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Current Directory: /usr/share/emacs/24.3/lisp/calc
Viewing File: /usr/share/emacs/24.3/lisp/calc/calc-rules.elc
;ELC ;;; Compiled by mockbuild@buildfarm01-new.corp.cloudlinux.com on Tue Nov 11 12:55:52 2025 ;;; from file /builddir/build/BUILD/emacs-24.3/lisp/calc/calc-rules.el ;;; in Emacs version 24.3.1 ;;; with all optimizations. ;;; This file uses dynamic docstrings, first added in Emacs 19.29. ;;; This file does not contain utf-8 non-ASCII characters, ;;; and so can be loaded in Emacs versions earlier than 23. ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; (byte-code "\300\301!\210\300\302!\207" [require calc-ext calc-macs] 2) (defalias 'calc-compile-rule-set #[(name rules) "\302\303\"\210\304 \305\"\302\306\"\210\207" [name rules message "Preparing rule set %s..." math-read-plain-expr t "Preparing rule set %s...done"] 4]) #@14 CommuteRules (defalias 'calc-CommuteRules #[nil "\300\301\302\"\207" [calc-compile-rule-set "CommuteRules" "[\niterations(1),\nselect(plain(a + b)) := select(plain(b + a)),\nselect(plain(a - b)) := select(plain((-b) + a)),\nselect(plain((1/a) * b)) := select(b / a),\nselect(plain(a * b)) := select(b * a),\nselect((1/a) / b) := select((1/b) / a),\nselect(a / b) := select((1/b) * a),\nselect((a^b) ^ c) := select((a^c) ^ b),\nselect(log(a, b)) := select(1 / log(b, a)),\nselect(plain(a && b)) := select(b && a),\nselect(plain(a || b)) := select(b || a),\nselect(plain(a = b)) := select(b = a),\nselect(plain(a != b)) := select(b != a),\nselect(a < b) := select(b > a),\nselect(a > b) := select(b < a),\nselect(a <= b) := select(b >= a),\nselect(a >= b) := select(b <= a) ]"] 3 (#$ . 832)]) #@11 JumpRules (defalias 'calc-JumpRules #[nil "\300\301\302\"\207" [calc-compile-rule-set "JumpRules" "[\niterations(1),\nplain(select(x) = y) := 0 = select(-x) + y,\nplain(a + select(x) = y) := a = select(-x) + y,\nplain(a - select(x) = y) := a = select(x) + y,\nplain(select(x) + a = y) := a = select(-x) + y,\nplain(a * select(x) = y) := a = y / select(x),\nplain(a / select(x) = y) := a = select(x) * y,\nplain(select(x) / a = y) := 1/a = y / select(x),\nplain(a ^ select(2) = y) := a = select(sqrt(y)),\nplain(a ^ select(x) = y) := a = y ^ select(1/x),\nplain(select(x) ^ a = y) := a = log(y, select(x)),\nplain(log(a, select(x)) = y) := a = select(x) ^ y,\nplain(log(select(x), a) = y) := a = select(x) ^ (1/y),\nplain(y = select(x)) := y - select(x) = 0,\nplain(y = a + select(x)) := y - select(x) = a,\nplain(y = a - select(x)) := y + select(x) = a,\nplain(y = select(x) + a) := y - select(x) = a,\nplain(y = a * select(x)) := y / select(x) = a,\nplain(y = a / select(x)) := y * select(x) = a,\nplain(y = select(x) / a) := y / select(x) = 1/a,\nplain(y = a ^ select(2)) := select(sqrt(y)) = a,\nplain(y = a ^ select(x)) := y ^ select(1/x) = a,\nplain(y = select(x) ^ a) := log(y, select(x)) = a,\nplain(y = log(a, select(x))) := select(x) ^ y = a,\nplain(y = log(select(x), a)) := select(x) ^ (1/y) = a ]"] 3 (#$ . 