; or for whether it serves any particular purpose or works at all,
  14 ;; unless he says so in writing.  Refer to the GNU Emacs General Public
  15 ;; License for full details.
  16
  17 ;; Everyone is granted permission to copy, modify and redistribute
  18 ;; GNU Emacs, but only under the conditions described in the
  19 ;; GNU Emacs General Public License.   A copy of this license is
  20 ;; supposed to have been given to you along with GNU Emacs so you
  21 ;; can know your rights and responsibilities.  It should be in a
  22 ;; file named COPYING.  Among other things, the copyright notice
  23 ;; and this notice must be preserved on all copies.
  24
  25 ;;; Commentary:
  26
  27 ;;; Code:
  28
  29 ;; This file is autoloaded from calc-ext.el.
  30
  31 (require 'calc-ext)
  32 (require 'calc-macs)
  33
  34 (defun calc-compile-rule-set (name rules)
  35   (prog2
  36    (message "Preparing rule set %s..." name)
  37    (math-read-plain-expr rules t)
  38    (message "Preparing rule set %s...done" name)))
  39
  40 (defun calc-CommuteRules ()
  41   "CommuteRules"
  42   (calc-compile-rule-set
  43    "CommuteRules" "[
  44 iterations(1),
  45 select(plain(a + b))            :=  select(plain(b + a)),
  46 select(plain(a - b))            :=  select(plain((-b) + a)),
  47 select(plain((1/a) * b))        :=  select(b / a),
  48 select(plain(a * b))            :=  select(b * a),
  49 select((1/a) / b)               :=  select((1/b) / a),
  50 select(a / b)                   :=  select((1/b) * a),
  51 select((a^b) ^ c)               :=  select((a^c) ^ b),
  52 select(log(a, b))               :=  select(1 / log(b, a)),
  53 select(plain(a && b))           :=  select(b && a),
  54 select(plain(a || b))           :=  select(b || a),
  55 select(plain(a = b))            :=  select(b = a),
  56 select(plain(a != b))           :=  select(b != a),
  57 select(a < b)                   :=  select(b > a),
  58 select(a > b)                   :=  select(b < a),
  59 select(a <= b)                  :=  select(b >= a),
  60 select(a >= b)                  :=  select(b <= a) ]"))
  61
  62 (defun calc-JumpRules ()
  63   "JumpRules"
  64   (calc-compile-rule-set
  65    "JumpRules" "[
  66 iterations(1),
  67 plain(select(x) = y)            :=  0 = select(-x) + y,
  68 plain(a + select(x) = y)        :=  a = select(-x) + y,
  69 plain(a - select(x) = y)        :=  a = select(x) + y,
  70 plain(select(x) + a = y)        :=  a = select(-x) + y,
  71 plain(a * select(x) = y)        :=  a = y / select(x),
  72 plain(a / select(x) = y)        :=  a = select(x) * y,
  73 plain(select(x) / a = y)        :=  1/a = y / select(x),
  74 plain(a ^ select(2) = y)        :=  a = select(sqrt(y)),
  75 plain(a ^ select(x) = y)        :=  a = y ^ select(1/x),
  76 plain(select(x) ^ a = y)        :=  a = log(y, select(x)),
  77 plain(log(a, select(x)) = y)    :=  a = select(x) ^ y,
  78 plain(log(select(x), a) = y)    :=  a = select(x) ^ (1/y),
  79 plain(y = select(x))            :=  y - select(x) = 0,
  80 plain(y = a + select(x))        :=  y - select(x) = a,
  81 plain(y = a - select(x))        :=  y + select(x) = a,
  82 plain(y = select(x) + a)        :=  y - select(x) = a,
  83 plain(y = a * select(x))        :=  y / select(x) = a,
