[bpt/emacs.git] / lisp / calc / calc-rules.el

;;; calc-rules.el --- rules for simplifying algebraic expressions in Calc

;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
;;   2005, 2006, 2007, 2008 Free Software Foundation, Inc.

;; Author: David Gillespie <daveg@synaptics.com>
;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>

;; This file is part of GNU Emacs.

;; GNU Emacs is free software; you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation; either version 3, or (at your option)
;; any later version.

;; GNU Emacs is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
;; GNU General Public License for more details.

;; You should have received a copy of the GNU General Public License
;; along with GNU Emacs; see the file COPYING.  If not, write to the
;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
;; Boston, MA 02110-1301, USA.

;;; Commentary:

;;; Code:

;; This file is autoloaded from calc-ext.el.

(require 'calc-ext)
(require 'calc-macs)

(defun calc-compile-rule-set (name rules)
  (prog2
   (message "Preparing rule set %s..." name)
   (math-read-plain-expr rules t)
   (message "Preparing rule set %s...done" name)))

(defun calc-CommuteRules ()
  "CommuteRules"
  (calc-compile-rule-set
   "CommuteRules" "[
iterations(1),
select(plain(a + b))		:=  select(plain(b + a)),
select(plain(a - b))		:=  select(plain((-b) + a)),
select(plain((1/a) * b))	:=  select(b / a),
select(plain(a * b))		:=  select(b * a),
select((1/a) / b)		:=  select((1/b) / a),
select(a / b)			:=  select((1/b) * a),
select((a^b) ^ c)		:=  select((a^c) ^ b),
select(log(a, b))		:=  select(1 / log(b, a)),
select(plain(a && b))		:=  select(b && a),
select(plain(a || b))		:=  select(b || a),
select(plain(a = b))		:=  select(b = a),
select(plain(a != b))		:=  select(b != a),
select(a < b)			:=  select(b > a),
select(a > b)			:=  select(b < a),
select(a <= b)			:=  select(b >= a),
select(a >= b)			:=  select(b <= a) ]"))

(defun calc-JumpRules ()
  "JumpRules"
  (calc-compile-rule-set
   "JumpRules" "[
iterations(1),
plain(select(x) = y)		:=  0 = select(-x) + y,
plain(a + select(x) = y)	:=  a = select(-x) + y,
plain(a - select(x) = y)	:=  a = select(x) + y,
plain(select(x) + a = y)	:=  a = select(-x) + y,
plain(a * select(x) = y)	:=  a = y / select(x),
plain(a / select(x) = y)	:=  a = select(x) * y,
plain(select(x) / a = y)	:=  1/a = y / select(x),
plain(a ^ select(2) = y)	:=  a = select(sqrt(y)),
plain(a ^ select(x) = y)	:=  a = y ^ select(1/x),
plain(select(x) ^ a = y)	:=  a = log(y, select(x)),
plain(log(a, select(x)) = y)	:=  a = select(x) ^ y,
plain(log(select(x), a) = y)	:=  a = select(x) ^ (1/y),
plain(y = select(x))		:=  y - select(x) = 0,
plain(y = a + select(x))	:=  y - select(x) = a,
plain(y = a - select(x))	:=  y + select(x) = a,
plain(y = select(x) + a)	:=  y - select(x) = a,
plain(y = a * select(x))	:=  y / select(x) = a,
plain(y = a / select(x))	:=  y * select(x) = a,
plain(y = select(x) / a)	:=  y / select(x) = 1/a,
plain(y = a ^ select(2))	:=  select(sqrt(y)) = a,
plain(y = a ^ select(x))	:=  y ^ select(1/x) = a,
plain(y = select(x) ^ a)	:=  log(y, select(x)) = a,
plain(y = log(a, select(x)))	:=  select(x) ^ y = a,
plain(y = log(select(x), a))	:=  select(x) ^ (1/y) = a ]"))

(defun calc-DistribRules ()
  "DistribRules"
  (calc-compile-rule-set
   "DistribRules" "[
iterations(1),
x * select(a + b)		:=  x*select(a) + x*b,
x * select(sum(a,b,c,d))	:=  sum(x*select(a),b,c,d),
x / select(a + b)		:=  1 / (select(a)/x + b/x),
select(a + b) / x		:=  select(a)/x + b/x,
sum(select(a),b,c,d) / x	:=  sum(select(a)/x,b,c,d),
x ^ select(a + b)		:=  x^select(a) * x^b,
x ^ select(sum(a,b,c,d))	:=  prod(x^select(a),b,c,d),
x ^ select(a * b)		:=  (x^a)^select(b),
x ^ select(a / b)		:=  (x^a)^select(1/b),
select(a + b) ^ n		:=  select(x)
				    :: integer(n) :: n >= 2
				    :: let(x, expandpow(a+b,n))
				    :: quote(matches(x,y+z)),
select(a + b) ^ x		:=  a*select(a+b)^(x-1) + b*select(a+b)^(x-1),
select(a * b) ^ x		:=  a^x * select(b)^x,
select(prod(a,b,c,d)) ^ x	:=  prod(select(a)^x,b,c,d),
select(a / b) ^ x		:=  select(a)^x / b^x,
select(- a) ^ x			:=  (-1)^x * select(a)^x,
plain(-select(a + b))		:=  select(-a) - b,
plain(-select(sum(a,b,c,d)))    :=  sum(select(-a),b,c,d),
plain(-select(a * b))	        :=  select(-a) * b,
plain(-select(a / b))	        :=  select(-a) / b,
sqrt(select(a * b))		:=  sqrt(select(a)) * sqrt(b),
sqrt(select(prod(a,b,c,d)))	:=  prod(sqrt(select(a)),b,c,d),
sqrt(select(a / b))		:=  sqrt(select(a)) / sqrt(b),
sqrt(select(- a))		:=  sqrt(-1) sqrt(select(a)),
exp(select(a + b))		:=  exp(select(a)) / exp(-b) :: negative(b),
exp(select(a + b))		:=  exp(select(a)) * exp(b),
exp(select(sum(a,b,c,d)))	:=  prod(exp(select(a)),b,c,d),
exp(select(a * b))		:=  exp(select(a)) ^ b :: constant(b),
exp(select(a * b))		:=  exp(select(a)) ^ b,
exp(select(a / b))		:=  exp(select(a)) ^ (1/b),
ln(select(a * b))		:=  ln(select(a)) + ln(b),
ln(select(prod(a,b,c,d)))	:=  sum(ln(select(a)),b,c,d),
ln(select(a / b))		:=  ln(select(a)) - ln(b),
ln(select(a ^ b))		:=  ln(select(a)) * b,
log10(select(a * b))		:=  log10(select(a)) + log10(b),
log10(select(prod(a,b,c,d)))	:=  sum(log10(select(a)),b,c,d),
log10(select(a / b))		:=  log10(select(a)) - log10(b),
log10(select(a ^ b))		:=  log10(select(a)) * b,
log(select(a * b), x)		:=  log(select(a), x) + log(b,x),
log(select(prod(a,b,c,d)),x)	:=  sum(log(select(a),x),b,c,d),
log(select(a / b), x)		:=  log(select(a), x) - log(b,x),
log(select(a ^ b), x)		:=  log(select(a), x) * b,
log(a, select(b))		:=  ln(a) / select(ln(b)),
sin(select(a + b))		:=  sin(select(a)) cos(b) + cos(a) sin(b),
sin(select(2 a))		:=  2 sin(select(a)) cos(a),
sin(select(n a))		:=  2sin((n-1) select(a)) cos(a) - sin((n-2) a)
				    :: integer(n) :: n > 2,
cos(select(a + b))		:=  cos(select(a)) cos(b) - sin(a) sin(b),
cos(select(2 a))		:=  2 cos(select(a))^2 - 1,
cos(select(n a))		:=  2cos((n-1) select(a)) cos(a) - cos((n-2) a)
				    :: integer(n) :: n > 2,
tan(select(a + b))		:=  (tan(select(a)) + tan(b)) /
				    (1 - tan(a) tan(b)),
tan(select(2 a))		:=  2 tan(select(a)) / (1 - tan(a)^2),
tan(select(n a))		:=  (tan((n-1) select(a)) + tan(a)) /
				    (1 - tan((n-1) a) tan(a))
				    :: integer(n) :: n > 2,
cot(select(a + b))		:=  (cot(select(a)) cot(b) - 1) /
				    (cot(a) + cot(b)),
sinh(select(a + b))		:=  sinh(select(a)) cosh(b) + cosh(a) sinh(b),
cosh(select(a + b))		:=  cosh(select(a)) cosh(b) + sinh(a) sinh(b),
tanh(select(a + b))		:=  (tanh(select(a)) + tanh(b)) /
				    (1 + tanh(a) tanh(b)),
coth(select(a + b))		:=  (coth(select(a)) coth(b) + 1) /
				    (coth(a) + coth(b)),
x && select(a || b)		:=  (x && select(a)) || (x && b),
select(a || b) && x		:=  (select(a) && x) || (b && x),
! select(a && b)		:=  (!a) || (!b),
! select(a || b)		:=  (!a) && (!b) ]"))