1665)]) #@14 DistribRules (defalias 'calc-DistribRules #[nil "\300\301\302\"\207" [calc-compile-rule-set "DistribRules" "[\niterations(1),\nx * select(a + b) := x*select(a) + x*b,\nx * select(sum(a,b,c,d)) := sum(x*select(a),b,c,d),\nx / select(a + b) := 1 / (select(a)/x + b/x),\nselect(a + b) / x := select(a)/x + b/x,\nsum(select(a),b,c,d) / x := sum(select(a)/x,b,c,d),\nx ^ select(a + b) := x^select(a) * x^b,\nx ^ select(sum(a,b,c,d)) := prod(x^select(a),b,c,d),\nx ^ select(a * b) := (x^a)^select(b),\nx ^ select(a / b) := (x^a)^select(1/b),\nselect(a + b) ^ n := select(x)\n :: integer(n) :: n >= 2\n :: let(x, expandpow(a+b,n))\n :: quote(matches(x,y+z)),\nselect(a + b) ^ x := a*select(a+b)^(x-1) + b*select(a+b)^(x-1),\nselect(a * b) ^ x := a^x * select(b)^x,\nselect(prod(a,b,c,d)) ^ x := prod(select(a)^x,b,c,d),\nselect(a / b) ^ x := select(a)^x / b^x,\nselect(- a) ^ x := (-1)^x * select(a)^x,\nplain(-select(a + b)) := select(-a) - b,\nplain(-select(sum(a,b,c,d))) := sum(select(-a),b,c,d),\nplain(-select(a * b)) := select(-a) * b,\nplain(-select(a / b)) := select(-a) / b,\nsqrt(select(a * b)) := sqrt(select(a)) * sqrt(b),\nsqrt(select(prod(a,b,c,d))) := prod(sqrt(select(a)),b,c,d),\nsqrt(select(a / b)) := sqrt(select(a)) / sqrt(b),\nsqrt(select(- a)) := sqrt(-1) sqrt(select(a)),\nexp(select(a + b)) := exp(select(a)) / exp(-b) :: negative(b),\nexp(select(a + b)) := exp(select(a)) * exp(b),\nexp(select(sum(a,b,c,d))) := prod(exp(select(a)),b,c,d),\nexp(select(a * b)) := exp(select(a)) ^ b :: constant(b),\nexp(select(a * b)) := exp(select(a)) ^ b,\nexp(select(a / b)) := exp(select(a)) ^ (1/b),\nln(select(a * b)) := ln(select(a)) + ln(b),\nln(select(prod(a,b,c,d))) := sum(ln(select(a)),b,c,d),\nln(select(a / b)) := ln(select(a)) - ln(b),\nln(select(a ^ b)) := ln(select(a)) * b,\nlog10(select(a * b)) := log10(select(a)) + log10(b),\nlog10(select(prod(a,b,c,d))) := sum(log10(select(a)),b,c,d),\nlog10(select(a / b)) := log10(select(a)) - log10(b),\nlog10(select(a ^ b)) := log10(select(a)) * b,\nlog(select(a * b), x) := log(select(a), x) + log(b,x),\nlog(select(prod(a,b,c,d)),x) := sum(log(select(a),x),b,c,d),\nlog(select(a / b), x) := log(select(a), x) - log(b,x),\nlog(select(a ^ b), x) := log(select(a), x) * b,\nlog(a, select(b)) := ln(a) / select(ln(b)),\nsin(select(a + b)) := sin(select(a)) cos(b) + cos(a) sin(b),\nsin(select(2 a)) := 2 sin(select(a)) cos(a),\nsin(select(n