  84 plain(y = a / select(x))        :=  y * select(x) = a,
  85 plain(y = select(x) / a)        :=  y / select(x) = 1/a,
  86 plain(y = a ^ select(2))        :=  select(sqrt(y)) = a,
  87 plain(y = a ^ select(x))        :=  y ^ select(1/x) = a,
  88 plain(y = select(x) ^ a)        :=  log(y, select(x)) = a,
  89 plain(y = log(a, select(x)))    :=  select(x) ^ y = a,
  90 plain(y = log(select(x), a))    :=  select(x) ^ (1/y) = a ]"))
  91
  92 (defun calc-DistribRules ()
  93   "DistribRules"
  94   (calc-compile-rule-set
  95    "DistribRules" "[
  96 iterations(1),
  97 x * select(a + b)               :=  x*select(a) + x*b,
  98 x * select(sum(a,b,c,d))        :=  sum(x*select(a),b,c,d),
  99 x / select(a + b)               :=  1 / (select(a)/x + b/x),
 100 select(a + b) / x               :=  select(a)/x + b/x,
 101 sum(select(a),b,c,d) / x        :=  sum(select(a)/x,b,c,d),
 102 x ^ select(a + b)               :=  x^select(a) * x^b,
 103 x ^ select(sum(a,b,c,d))        :=  prod(x^select(a),b,c,d),
 104 x ^ select(a * b)               :=  (x^a)^select(b),
 105 x ^ select(a / b)               :=  (x^a)^select(1/b),
 106 select(a + b) ^ n               :=  select(x)
 107                                     :: integer(n) :: n >= 2
 108                                     :: let(x, expandpow(a+b,n))
 109                                     :: quote(matches(x,y+z)),
 110 select(a + b) ^ x               :=  a*select(a+b)^(x-1) + b*select(a+b)^(x-1),
 111 select(a * b) ^ x               :=  a^x * select(b)^x,
 112 select(prod(a,b,c,d)) ^ x       :=  prod(select(a)^x,b,c,d),
 113 select(a / b) ^ x               :=  select(a)^x / b^x,
 114 select(- a) ^ x                 :=  (-1)^x * select(a)^x,
 115 plain(-select(a + b))           :=  select(-a) - b,
 116 plain(-select(sum(a,b,c,d)))    :=  sum(select(-a),b,c,d),
 117 plain(-select(a * b))           :=  select(-a) * b,
 118 plain(-select(a / b))           :=  select(-a) / b,
 119 sqrt(select(a * b))             :=  sqrt(select(a)) * sqrt(b),
 120 sqrt(select(prod(a,b,c,d)))     :=  prod(sqrt(select(a)),b,c,d),
 121 sqrt(select(a / b))             :=  sqrt(select(a)) / sqrt(b),
 122 sqrt(select(- a))               :=  sqrt(-1) sqrt(select(a)),
 123 exp(select(a + b))              :=  exp(select(a)) / exp(-b) :: negative(b),
 124 exp(select(a + b))              :=  exp(select(a)) * exp(b),
 125 exp(select(sum(a,b,c,d)))       :=  prod(exp(select(a)),b,c,d),
 126 exp(select(a * b))              :=  exp(select(a)) ^ b :: constant(b),
 127 exp(select(a * b))              :=  exp(select(a)) ^ b,
 128 exp(select(a / b))              :=  exp(select(a)) ^ (1/b),
 129 ln(select(a * b))               :=  ln(select(a)) + ln(b),
 130 ln(select(prod(a,b,c,d)))       :=  sum(ln(select(a)),b,c,d),
 131 ln(select(a / b))               :=  ln(select(a)) - ln(b),
 132 ln(select(a ^ b))               :=  ln(select(a)) * b,
 133 log10(select(a * b))            :=  log10(select(a)) + log10(b),
 134 log10(select(prod(a,b,c,d)))    :=  sum(log10(select(a)),b,c,d),
 135 log10(select(a / b))            :=  log10(select(a)) - log10(b),
 136 log10(select(a ^ b))            :=  log10(select(a)) * b,
 137 log(select(a * b), x)           :=  log(select(a), x) + log(b,x),