(defun calc-MergeRules ()
  "MergeRules"
  (calc-compile-rule-set
   "MergeRules" "[
iterations(1),
 (x*opt(a)) + select(x*b)	:=  x * (a + select(b)),
 (x*opt(a)) - select(x*b)	:=  x * (a - select(b)),
sum(select(x)*a,b,c,d)		:=  x * sum(select(a),b,c,d),
 (a/x) + select(b/x)		:=  (a + select(b)) / x,
 (a/x) - select(b/x)		:=  (a - select(b)) / x,
sum(a/select(x),b,c,d)		:=  sum(select(a),b,c,d) / x,
 (a/opt(b)) + select(c/d)	:=  ((select(a)*d) + (b*c)) / (b*d),
 (a/opt(b)) - select(c/d)	:=  ((select(a)*d) - (b*c)) / (b*d),
 (x^opt(a)) * select(x^b)	:=  x ^ (a + select(b)),
 (x^opt(a)) / select(x^b)	:=  x ^ (a - select(b)),
select(x^a) / (x^opt(b))	:=  x ^ (select(a) - b),
prod(select(x)^a,b,c,d)		:=  x ^ sum(select(a),b,c,d),
select(x^a) / (x^opt(b))	:=  x ^ (select(a) - b),
 (a^x) * select(b^x)		:=  select((a * b) ^x),
 (a^x) / select(b^x)		:=  select((b / b) ^ x),
select(a^x) / (b^x)		:=  select((a / b) ^ x),
prod(a^select(x),b,c,d)		:=  select(prod(a,b,c,d) ^ x),
 (a^x) * select(b^y)		:=  select((a * b^(y-x)) ^x),
 (a^x) / select(b^y)		:=  select((b / b^(y-x)) ^ x),
select(a^x) / (b^y)		:=  select((a / b^(y-x)) ^ x),
select(x^a) ^ b			:=  x ^ select(a * b),
 (x^a) ^ select(b)		:=  x ^ select(a * b),
select(sqrt(a)) ^ b		:=  select(a ^ (b / 2)),
sqrt(a) ^ select(b)		:=  select(a ^ (b / 2)),
sqrt(select(a) ^ b)		:=  select(a ^ (b / 2)),
sqrt(a ^ select(b))		:=  select(a ^ (b / 2)),
sqrt(a) * select(sqrt(b))	:=  select(sqrt(a * b)),
sqrt(a) / select(sqrt(b))	:=  select(sqrt(a / b)),
select(sqrt(a)) / sqrt(b)	:=  select(sqrt(a / b)),
prod(select(sqrt(a)),b,c,d)	:=  select(sqrt(prod(a,b,c,d))),
exp(a) * select(exp(b))		:=  select(exp(a + b)),
exp(a) / select(exp(b))		:=  select(exp(a - b)),
select(exp(a)) / exp(b)		:=  select(exp(a - b)),
prod(select(exp(a)),b,c,d)	:=  select(exp(sum(a,b,c,d))),
select(exp(a)) ^ b		:=  select(exp(a * b)),
exp(a) ^ select(b)		:=  select(exp(a * b)),
ln(a) + select(ln(b))		:=  select(ln(a * b)),
ln(a) - select(ln(b))		:=  select(ln(a / b)),
select(ln(a)) - ln(b)		:=  select(ln(a / b)),
sum(select(ln(a)),b,c,d)	:=  select(ln(prod(a,b,c,d))),
b * select(ln(a))		:=  select(ln(a ^ b)),
select(b) * ln(a)		:=  select(ln(a ^ b)),
select(ln(a)) / ln(b)		:=  select(log(a, b)),
ln(a) / select(ln(b))		:=  select(log(a, b)),
select(ln(a)) / b		:=  select(ln(a ^ (1/b))),
ln(a) / select(b)		:=  select(ln(a ^ (1/b))),
log10(a) + select(log10(b))	:=  select(log10(a * b)),
log10(a) - select(log10(b))	:=  select(log10(a / b)),
select(log10(a)) - log10(b)	:=  select(log10(a / b)),
sum(select(log10(a)),b,c,d)	:=  select(log10(prod(a,b,c,d))),
b * select(log10(a))		:=  select(log10(a ^ b)),
select(b) * log10(a)		:=  select(log10(a ^ b)),
select(log10(a)) / log10(b)	:=  select(log(a, b)),
log10(a) / select(log10(b))	:=  select(log(a, b)),
select(log10(a)) / b		:=  select(log10(a ^ (1/b))),
log10(a) / select(b)		:=  select(log10(a ^ (1/b))),
log(a,x) + select(log(b,x))	:=  select(log(a * b,x)),
log(a,x) - select(log(b,x))	:=  select(log(a / b,x)),
select(log(a,x)) - log(b,x)	:=  select(log(a / b,x)),
sum(select(log(a,x)),b,c,d)	:=  select(log(prod(a,b,c,d),x)),
b * select(log(a,x))		:=  select(log(a ^ b,x)),
select(b) * log(a,x)		:=  select(log(a ^ b,x)),
select(log(a,x)) / log(b,x)	:=  select(log(a, b)),
log(a,x) / select(log(b,x))	:=  select(log(a, b)),
select(log(a,x)) / b		:=  select(log(a ^ (1/b),x)),
log(a,x) / select(b)		:=  select(log(a ^ (1/b),x)),
select(x && a) || (x && opt(b)) :=  x && (select(a) || b) ]"))

