;; Calculator for GNU Emacs, part II [calc-rules.el] ;; Copyright (C) 1990, 1991, 1992, 1993 Free Software Foundation, Inc. ;; Written by Dave Gillespie, daveg@synaptics.com. ;; This file is part of GNU Emacs. ;; GNU Emacs is distributed in the hope that it will be useful, ;; but WITHOUT ANY WARRANTY. No author or distributor ;; accepts responsibility to anyone for the consequences of using it ;; or for whether it serves any particular purpose or works at all, ;; unless he says so in writing. Refer to the GNU Emacs General Public ;; License for full details. ;; Everyone is granted permission to copy, modify and redistribute ;; GNU Emacs, but only under the conditions described in the ;; GNU Emacs General Public License. A copy of this license is ;; supposed to have been given to you along with GNU Emacs so you ;; can know your rights and responsibilities. It should be in a ;; file named COPYING. Among other things, the copyright notice ;; and this notice must be preserved on all copies. ;; This file is autoloaded from calc-ext.el. (require 'calc-ext) (require 'calc-macs) (defun calc-Need-calc-rules () nil) (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, 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)), 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)), 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)), 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 ]") )