 138 log(select(prod(a,b,c,d)),x)    :=  sum(log(select(a),x),b,c,d),
 139 log(select(a / b), x)           :=  log(select(a), x) - log(b,x),
 140 log(select(a ^ b), x)           :=  log(select(a), x) * b,
 141 log(a, select(b))               :=  ln(a) / select(ln(b)),
 142 sin(select(a + b))              :=  sin(select(a)) cos(b) + cos(a) sin(b),
 143 sin(select(2 a))                :=  2 sin(select(a)) cos(a),
 144 sin(select(n a))                :=  2sin((n-1) select(a)) cos(a) - sin((n-2) a)
 145                                     :: integer(n) :: n > 2,
 146 cos(select(a + b))              :=  cos(select(a)) cos(b) - sin(a) sin(b),
 147 cos(select(2 a))                :=  2 cos(select(a))^2 - 1,
 148 cos(select(n a))                :=  2cos((n-1) select(a)) cos(a) - cos((n-2) a)
 149                                     :: integer(n) :: n > 2,
 150 tan(select(a + b))              :=  (tan(select(a)) + tan(b)) /
 151                                     (1 - tan(a) tan(b)),
 152 tan(select(2 a))                :=  2 tan(select(a)) / (1 - tan(a)^2),
 153 tan(select(n a))                :=  (tan((n-1) select(a)) + tan(a)) /
 154                                     (1 - tan((n-1) a) tan(a))
 155                                     :: integer(n) :: n > 2,
 156 cot(select(a + b))              :=  (cot(select(a)) cot(b) - 1) /
 157                                     (cot(a) + cot(b)),
 158 sinh(select(a + b))             :=  sinh(select(a)) cosh(b) + cosh(a) sinh(b),
 159 cosh(select(a + b))             :=  cosh(select(a)) cosh(b) + sinh(a) sinh(b),
 160 tanh(select(a + b))             :=  (tanh(select(a)) + tanh(b)) /
 161                                     (1 + tanh(a) tanh(b)),
 162 coth(select(a + b))             :=  (coth(select(a)) coth(b) + 1) /
 163                                     (coth(a) + coth(b)),
 164 x && select(a || b)             :=  (x && select(a)) || (x && b),
 165 select(a || b) && x             :=  (select(a) && x) || (b && x),
 166 ! select(a && b)                :=  (!a) || (!b),
 167 ! select(a || b)                :=  (!a) && (!b) ]"))
 168
 169 (defun calc-MergeRules ()
 170   "MergeRules"
 171   (calc-compile-rule-set
 172    "MergeRules" "[
 173 iterations(1),
 174  (x*opt(a)) + select(x*b)       :=  x * (a + select(b)),
 175  (x*opt(a)) - select(x*b)       :=  x * (a - select(b)),
 176 sum(select(x)*a,b,c,d)          :=  x * sum(select(a),b,c,d),
 177  (a/x) + select(b/x)            :=  (a + select(b)) / x,
 178  (a/x) - select(b/x)            :=  (a - select(b)) / x,
 179 sum(a/select(x),b,c,d)          :=  sum(select(a),b,c,d) / x,
 180  (a/opt(b)) + select(c/d)       :=  ((select(a)*d) + (b*c)) / (b*d),
 181  (a/opt(b)) - select(c/d)       :=  ((select(a)*d) - (b*c)) / (b*d),
 182  (x^opt(a)) * select(x^b)       :=  x ^ (a + select(b)),
 183  (x^opt(a)) / select(x^b)       :=  x ^ (a - select(b)),
 184 select(x^a) / (x^opt(b))        :=  x ^ (select(a) - b),
 185 prod(select(x)^a,b,c,d)         :=  x ^ sum(select(a),b,c,d),
 186 select(x^a) / (x^opt(b))        :=  x ^ (select(a) - b),
 187  (a^x) * select(b^x)            :=  select((a * b) ^x),
 188  (a^x) / select(b^x)            :=  select((b / b) ^ x),
 189 select(a^x) / (b^x)             :=  select((a / b) ^ x),
 190 prod(a^select(x),b,c,d)         :=  select(prod(a,b,c,d) ^ x),