(defun calc-NegateRules ()
  "NegateRules"
  (calc-compile-rule-set
   "NegateRules" "[
iterations(1),
a + select(x)			:=  a - select(-x),
a - select(x)			:=  a + select(-x),
sum(select(x),b,c,d)		:=  -sum(select(-x),b,c,d),
a * select(x)			:=  -a * select(-x),
a / select(x)			:=  -a / select(-x),
select(x) / a			:=  -select(-x) / a,
prod(select(x),b,c,d)		:=  (-1)^(d-c+1) * prod(select(-x),b,c,d),
select(x) ^ n			:=  select(-x) ^ a :: integer(n) :: n%2 = 0,
select(x) ^ n			:=  -(select(-x) ^ a) :: integer(n) :: n%2 = 1,
select(x) ^ a			:=  (-select(-x)) ^ a,
a ^ select(x)			:=  (1 / a)^select(-x),
abs(select(x))			:=  abs(select(-x)),
i sqrt(select(x))		:=  -sqrt(select(-x)),
sqrt(select(x))			:=  i sqrt(select(-x)),
re(select(x))			:=  -re(select(-x)),
im(select(x))			:=  -im(select(-x)),
conj(select(x))			:=  -conj(select(-x)),
trunc(select(x))		:=  -trunc(select(-x)),
round(select(x))		:=  -round(select(-x)),
floor(select(x))		:=  -ceil(select(-x)),
ceil(select(x))			:=  -floor(select(-x)),
ftrunc(select(x))		:=  -ftrunc(select(-x)),
fround(select(x))		:=  -fround(select(-x)),
ffloor(select(x))		:=  -fceil(select(-x)),
fceil(select(x))		:=  -ffloor(select(-x)),
exp(select(x))			:=  1 / exp(select(-x)),
sin(select(x))			:=  -sin(select(-x)),
cos(select(x))			:=  cos(select(-x)),
tan(select(x))			:=  -tan(select(-x)),
sec(select(x))			:=  sec(select(-x)),
csc(select(x))			:=  -csc(select(-x)),
cot(select(x))			:=  -cot(select(-x)),
arcsin(select(x))		:=  -arcsin(select(-x)),
arccos(select(x))		:=  4 arctan(1) - arccos(select(-x)),
arctan(select(x))		:=  -arctan(select(-x)),
sinh(select(x))			:=  -sinh(select(-x)),
cosh(select(x))			:=  cosh(select(-x)),
tanh(select(x))			:=  -tanh(select(-x)),
sech(select(x))			:=  sech(select(-x)),
csch(select(x))			:=  -csch(select(-x)),
coth(select(x))			:=  -coth(select(-x)),
arcsinh(select(x))		:=  -arcsinh(select(-x)),
arctanh(select(x))		:=  -arctanh(select(-x)),
select(x) = a			:=  select(-x) = -a,
select(x) != a			:=  select(-x) != -a,
select(x) < a			:=  select(-x) > -a,
select(x) > a			:=  select(-x) < -a,
select(x) <= a			:=  select(-x) >= -a,
select(x) >= a			:=  select(-x) <= -a,
a < select(x)			:=  -a > select(-x),
a > select(x)			:=  -a < select(-x),
a <= select(x)			:=  -a >= select(-x),
a >= select(x)			:=  -a <= select(-x),
select(x)			:=  -select(-x) ]"))

(defun calc-InvertRules ()
  "InvertRules"
  (calc-compile-rule-set
   "InvertRules" "[
iterations(1),
a * select(x)			:=  a / select(1/x),
a / select(x)			:=  a * select(1/x),
select(x) / a			:=  1 / (select(1/x) a),
prod(select(x),b,c,d)		:=  1 / prod(select(1/x),b,c,d),
abs(select(x))			:=  1 / abs(select(1/x)),
sqrt(select(x))			:=  1 / sqrt(select(1/x)),
ln(select(x))			:=  -ln(select(1/x)),
log10(select(x))		:=  -log10(select(1/x)),
log(select(x), a)		:=  -log(select(1/x), a),
log(a, select(x))		:=  -log(a, select(1/x)),
arctan(select(x))               :=  simplify(2 arctan(1))-arctan(select(1/x)),
select(x) = a			:=  select(1/x) = 1/a,
select(x) != a			:=  select(1/x) != 1/a,
select(x) < a			:=  select(1/x) > 1/a,
select(x) > a			:=  select(1/x) < 1/a,
select(x) <= a			:=  select(1/x) >= 1/a,
select(x) >= a			:=  select(1/x) <= 1/a,
a < select(x)			:=  1/a > select(1/x),
a > select(x)			:=  1/a < select(1/x),
a <= select(x)			:=  1/a >= select(1/x),
a >= select(x)			:=  1/a <= select(1/x),
select(x)			:=  1 / select(1/x) ]"))


(defun calc-FactorRules ()
  "FactorRules"
  (calc-compile-rule-set
   "FactorRules" "[
thecoefs(x, [z, a+b, c]) := thefactors(x, [d x + d a/c, (c/d) x + (b/d)])
        :: z = a b/c :: let(d := pgcd(pcont(c), pcont(b))),
thecoefs(x, [z, a, c]) := thefactors(x, [(r x + a/(2 r))^2])
        :: z = (a/2)^2/c :: let(r := esimplify(sqrt(c)))
        :: !matches(r, sqrt(rr)),
thecoefs(x, [z, 0, c]) := thefactors(x, [rc x + rz, rc x - rz])
        :: negative(z)
        :: let(rz := esimplify(sqrt(-z))) :: !matches(rz, sqrt(rzz))
        :: let(rc := esimplify(sqrt(c))) :: !matches(rc, sqrt(rcc)),
thecoefs(x, [z, 0, c]) := thefactors(x, [rz + rc x, rz - rc x])
        :: negative(c)
        :: let(rz := esimplify(sqrt(z))) :: !matches(rz, sqrt(rzz))
        :: let(rc := esimplify(sqrt(-c))) :: !matches(rc, sqrt(rcc))
 ]"))
;;(setq var-FactorRules 'calc-FactorRules)


(defun calc-IntegAfterRules ()
  "IntegAfterRules"
  (calc-compile-rule-set
   "IntegAfterRules" "[
 opt(a) ln(x) + opt(b) ln(y) := 2 a esimplify(arctanh(x-1))
     :: a + b = 0 :: nrat(x + y) = 2 || nrat(x - y) = 2,
 a * (b + c) := a b + a c :: constant(a)
 ]"))

;;(setq var-IntegAfterRules 'calc-IntegAfterRules)


(defun calc-FitRules ()
  "FitRules"
  (calc-compile-rule-set
   "FitRules" "[

schedule(1,2,3,4),
iterations(inf),

phase(1),
e^x  		:=  exp(x),
x^y		:=  exp(y ln(x))  :: !istrue(constant(y)),
x/y		:=  x fitinv(y),
fitinv(x y)	:=  fitinv(x) fitinv(y),
exp(a) exp(b)	:=  exp(a + b),
a exp(b)	:=  exp(ln(a) + b)  :: !hasfitvars(a),
fitinv(exp(a))  :=  exp(-a),
ln(a b)		:=  ln(a) + ln(b),
ln(fitinv(a))	:=  -ln(a),
log10(a b)	:=  log10(a) + log10(b),
log10(fitinv(a)) := -log10(a),
log(a,b)	:=  ln(a)/ln(b),
ln(exp(a))	:=  a,
a*(b+c)		:=  a*b + a*c,
(a+b)^n		:=  x  :: integer(n) :: n >= 2
		       :: let(x, expandpow(a+b,n))
		       :: quote(matches(x,y+z)),

phase(1,2),
fitmodel(y = x)   :=  fitmodel(0, y - x),
fitmodel(y, x+c)  :=  fitmodel(y-c, x)  :: !hasfitparams(c),
fitmodel(y, x c)  :=  fitmodel(y/c, x)  :: !hasfitparams(c),
fitmodel(y, x/(c opt(d)))  :=  fitmodel(y c, x/d)  :: !hasfitparams(c),
fitmodel(y, apply(f,[x]))  :=  fitmodel(yy, x)
			       :: hasfitparams(x)
			       :: let(FTemp() = yy,
			              solve(apply(f,[FTemp()]) = y,
					    FTemp())),
fitmodel(y, apply(f,[x,c]))  :=  fitmodel(yy, x)
				 :: !hasfitparams(c)
				 :: let(FTemp() = yy,
				        solve(apply(f,[FTemp(),c]) = y,
					      FTemp())),
fitmodel(y, apply(f,[c,x]))  :=  fitmodel(yy, x)
				 :: !hasfitparams(c)
				 :: let(FTemp() = yy,
				        solve(apply(f,[c,FTemp()]) = y,
					      FTemp())),

phase(2,3),
fitmodel(y, x)              :=  fitsystem(y, [], [], fitpart(1,1,x)),
fitpart(a,b,plain(x + y))   :=  fitpart(a,b,x) + fitpart(a,b,y),
fitpart(a,b,plain(x - y))   :=  fitpart(a,b,x) + fitpart(-a,b,y),
fitpart(a,b,plain(-x))	    :=  fitpart(-a,b,x),
fitpart(a,b,x opt(c))	    :=  fitpart(a,x b,c)  :: !hasfitvars(x),
fitpart(a,x opt(b),c)	    :=  fitpart(x a,b,c)  :: !hasfitparams(x),
fitpart(a,x y + x opt(z),c) :=	fitpart(a,x*(y+z),c),
fitpart(a,b,c)		    :=  fitpart2(a,b,c),

phase(3),
fitpart2(a1,b1,x) + fitpart2(a2,b2,x)  :=  fitpart(1, a1 b1 + a2 b2, x),
fitpart2(a1,x,c1) + fitpart2(a2,x,c2)  :=  fitpart2(1, x, a1 c1 + a2 c2),

phase(4),
fitinv(x)  	:=  1 / x,
exp(x + ln(y))  :=  y exp(x),
exp(x ln(y))	:=  y^x,
ln(x) + ln(y)	:=  ln(x y),
ln(x) - ln(y)	:=  ln(x/y),
x*y + x*z	:=  x*(y+z),
fitsystem(y, xv, pv, fitpart2(a,fitparam(b),c) + opt(d))
		:=  fitsystem(y, rcons(xv, a c),
      		              rcons(pv, fitdummy(b) = fitparam(b)), d)
		    :: b = vlen(pv)+1,
fitsystem(y, xv, pv, fitpart2(a,b,c) + opt(d))
		:=  fitsystem(y, rcons(xv, a c),
			      rcons(pv, fitdummy(vlen(pv)+1) = b), d),
fitsystem(y, xv, pv, 0)  :=  fitsystem(y, xv, cons(fvh,fvt))
			     :: !hasfitparams(xv)
			     :: let(cons(fvh,fvt),
				    solve(pv, table(fitparam(j), j, 1,
						    hasfitparams(pv)))),
fitparam(n) = x  :=  x ]"))

(provide 'calc-rules)