 191  (a^x) * select(b^y)            :=  select((a * b^(y-x)) ^x),
 192  (a^x) / select(b^y)            :=  select((b / b^(y-x)) ^ x),
 193 select(a^x) / (b^y)             :=  select((a / b^(y-x)) ^ x),
 194 select(x^a) ^ b                 :=  x ^ select(a * b),
 195  (x^a) ^ select(b)              :=  x ^ select(a * b),
 196 select(sqrt(a)) ^ b             :=  select(a ^ (b / 2)),
 197 sqrt(a) ^ select(b)             :=  select(a ^ (b / 2)),
 198 sqrt(select(a) ^ b)             :=  select(a ^ (b / 2)),
 199 sqrt(a ^ select(b))             :=  select(a ^ (b / 2)),
 200 sqrt(a) * select(sqrt(b))       :=  select(sqrt(a * b)),
 201 sqrt(a) / select(sqrt(b))       :=  select(sqrt(a / b)),
 202 select(sqrt(a)) / sqrt(b)       :=  select(sqrt(a / b)),
 203 prod(select(sqrt(a)),b,c,d)     :=  select(sqrt(prod(a,b,c,d))),
 204 exp(a) * select(exp(b))         :=  select(exp(a + b)),
 205 exp(a) / select(exp(b))         :=  select(exp(a - b)),
 206 select(exp(a)) / exp(b)         :=  select(exp(a - b)),
 207 prod(select(exp(a)),b,c,d)      :=  select(exp(sum(a,b,c,d))),
 208 select(exp(a)) ^ b              :=  select(exp(a * b)),
 209 exp(a) ^ select(b)              :=  select(exp(a * b)),
 210 ln(a) + select(ln(b))           :=  select(ln(a * b)),
 211 ln(a) - select(ln(b))           :=  select(ln(a / b)),
 212 select(ln(a)) - ln(b)           :=  select(ln(a / b)),
 213 sum(select(ln(a)),b,c,d)        :=  select(ln(prod(a,b,c,d))),
 214 b * select(ln(a))               :=  select(ln(a ^ b)),
 215 select(b) * ln(a)               :=  select(ln(a ^ b)),
 216 select(ln(a)) / ln(b)           :=  select(log(a, b)),
 217 ln(a) / select(ln(b))           :=  select(log(a, b)),
 218 select(ln(a)) / b               :=  select(ln(a ^ (1/b))),
 219 ln(a) / select(b)               :=  select(ln(a ^ (1/b))),
 220 log10(a) + select(log10(b))     :=  select(log10(a * b)),
 221 log10(a) - select(log10(b))     :=  select(log10(a / b)),
 222 select(log10(a)) - log10(b)     :=  select(log10(a / b)),
 223 sum(select(log10(a)),b,c,d)     :=  select(log10(prod(a,b,c,d))),
 224 b * select(log10(a))            :=  select(log10(a ^ b)),
 225 select(b) * log10(a)            :=  select(log10(a ^ b)),
 226 select(log10(a)) / log10(b)     :=  select(log(a, b)),
 227 log10(a) / select(log10(b))     :=  select(log(a, b)),
 228 select(log10(a)) / b            :=  select(log10(a ^ (1/b))),
 229 log10(a) / select(b)            :=  select(log10(a ^ (1/b))),
 230 log(a,x) + select(log(b,x))     :=  select(log(a * b,x)),
 231 log(a,x) - select(log(b,x))     :=  select(log(a / b,x)),
 232 select(log(a,x)) - log(b,x)     :=  select(log(a / b,x)),
 233 sum(select(log(a,x)),b,c,d)     :=  select(log(prod(a,b,c,d),x)),
 234 b * select(log(a,x))            :=  select(log(a ^ b,x)),
 235 select(b) * log(a,x)            :=  select(log(a ^ b,x)),
 236 select(log(a,x)) / log(b,x)     :=  select(log(a, b)),
 237 log(a,x) / select(log(b,x))     :=  select(log(a, b)),
 238 select(log(a,x)) / b            :=  select(log(a ^ (1/b),x)),
 239 log(a,x) / select(b)            :=  select(log(a ^ (1/b),x)),
 240 select(x && a) || (x && opt(b)) :=  x && (select(a) || b) ]"))
 241
 242 (defun calc-NegateRules ()
 243   "NegateRules"
 244   (calc-compile-rule-set