;; arch-tag: 0ed54a52-38f3-4ed7-9ca7-b8ecf8f2febe
;;; calc-rules.el ends here
Commit	Line	Data
c567a7db	1	;;; calc-rules.el --- rules for simplifying algebraic expressions in Calc
3132f345	2
58ba2f8f	3	;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
8b72699e	4	;; 2005, 2006, 2007, 2008 Free Software Foundation, Inc.
3132f345 CW	5
3132f345 CW	6	;; Author: David Gillespie <daveg@synaptics.com>
e8fff8ed	7	;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
136211a9 EZ	8
	9	;; This file is part of GNU Emacs.
	10
7c671b23 GM	11	;; GNU Emacs is free software; you can redistribute it and/or modify
7c671b23 GM	12	;; it under the terms of the GNU General Public License as published by
075969b4	13	;; the Free Software Foundation; either version 3, or (at your option)
7c671b23 GM	14	;; any later version.
7c671b23 GM	15
136211a9	16	;; GNU Emacs is distributed in the hope that it will be useful,
7c671b23 GM	17	;; but WITHOUT ANY WARRANTY; without even the implied warranty of
	18	;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
	19	;; GNU General Public License for more details.
	20
	21	;; You should have received a copy of the GNU General Public License
	22	;; along with GNU Emacs; see the file COPYING. If not, write to the
	23	;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
	24	;; Boston, MA 02110-1301, USA.
136211a9	25
3132f345	26	;;; Commentary:
136211a9	27
3132f345	28	;;; Code:
136211a9 EZ	29
136211a9 EZ	30	;; This file is autoloaded from calc-ext.el.
136211a9	31
51b5c91c	32	(require 'calc-ext)
136211a9 EZ	33	(require 'calc-macs)
136211a9 EZ	34
136211a9 EZ	35	(defun calc-compile-rule-set (name rules)
	36	(prog2
	37	(message "Preparing rule set %s..." name)
	38	(math-read-plain-expr rules t)
bf77c646	39	(message "Preparing rule set %s...done" name)))
136211a9 EZ	40
	41	(defun calc-CommuteRules ()
	42	"CommuteRules"
	43	(calc-compile-rule-set
	44	"CommuteRules" "[
	45	iterations(1),
	46	select(plain(a + b)) := select(plain(b + a)),
	47	select(plain(a - b)) := select(plain((-b) + a)),
	48	select(plain((1/a) * b)) := select(b / a),
	49	select(plain(a * b)) := select(b * a),
	50	select((1/a) / b) := select((1/b) / a),
	51	select(a / b) := select((1/b) * a),
	52	select((a^b) ^ c) := select((a^c) ^ b),
	53	select(log(a, b)) := select(1 / log(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(plain(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),
bf77c646	61	select(a >= b) := select(b <= a) ]"))
136211a9 EZ	62
	63	(defun calc-JumpRules ()
	64	"JumpRules"
	65	(calc-compile-rule-set
	66	"JumpRules" "[
	67	iterations(1),
	68	plain(select(x) = y) := 0 = select(-x) + y,
	69	plain(a + select(x) = y) := a = select(-x) + y,
	70	plain(a - select(x) = y) := a = select(x) + y,
	71	plain(select(x) + a = y) := a = select(-x) + y,
	72	plain(a * select(x) = y) := a = y / select(x),
	73	plain(a / select(x) = y) := a = select(x) * y,
	74	plain(select(x) / a = y) := 1/a = y / select(x),
	75	plain(a ^ select(2) = y) := a = select(sqrt(y)),
	76	plain(a ^ select(x) = y) := a = y ^ select(1/x),
	77	plain(select(x) ^ a = y) := a = log(y, select(x)),
	78	plain(log(a, select(x)) = y) := a = select(x) ^ y,
	79	plain(log(select(x), a) = y) := a = select(x) ^ (1/y),
	80	plain(y = select(x)) := y - select(x) = 0,
	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) = a,
	84	plain(y = a * select(x)) := y / select(x) = a,
	85	plain(y = a / select(x)) := y * select(x) = a,
	86	plain(y = select(x) / a) := y / select(x) = 1/a,
	87	plain(y = a ^ select(2)) := select(sqrt(y)) = a,
	88	plain(y = a ^ select(x)) := y ^ select(1/x) = a,
	89	plain(y = select(x) ^ a) := log(y, select(x)) = a,
	90	plain(y = log(a, select(x))) := select(x) ^ y = a,
bf77c646	91	plain(y = log(select(x), a)) := select(x) ^ (1/y) = a ]"))
136211a9 EZ	92
	93	(defun calc-DistribRules ()
	94	"DistribRules"
	95	(calc-compile-rule-set
	96	"DistribRules" "[
	97	iterations(1),
	98	x * select(a + b) := xselect(a) + xb,
	99	x * select(sum(a,b,c,d)) := sum(x*select(a),b,c,d),
	100	x / select(a + b) := 1 / (select(a)/x + b/x),
	101	select(a + b) / x := select(a)/x + b/x,
	102	sum(select(a),b,c,d) / x := sum(select(a)/x,b,c,d),
	103	x ^ select(a + b) := x^select(a) * x^b,
	104	x ^ select(sum(a,b,c,d)) := prod(x^select(a),b,c,d),
	105	x ^ select(a * b) := (x^a)^select(b),
	106	x ^ select(a / b) := (x^a)^select(1/b),
	107	select(a + b) ^ n := select(x)
	108	:: integer(n) :: n >= 2
	109	:: let(x, expandpow(a+b,n))
	110	:: quote(matches(x,y+z)),
	111	select(a + b) ^ x := aselect(a+b)^(x-1) + bselect(a+b)^(x-1),
	112	select(a * b) ^ x := a^x * select(b)^x,
	113	select(prod(a,b,c,d)) ^ x := prod(select(a)^x,b,c,d),
	114	select(a / b) ^ x := select(a)^x / b^x,
	115	select(- a) ^ x := (-1)^x * select(a)^x,