 245    "NegateRules" "[
 246 iterations(1),
 247 a + select(x)                   :=  a - select(-x),
 248 a - select(x)                   :=  a + select(-x),
 249 sum(select(x),b,c,d)            :=  -sum(select(-x),b,c,d),
 250 a * select(x)                   :=  -a * select(-x),
 251 a / select(x)                   :=  -a / select(-x),
 252 select(x) / a                   :=  -select(-x) / a,
 253 prod(select(x),b,c,d)           :=  (-1)^(d-c+1) * prod(select(-x),b,c,d),
 254 select(x) ^ n                   :=  select(-x) ^ a :: integer(n) :: n%2 = 0,
 255 select(x) ^ n                   :=  -(select(-x) ^ a) :: integer(n) :: n%2 = 1,
 256 select(x) ^ a                   :=  (-select(-x)) ^ a,
 257 a ^ select(x)                   :=  (1 / a)^select(-x),
 258 abs(select(x))                  :=  abs(select(-x)),
 259 i sqrt(select(x))               :=  -sqrt(select(-x)),
 260 sqrt(select(x))                 :=  i sqrt(select(-x)),
 261 re(select(x))                   :=  -re(select(-x)),
 262 im(select(x))                   :=  -im(select(-x)),
 263 conj(select(x))                 :=  -conj(select(-x)),
 264 trunc(select(x))                :=  -trunc(select(-x)),
 265 round(select(x))                :=  -round(select(-x)),
 266 floor(select(x))                :=  -ceil(select(-x)),
 267 ceil(select(x))                 :=  -floor(select(-x)),
 268 ftrunc(select(x))               :=  -ftrunc(select(-x)),
 269 fround(select(x))               :=  -fround(select(-x)),
 270 ffloor(select(x))               :=  -fceil(select(-x)),
 271 fceil(select(x))                :=  -ffloor(select(-x)),
 272 exp(select(x))                  :=  1 / exp(select(-x)),
 273 sin(select(x))                  :=  -sin(select(-x)),
 274 cos(select(x))                  :=  cos(select(-x)),
 275 tan(select(x))                  :=  -tan(select(-x)),
 276 sec(select(x))                  :=  sec(select(-x)),
 277 csc(select(x))                  :=  -csc(select(-x)),
 278 cot(select(x))                  :=  -cot(select(-x)),
 279 arcsin(select(x))               :=  -arcsin(select(-x)),
 280 arccos(select(x))               :=  4 arctan(1) - arccos(select(-x)),
 281 arctan(select(x))               :=  -arctan(select(-x)),
 282 sinh(select(x))                 :=  -sinh(select(-x)),
 283 cosh(select(x))                 :=  cosh(select(-x)),
 284 tanh(select(x))                 :=  -tanh(select(-x)),
 285 sech(select(x))                 :=  sech(select(-x)),
 286 csch(select(x))                 :=  -csch(select(-x)),
 287 coth(select(x))                 :=  -coth(select(-x)),
 288 arcsinh(select(x))              :=  -arcsinh(select(-x)),
 289 arctanh(select(x))              :=  -arctanh(select(-x)),
 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 select(x) <= a                  :=  select(-x) >= -a,
 295 select(x) >= a                  :=  select(-x) <= -a,
 296 a < select(x)                   :=  -a > select(-x),
 297 a > select(x)                   :=  -a < select(-x),
 298 a <= select(x)                  :=  -a >= select(-x),
 299 a >= select(x)                  :=  -a <= select(-x),
 300 select(x)                       :=  -select(-x) ]"))
 301
 302 (defun calc-InvertRules ()
 303   "InvertRules"
 304   (calc-compile-rule-set
 305    "InvertRules" "[
 306 iterations(1),
 307 a * select(x)                   :=  a / select(1/x),
 308 a / select(x)                   :=  a * select(1/x),
 309 select(x) / a                   :=  1 / (select(1/x) a),
 310 prod(select(x),b,c,d)           :=  1 / prod(select(1/x),b,c,d),
 311 abs(select(x))                  :=  1 / abs(select(1/x)),
 312 sqrt(select(x))                 :=  1 / sqrt(select(1/x)),
 313 ln(select(x))                   :=  -ln(select(1/x)),
 314 log10(select(x))                :=  -log10(select(1/x)),
 315 log(select(x), a)               :=  -log(select(1/x), a),
 316 log(a, select(x))               :=  -log(a, select(1/x)),
 317 arctan(select(x))               :=  simplify(2 arctan(1))-arctan(select(1/x)),
 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 select(x) <= a                  :=  select(1/x) >= 1/a,
 323 select(x) >= a                  :=  select(1/x) <= 1/a,
 324 a < select(x)                   :=  1/a > select(1/x),
 325 a > select(x)                   :=  1/a < select(1/x),
 326 a <= select(x)                  :=  1/a >= select(1/x),
 327 a >= select(x)                  :=  1/a <= select(1/x),
 328 select(x)                       :=  1 / select(1/x) ]"))
 329
 330
 331 (defun calc-FactorRules ()
 332   "FactorRules"
 333   (calc-compile-rule-set
 334    "FactorRules" "[
 335 thecoefs(x, [z, a+b, c]) := thefactors(x, [d x + d a/c, (c/d) x + (b/d)])
 336         :: z = a b/c :: let(d := pgcd(pcont(c), pcont(b))),
 337 thecoefs(x, [z, a, c]) := thefactors(x, [(r x + a/(2 r))^2])
 338         :: z = (a/2)^2/c :: let(r := esimplify(sqrt(c)))
 339         :: !matches(r, sqrt(rr)),
 340 thecoefs(x, [z, 0, c]) := thefactors(x, [rc x + rz, rc x - rz])
 341         :: negative(z)
 342         :: let(rz := esimplify(sqrt(-z))) :: !matches(rz, sqrt(rzz))
 343         :: let(rc := esimplify(sqrt(c))) :: !matches(rc, sqrt(rcc)),
 344 thecoefs(x, [z, 0, c]) := thefactors(x, [rz + rc x, rz - rc x])
 345         :: negative(c)
 346         :: let(rz := esimplify(sqrt(z))) :: !matches(rz, sqrt(rzz))
 347         :: let(rc := esimplify(sqrt(-c))) :: !matches(rc, sqrt(rcc))
 348  ]"))
 349 ;;(setq var-FactorRules 'calc-FactorRules)
 350
 351
 352 (defun calc-IntegAfterRules ()
 353   "IntegAfterRules"
 354   (calc-compile-rule-set
 355    "IntegAfterRules" "[
 356  opt(a) ln(x) + opt(b) ln(y) := 2 a esimplify(arctanh(x-1))
 357      :: a + b = 0 :: nrat(x + y) = 2 || nrat(x - y) = 2,
 358  a * (b + c) := a b + a c :: constant(a)
 359  ]"))
 360
 361 ;;(setq var-IntegAfterRules 'calc-IntegAfterRules)
 362
 363
 364 (defun calc-FitRules ()
 365   "FitRules"
 366   (calc-compile-rule-set
 367    "FitRules" "[
 368
 369 schedule(1,2,3,4),
 370 iterations(inf),
 371
 372 phase(1),
 373 e^x             :=  exp(x),
 374 x^y             :=  exp(y ln(x))  :: !istrue(constant(y)),
 375 x/y             :=  x fitinv(y),
 376 fitinv(x y)     :=  fitinv(x) fitinv(y),
 377 exp(a) exp(b)   :=  exp(a + b),
 378 a exp(b)        :=  exp(ln(a) + b)  :: !hasfitvars(a),
 379 fitinv(exp(a))  :=  exp(-a),
 380 ln(a b)         :=  ln(a) + ln(b),
 381 ln(fitinv(a))   :=  -ln(a),
 382 log10(a b)      :=  log10(a) + log10(b),
 383 log10(fitinv(a)) := -log10(a),
 384 log(a,b)        :=  ln(a)/ln(b),