	116	plain(-select(a + b)) := select(-a) - b,
	117	plain(-select(sum(a,b,c,d))) := sum(select(-a),b,c,d),
	118	plain(-select(a * b)) := select(-a) * b,
	119	plain(-select(a / b)) := select(-a) / b,
	120	sqrt(select(a * b)) := sqrt(select(a)) * sqrt(b),
	121	sqrt(select(prod(a,b,c,d))) := prod(sqrt(select(a)),b,c,d),
	122	sqrt(select(a / b)) := sqrt(select(a)) / sqrt(b),
	123	sqrt(select(- a)) := sqrt(-1) sqrt(select(a)),
	124	exp(select(a + b)) := exp(select(a)) / exp(-b) :: negative(b),
	125	exp(select(a + b)) := exp(select(a)) * exp(b),
	126	exp(select(sum(a,b,c,d))) := prod(exp(select(a)),b,c,d),
	127	exp(select(a * b)) := exp(select(a)) ^ b :: constant(b),
	128	exp(select(a * b)) := exp(select(a)) ^ b,
	129	exp(select(a / b)) := exp(select(a)) ^ (1/b),
	130	ln(select(a * b)) := ln(select(a)) + ln(b),
	131	ln(select(prod(a,b,c,d))) := sum(ln(select(a)),b,c,d),
	132	ln(select(a / b)) := ln(select(a)) - ln(b),
	133	ln(select(a ^ b)) := ln(select(a)) * b,
	134	log10(select(a * b)) := log10(select(a)) + log10(b),
	135	log10(select(prod(a,b,c,d))) := sum(log10(select(a)),b,c,d),
	136	log10(select(a / b)) := log10(select(a)) - log10(b),
	137	log10(select(a ^ b)) := log10(select(a)) * b,
	138	log(select(a * b), x) := log(select(a), x) + log(b,x),
	139	log(select(prod(a,b,c,d)),x) := sum(log(select(a),x),b,c,d),
	140	log(select(a / b), x) := log(select(a), x) - log(b,x),
	141	log(select(a ^ b), x) := log(select(a), x) * b,
	142	log(a, select(b)) := ln(a) / select(ln(b)),
	143	sin(select(a + b)) := sin(select(a)) cos(b) + cos(a) sin(b),
	144	sin(select(2 a)) := 2 sin(select(a)) cos(a),
	145	sin(select(n a)) := 2sin((n-1) select(a)) cos(a) - sin((n-2) a)
	146	:: integer(n) :: n > 2,
	147	cos(select(a + b)) := cos(select(a)) cos(b) - sin(a) sin(b),
	148	cos(select(2 a)) := 2 cos(select(a))^2 - 1,
	149	cos(select(n a)) := 2cos((n-1) select(a)) cos(a) - cos((n-2) a)
	150	:: integer(n) :: n > 2,
	151	tan(select(a + b)) := (tan(select(a)) + tan(b)) /
	152	(1 - tan(a) tan(b)),
	153	tan(select(2 a)) := 2 tan(select(a)) / (1 - tan(a)^2),
	154	tan(select(n a)) := (tan((n-1) select(a)) + tan(a)) /
	155	(1 - tan((n-1) a) tan(a))
156	:: integer(n) :: n > 2,
6fc5a7da JB	157	cot(select(a + b)) := (cot(select(a)) cot(b) - 1) /
6fc5a7da JB	158	(cot(a) + cot(b)),
136211a9 EZ	159	sinh(select(a + b)) := sinh(select(a)) cosh(b) + cosh(a) sinh(b),
	160	cosh(select(a + b)) := cosh(select(a)) cosh(b) + sinh(a) sinh(b),
	161	tanh(select(a + b)) := (tanh(select(a)) + tanh(b)) /
	162	(1 + tanh(a) tanh(b)),
6fc5a7da JB	163	coth(select(a + b)) := (coth(select(a)) coth(b) + 1) /
6fc5a7da JB	164	(coth(a) + coth(b)),
136211a9 EZ	165	x && select(a \|\| b) := (x && select(a)) \|\| (x && b),
	166	select(a \|\| b) && x := (select(a) && x) \|\| (b && x),
	167	! select(a && b) := (!a) \|\| (!b),
bf77c646	168	! select(a \|\| b) := (!a) && (!b) ]"))
136211a9 EZ	169
	170	(defun calc-MergeRules ()
	171	"MergeRules"
	172	(calc-compile-rule-set
	173	"MergeRules" "[
	174	iterations(1),
	175	(xopt(a)) + select(xb) := x * (a + select(b)),
	176	(xopt(a)) - select(xb) := x * (a - select(b)),
	177	sum(select(x)a,b,c,d) := x sum(select(a),b,c,d),
	178	(a/x) + select(b/x) := (a + select(b)) / x,
	179	(a/x) - select(b/x) := (a - select(b)) / x,
	180	sum(a/select(x),b,c,d) := sum(select(a),b,c,d) / x,
	181	(a/opt(b)) + select(c/d) := ((select(a)d) + (bc)) / (b*d),
	182	(a/opt(b)) - select(c/d) := ((select(a)d) - (bc)) / (b*d),
	183	(x^opt(a)) * select(x^b) := x ^ (a + select(b)),
	184	(x^opt(a)) / select(x^b) := x ^ (a - select(b)),
	185	select(x^a) / (x^opt(b)) := x ^ (select(a) - b),
	186	prod(select(x)^a,b,c,d) := x ^ sum(select(a),b,c,d),
	187	select(x^a) / (x^opt(b)) := x ^ (select(a) - b),
	188	(a^x) * select(b^x) := select((a * b) ^x),
	189	(a^x) / select(b^x) := select((b / b) ^ x),
	190	select(a^x) / (b^x) := select((a / b) ^ x),
	191	prod(a^select(x),b,c,d) := select(prod(a,b,c,d) ^ x),
	192	(a^x) * select(b^y) := select((a * b^(y-x)) ^x),
	193	(a^x) / select(b^y) := select((b / b^(y-x)) ^ x),
	194	select(a^x) / (b^y) := select((a / b^(y-x)) ^ x),
	195	select(x^a) ^ b := x ^ select(a * b),
	196	(x^a) ^ select(b) := x ^ select(a * b),
	197	select(sqrt(a)) ^ b := select(a ^ (b / 2)),
	198	sqrt(a) ^ select(b) := select(a ^ (b / 2)),
	199	sqrt(select(a) ^ b) := select(a ^ (b / 2)),
	200	sqrt(a ^ select(b)) := select(a ^ (b / 2)),
	201	sqrt(a) * select(sqrt(b)) := select(sqrt(a * b)),
	202	sqrt(a) / select(sqrt(b)) := select(sqrt(a / b)),
	203	select(sqrt(a)) / sqrt(b) := select(sqrt(a / b)),
	204	prod(select(sqrt(a)),b,c,d) := select(sqrt(prod(a,b,c,d))),
	205	exp(a) * select(exp(b)) := select(exp(a + b)),
	206	exp(a) / select(exp(b)) := select(exp(a - b)),
	207	select(exp(a)) / exp(b) := select(exp(a - b)),
	208	prod(select(exp(a)),b,c,d) := select(exp(sum(a,b,c,d))),
	209	select(exp(a)) ^ b := select(exp(a * b)),
	210	exp(a) ^ select(b) := select(exp(a * b)),
	211	ln(a) + select(ln(b)) := select(ln(a * b)),
	212	ln(a) - select(ln(b)) := select(ln(a / b)),
	213	select(ln(a)) - ln(b) := select(ln(a / b)),
	214	sum(select(ln(a)),b,c,d) := select(ln(prod(a,b,c,d))),
	215	b * select(ln(a)) := select(ln(a ^ b)),
	216	select(b) * ln(a) := select(ln(a ^ b)),
	217	select(ln(a)) / ln(b) := select(log(a, b)),
	218	ln(a) / select(ln(b)) := select(log(a, b)),
	219	select(ln(a)) / b := select(ln(a ^ (1/b))),
	220	ln(a) / select(b) := select(ln(a ^ (1/b))),
	221	log10(a) + select(log10(b)) := select(log10(a * b)),
	222	log10(a) - select(log10(b)) := select(log10(a / b)),
	223	select(log10(a)) - log10(b) := select(log10(a / b)),
	224	sum(select(log10(a)),b,c,d) := select(log10(prod(a,b,c,d))),
	225	b * select(log10(a)) := select(log10(a ^ b)),
	226	select(b) * log10(a) := select(log10(a ^ b)),
	227	select(log10(a)) / log10(b) := select(log(a, b)),
	228	log10(a) / select(log10(b)) := select(log(a, b)),
	229	select(log10(a)) / b := select(log10(a ^ (1/b))),
	230	log10(a) / select(b) := select(log10(a ^ (1/b))),
	231	log(a,x) + select(log(b,x)) := select(log(a * b,x)),
	232	log(a,x) - select(log(b,x)) := select(log(a / b,x)),
233	select(log(a,x)) - log(b,x) := select(log(a / b,x)),
234	sum(select(log(a,x)),b,c,d) := select(log(prod(a,b,c,d),x)),
235	b * select(log(a,x)) := select(log(a ^ b,x)),
236	select(b) * log(a,x) := select(log(a ^ b,x)),
237	select(log(a,x)) / log(b,x) := select(log(a, b)),
238	log(a,x) / select(log(b,x)) := select(log(a, b)),
239	select(log(a,x)) / b := select(log(a ^ (1/b),x)),
240	log(a,x) / select(b) := select(log(a ^ (1/b),x)),
bf77c646	241	select(x && a) \|\| (x && opt(b)) := x && (select(a) \|\| b) ]"))
136211a9 EZ	242
	243	(defun calc-NegateRules ()
	244	"NegateRules"
	245	(calc-compile-rule-set
	246	"NegateRules" "[
	247	iterations(1),
	248	a + select(x) := a - select(-x),
	249	a - select(x) := a + select(-x),
	250	sum(select(x),b,c,d) := -sum(select(-x),b,c,d),
	251	a * select(x) := -a * select(-x),
	252	a / select(x) := -a / select(-x),
	253	select(x) / a := -select(-x) / a,
	254	prod(select(x),b,c,d) := (-1)^(d-c+1) * prod(select(-x),b,c,d),
	255	select(x) ^ n := select(-x) ^ a :: integer(n) :: n%2 = 0,
	256	select(x) ^ n := -(select(-x) ^ a) :: integer(n) :: n%2 = 1,
	257	select(x) ^ a := (-select(-x)) ^ a,
	258	a ^ select(x) := (1 / a)^select(-x),
	259	abs(select(x)) := abs(select(-x)),
	260	i sqrt(select(x)) := -sqrt(select(-x)),
	261	sqrt(select(x)) := i sqrt(select(-x)),
	262	re(select(x)) := -re(select(-x)),
	263	im(select(x)) := -im(select(-x)),
	264	conj(select(x)) := -conj(select(-x)),
	265	trunc(select(x)) := -trunc(select(-x)),
	266	round(select(x)) := -round(select(-x)),
	267	floor(select(x)) := -ceil(select(-x)),
	268	ceil(select(x)) := -floor(select(-x)),
	269	ftrunc(select(x)) := -ftrunc(select(-x)),
	270	fround(select(x)) := -fround(select(-x)),
	271	ffloor(select(x)) := -fceil(select(-x)),
	272	fceil(select(x)) := -ffloor(select(-x)),
	273	exp(select(x)) := 1 / exp(select(-x)),
	274	sin(select(x)) := -sin(select(-x)),
	275	cos(select(x)) := cos(select(-x)),
	276	tan(select(x)) := -tan(select(-x)),
6fc5a7da JB	277	sec(select(x)) := sec(select(-x)),
	278	csc(select(x)) := -csc(select(-x)),
	279	cot(select(x)) := -cot(select(-x)),
136211a9 EZ	280	arcsin(select(x)) := -arcsin(select(-x)),
	281	arccos(select(x)) := 4 arctan(1) - arccos(select(-x)),
	282	arctan(select(x)) := -arctan(select(-x)),
	283	sinh(select(x)) := -sinh(select(-x)),
	284	cosh(select(x)) := cosh(select(-x)),
	285	tanh(select(x)) := -tanh(select(-x)),
6fc5a7da JB	286	sech(select(x)) := sech(select(-x)),
	287	csch(select(x)) := -csch(select(-x)),
	288	coth(select(x)) := -coth(select(-x)),
136211a9 EZ	289	arcsinh(select(x)) := -arcsinh(select(-x)),
	290	arctanh(select(x)) := -arctanh(select(-x)),
	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	select(x) >= a := select(-x) <= -a,
	297	a < select(x) := -a > select(-x),
	298	a > select(x) := -a < select(-x),
	299	a <= select(x) := -a >= select(-x),
	300	a >= select(x) := -a <= select(-x),
bf77c646	301	select(x) := -select(-x) ]"))
136211a9 EZ	302
	303	(defun calc-InvertRules ()
	304	"InvertRules"
	305	(calc-compile-rule-set
	306	"InvertRules" "[
	307	iterations(1),
	308	a * select(x) := a / select(1/x),
	309	a / select(x) := a * select(1/x),
	310	select(x) / a := 1 / (select(1/x) a),
	311	prod(select(x),b,c,d) := 1 / prod(select(1/x),b,c,d),
	312	abs(select(x)) := 1 / abs(select(1/x)),
	313	sqrt(select(x)) := 1 / sqrt(select(1/x)),
	314	ln(select(x)) := -ln(select(1/x)),
	315	log10(select(x)) := -log10(select(1/x)),