 385 ln(exp(a))      :=  a,
 386 a*(b+c)         :=  a*b + a*c,
 387 (a+b)^n         :=  x  :: integer(n) :: n >= 2
 388                        :: let(x, expandpow(a+b,n))
 389                        :: quote(matches(x,y+z)),
 390
 391 phase(1,2),
 392 fitmodel(y = x)   :=  fitmodel(0, y - x),
 393 fitmodel(y, x+c)  :=  fitmodel(y-c, x)  :: !hasfitparams(c),
 394 fitmodel(y, x c)  :=  fitmodel(y/c, x)  :: !hasfitparams(c),
 395 fitmodel(y, x/(c opt(d)))  :=  fitmodel(y c, x/d)  :: !hasfitparams(c),
 396 fitmodel(y, apply(f,[x]))  :=  fitmodel(yy, x)
 397                                :: hasfitparams(x)
 398                                :: let(FTemp() = yy,
 399                                       solve(apply(f,[FTemp()]) = y,
 400                                             FTemp())),
 401 fitmodel(y, apply(f,[x,c]))  :=  fitmodel(yy, x)
 402                                  :: !hasfitparams(c)
 403                                  :: let(FTemp() = yy,
 404                                         solve(apply(f,[FTemp(),c]) = y,
 405                                               FTemp())),
 406 fitmodel(y, apply(f,[c,x]))  :=  fitmodel(yy, x)
 407                                  :: !hasfitparams(c)
 408                                  :: let(FTemp() = yy,
 409                                         solve(apply(f,[c,FTemp()]) = y,
 410                                               FTemp())),
 411
 412 phase(2,3),
 413 fitmodel(y, x)              :=  fitsystem(y, [], [], fitpart(1,1,x)),
 414 fitpart(a,b,plain(x + y))   :=  fitpart(a,b,x) + fitpart(a,b,y),
 415 fitpart(a,b,plain(x - y))   :=  fitpart(a,b,x) + fitpart(-a,b,y),
 416 fitpart(a,b,plain(-x))      :=  fitpart(-a,b,x),
 417 fitpart(a,b,x opt(c))       :=  fitpart(a,x b,c)  :: !hasfitvars(x),
 418 fitpart(a,x opt(b),c)       :=  fitpart(x a,b,c)  :: !hasfitparams(x),
 419 fitpart(a,x y + x opt(z),c) :=  fitpart(a,x*(y+z),c),
 420 fitpart(a,b,c)              :=  fitpart2(a,b,c),
 421
 422 phase(3),
 423 fitpart2(a1,b1,x) + fitpart2(a2,b2,x)  :=  fitpart(1, a1 b1 + a2 b2, x),
 424 fitpart2(a1,x,c1) + fitpart2(a2,x,c2)  :=  fitpart2(1, x, a1 c1 + a2 c2),
 425
 426 phase(4),
 427 fitinv(x)       :=  1 / x,
 428 exp(x + ln(y))  :=  y exp(x),
 429 exp(x ln(y))    :=  y^x,
 430 ln(x) + ln(y)   :=  ln(x y),
 431 ln(x) - ln(y)   :=  ln(x/y),
 432 x*y + x*z       :=  x*(y+z),
 433 fitsystem(y, xv, pv, fitpart2(a,fitparam(b),c) + opt(d))
 434                 :=  fitsystem(y, rcons(xv, a c),
 435                               rcons(pv, fitdummy(b) = fitparam(b)), d)
 436                     :: b = vlen(pv)+1,
 437 fitsystem(y, xv, pv, fitpart2(a,b,c) + opt(d))
 438                 :=  fitsystem(y, rcons(xv, a c),
 439                               rcons(pv, fitdummy(vlen(pv)+1) = b), d),
 440 fitsystem(y, xv, pv, 0)  :=  fitsystem(y, xv, cons(fvh,fvt))
 441                              :: !hasfitparams(xv)
 442                              :: let(cons(fvh,fvt),
 443                                     solve(pv, table(fitparam(j), j, 1,
 444                                                     hasfitparams(pv)))),
 445 fitparam(n) = x  :=  x ]"))
 446
 447 (provide 'calc-rules)
 448
 449 ;;; arch-tag: 0ed54a52-38f3-4ed7-9ca7-b8ecf8f2febe
 450 ;;; calc-rules.el ends here