	316	log(select(x), a) := -log(select(1/x), a),
	317	log(a, select(x)) := -log(a, select(1/x)),
	318	arctan(select(x)) := simplify(2 arctan(1))-arctan(select(1/x)),
	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	select(x) >= a := select(1/x) <= 1/a,
	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	a >= select(x) := 1/a <= select(1/x),
bf77c646	329	select(x) := 1 / select(1/x) ]"))
136211a9 EZ	330
	331
	332	(defun calc-FactorRules ()
	333	"FactorRules"
	334	(calc-compile-rule-set
	335	"FactorRules" "[
	336	thecoefs(x, [z, a+b, c]) := thefactors(x, [d x + d a/c, (c/d) x + (b/d)])
	337	:: z = a b/c :: let(d := pgcd(pcont(c), pcont(b))),
	338	thecoefs(x, [z, a, c]) := thefactors(x, [(r x + a/(2 r))^2])
	339	:: z = (a/2)^2/c :: let(r := esimplify(sqrt(c)))
	340	:: !matches(r, sqrt(rr)),
	341	thecoefs(x, [z, 0, c]) := thefactors(x, [rc x + rz, rc x - rz])
	342	:: negative(z)
	343	:: let(rz := esimplify(sqrt(-z))) :: !matches(rz, sqrt(rzz))
	344	:: let(rc := esimplify(sqrt(c))) :: !matches(rc, sqrt(rcc)),
	345	thecoefs(x, [z, 0, c]) := thefactors(x, [rz + rc x, rz - rc x])
	346	:: negative(c)
	347	:: let(rz := esimplify(sqrt(z))) :: !matches(rz, sqrt(rzz))
	348	:: let(rc := esimplify(sqrt(-c))) :: !matches(rc, sqrt(rcc))
bf77c646	349	]"))
136211a9 EZ	350	;;(setq var-FactorRules 'calc-FactorRules)
	351
	352
	353	(defun calc-IntegAfterRules ()
	354	"IntegAfterRules"
	355	(calc-compile-rule-set
	356	"IntegAfterRules" "[
	357	opt(a) ln(x) + opt(b) ln(y) := 2 a esimplify(arctanh(x-1))
	358	:: a + b = 0 :: nrat(x + y) = 2 \|\| nrat(x - y) = 2,
	359	a * (b + c) := a b + a c :: constant(a)
bf77c646	360	]"))
136211a9 EZ	361
	362	;;(setq var-IntegAfterRules 'calc-IntegAfterRules)
	363
	364
	365	(defun calc-FitRules ()
	366	"FitRules"
	367	(calc-compile-rule-set
	368	"FitRules" "[
	369
	370	schedule(1,2,3,4),
	371	iterations(inf),
	372
	373	phase(1),
	374	e^x := exp(x),
	375	x^y := exp(y ln(x)) :: !istrue(constant(y)),
	376	x/y := x fitinv(y),
	377	fitinv(x y) := fitinv(x) fitinv(y),
	378	exp(a) exp(b) := exp(a + b),
	379	a exp(b) := exp(ln(a) + b) :: !hasfitvars(a),
	380	fitinv(exp(a)) := exp(-a),
	381	ln(a b) := ln(a) + ln(b),
	382	ln(fitinv(a)) := -ln(a),
	383	log10(a b) := log10(a) + log10(b),
	384	log10(fitinv(a)) := -log10(a),
	385	log(a,b) := ln(a)/ln(b),
	386	ln(exp(a)) := a,
	387	a(b+c) := ab + a*c,
	388	(a+b)^n := x :: integer(n) :: n >= 2
	389	:: let(x, expandpow(a+b,n))
	390	:: quote(matches(x,y+z)),
	391
	392	phase(1,2),
	393	fitmodel(y = x) := fitmodel(0, y - x),
	394	fitmodel(y, x+c) := fitmodel(y-c, x) :: !hasfitparams(c),
	395	fitmodel(y, x c) := fitmodel(y/c, x) :: !hasfitparams(c),
	396	fitmodel(y, x/(c opt(d))) := fitmodel(y c, x/d) :: !hasfitparams(c),
	397	fitmodel(y, apply(f,[x])) := fitmodel(yy, x)
	398	:: hasfitparams(x)
	399	:: let(FTemp() = yy,
	400	solve(apply(f,[FTemp()]) = y,
	401	FTemp())),
	402	fitmodel(y, apply(f,[x,c])) := fitmodel(yy, x)
	403	:: !hasfitparams(c)
	404	:: let(FTemp() = yy,
	405	solve(apply(f,[FTemp(),c]) = y,
	406	FTemp())),
	407	fitmodel(y, apply(f,[c,x])) := fitmodel(yy, x)
	408	:: !hasfitparams(c)
	409	:: let(FTemp() = yy,
	410	solve(apply(f,[c,FTemp()]) = y,
	411	FTemp())),
	412
	413	phase(2,3),
	414	fitmodel(y, x) := fitsystem(y, [], [], fitpart(1,1,x)),
	415	fitpart(a,b,plain(x + y)) := fitpart(a,b,x) + fitpart(a,b,y),
	416	fitpart(a,b,plain(x - y)) := fitpart(a,b,x) + fitpart(-a,b,y),
	417	fitpart(a,b,plain(-x)) := fitpart(-a,b,x),
	418	fitpart(a,b,x opt(c)) := fitpart(a,x b,c) :: !hasfitvars(x),
	419	fitpart(a,x opt(b),c) := fitpart(x a,b,c) :: !hasfitparams(x),
	420	fitpart(a,x y + x opt(z),c) := fitpart(a,x*(y+z),c),
	421	fitpart(a,b,c) := fitpart2(a,b,c),
	422
	423	phase(3),
	424	fitpart2(a1,b1,x) + fitpart2(a2,b2,x) := fitpart(1, a1 b1 + a2 b2, x),
425	fitpart2(a1,x,c1) + fitpart2(a2,x,c2) := fitpart2(1, x, a1 c1 + a2 c2),
426
427	phase(4),
428	fitinv(x) := 1 / x,
429	exp(x + ln(y)) := y exp(x),
430	exp(x ln(y)) := y^x,
431	ln(x) + ln(y) := ln(x y),
432	ln(x) - ln(y) := ln(x/y),
433	xy + xz := x*(y+z),
434	fitsystem(y, xv, pv, fitpart2(a,fitparam(b),c) + opt(d))
435	:= fitsystem(y, rcons(xv, a c),
436	rcons(pv, fitdummy(b) = fitparam(b)), d)
437	:: b = vlen(pv)+1,
438	fitsystem(y, xv, pv, fitpart2(a,b,c) + opt(d))
439	:= fitsystem(y, rcons(xv, a c),
440	rcons(pv, fitdummy(vlen(pv)+1) = b), d),
441	fitsystem(y, xv, pv, 0) := fitsystem(y, xv, cons(fvh,fvt))
442	:: !hasfitparams(xv)
443	:: let(cons(fvh,fvt),
444	solve(pv, table(fitparam(j), j, 1,
445	hasfitparams(pv)))),
bf77c646	446	fitparam(n) = x := x ]"))
136211a9	447
51b5c91c JB	448	(provide 'calc-rules)
51b5c91c JB	449
cbee283d	450	;; arch-tag: 0ed54a52-38f3-4ed7-9ca7-b8ecf8f2febe
bf77c646	451	;;; calc-rules.el ends here