a)) := 2sin((n-1) select(a)) cos(a) - sin((n-2) a)\n :: integer(n) :: n > 2,\ncos(select(a + b)) := cos(select(a)) cos(b) - sin(a) sin(b),\ncos(select(2 a)) := 2 cos(select(a))^2 - 1,\ncos(select(n a)) := 2cos((n-1) select(a)) cos(a) - cos((n-2) a)\n :: integer(n) :: n > 2,\ntan(select(a + b)) := (tan(select(a)) + tan(b)) /\n (1 - tan(a) tan(b)),\ntan(select(2 a)) := 2 tan(select(a)) / (1 - tan(a)^2),\ntan(select(n a)) := (tan((n-1) select(a)) + tan(a)) /\n (1 - tan((n-1) a) tan(a))\n :: integer(n) :: n > 2,\ncot(select(a + b)) := (cot(select(a)) cot(b) - 1) /\n (cot(a) + cot(b)),\nsinh(select(a + b)) := sinh(select(a)) cosh(b) + cosh(a) sinh(b),\ncosh(select(a + b)) := cosh(select(a)) cosh(b) + sinh(a) sinh(b),\ntanh(select(a + b)) := (tanh(select(a)) + tanh(b)) /\n (1 + tanh(a) tanh(b)),\ncoth(select(a + b)) := (coth(select(a)) coth(b) + 1) /\n (coth(a) + coth(b)),\nx && select(a || b) := (x && select(a)) || (x && b),\nselect(a || b) && x := (select(a) && x) || (b && x),\n! select(a && b) := (!a) || (!b),\n! select(a || b) := (!a) && (!b) ]"] 3 (#$ . 3024)]) #@12 MergeRules (defalias 'calc-MergeRules #[nil "\300\301\302\"\207" [calc-compile-rule-set "MergeRules" "[\niterations(1),\n (x*opt(a)) + select(x*b) := x * (a + select(b)),\n (x*opt(a)) - select(x*b) := x * (a - select(b)),\nsum(select(x)*a,b,c,d) := x * sum(select(a),b,c,d),\n (a/x) + select(b/x) := (a + select(b)) / x,\n (a/x) - select(b/x) := (a - select(b)) / x,\nsum(a/select(x),b,c,d) := sum(select(a),b,c,d) / x,\n (a/opt(b)) + select(c/d) := ((select(a)*d) + (b*c)) / (b*d),\n (a/opt(b)) - select(c/d) := ((select(a)*d) - (b*c)) / (b*d),\n (x^opt(a)) * select(x^b) := x ^ (a + select(b)),\n (x^opt(a)) / select(x^b) := x ^ (a - select(b)),\nselect(x^a) / (x^opt(b)) := x ^ (select(a) - b),\nprod(select(x)^a,b,c,d) := x ^ sum(select(a),b,c,d),\nselect(x^a) / (x^opt(b)) := x ^ (select(a) - b),\n (a^x) * select(b^x) := select((a * b) ^x),\n (a^x) / select(b^x) := select((b / b) ^ x),\nselect(a^x) / (b^x) := select((a / b) ^ x),\nprod(a^select(x),b,c,d) := select(prod(a,b,c,d) ^ x),\n (a^x) * select(b^y) := select((a * b^(y-x)) ^x),\n (a^x) / select(b^y) := select((b / b^(y-x)) ^ x),\nselect(a^x) / (b^y) := select((a / b^(y-x)) ^ x),\nselect(x^a) ^ b := x ^ select(a * b),\n (x^a) ^ select(b) := x ^ select(a * b),\nselect(sqrt(a)) ^ b := select(a ^ (b / 2)),\nsqrt(a) ^ select(b) := select(a ^ (b / 2)),\nsqrt(select(a) ^ b) := select(a ^ (b / 2)),\nsqrt(a ^ select(b)) := select(a ^ (b / 2)),\nsqrt(a) * select(sqrt(b)) := select(sqrt(a * b)),\nsqrt(a) / select(sqrt(b)) := select(sqrt(a / b)),\nselect(sqrt(a)) / sqrt(b) := select(sqrt(a / b)),\nprod(select(sqrt(a)),b,c,d) := select(sqrt(prod(a,b,c,d))),\nexp(a) * select(exp(b)) := select(exp(a + b)),\nexp(a) / select(exp(b)) := select(exp(a - b)),\nselect(exp(a)) / exp(b) := select(exp(a - b)),\nprod(select(exp(a)),b,c,d) := select(exp(sum(a,b,c,d))),\nselect(exp(a)) ^ b := select(exp(a * b)),\nexp(a) ^ select(b) := select(exp(a * b)),\nln(a) + select(ln(b)) := select(ln(a * b)),\nln(a) - select(ln(b)) := select(ln(a / b)),\nselect(ln(a)) - ln(b) := select(ln(a / b)),\nsum(select(ln(a)),b,c,d) := select(ln(prod(a,b,c,d))),\nb * select(ln(a)) := select(ln(a ^ b)),\nselect(b) * ln(a) := select(ln(a ^ b)),\nselect(ln(a)) / ln(b) := select(log(a, b)),\nln(a) / select(ln(b)) := select(log(a, b)),\nselect(ln(a)) / b := select(ln(a ^ (1/b))),\nln(a) / select(b) := select(ln(a ^ (1/b))),\nlog10(a) + select(log10(b)) := select(log10(a * b)),\nlog10(a) - select(log10(b)) := select(log10(a / b)),\nselect(log10(a)) - log10(b) := select(log10(a / b)),\nsum(select(log10(a)),b,c,d) := select(log10(prod(a,b,c,d))),\nb * select(log10(a)) := select(log10(a ^ b)),\nselect(b) * log10(a) := select(log10(a ^ b)),\nselect(log10(a)) / log10(b) := select(log(a, b)),\nlog10(a) / select(log10(b)) := select(log(a, b)),\nselect(log10(a)) / b := select(log10(a ^ (1/b))),\nlog10(a) / select(b) := select(log10(a ^ (1/b))),\nlog(a,x) + select(log(b,x)) := select(log(a * b,x)),\nlog(a,x) - select(log(b,x)) := select(log(a / b,x)),\nselect(log(a,x)) - log(b,x) := select(log(a / b,x)),\nsum(select(log(a,x)),b,c,d) := select(log(prod(a,b,c,d),x)),\nb * select(log(a,x)) := select(log(a ^ b,x)),\nselect(b) * log(a,x) := select(log(a ^ b,x)),\nselect(log(a,x)) / log(b,x) := select(log(a, b)),\nlog(a,x) / select(log(b,x)) := select(log(a, b)),\nselect(log(a,x)) / b := select(log(a ^ (1/b),x)),\nlog(a,x) / select(b) := select(log(a ^ (1/b),x)),\nselect(x && a) || (x && opt(b)) := x && (select(a) || b) ]"] 3 (#$ . 6713)]) #@13 NegateRules (defalias 'calc-NegateRules #[nil "\300\301\302\"\207" [calc-compile-rule-set "NegateRules" "[\niterations(1),\na + select(x) := a - select(-x),\na - select(x) := a + select(-x),\nsum(select(x),b,c,d) := -sum(select(-x),b,c,d),\na * select(x) := -a * select(-x),\na / select(x) := -a / select(-x),\nselect(x) / a := -select(-x) / a,\nprod(select(x),b,c,d) := (-1)^(d-c+1) * prod(select(-x),b,c,d),\nselect(x) ^ n := select(-x) ^ a :: integer(n) :: n%2 = 0,\nselect(x) ^ n := -(select(-x) ^ a) :: integer(n) :: n%2 = 1,\nselect(x) ^ a := (-select(-x)) ^ a,\na ^ select(x) := (1 / a)^select(-x),\nabs(select(x)) := abs(select(-x)),\ni sqrt(select(x)) := -sqrt(select(-x)),\nsqrt(select(x)) := i sqrt(select(-x)),\nre(select(x)) := -re(select(-x)),\nim(select(x)) := -im(select(-x)),\nconj(select(x)) := -conj(select(-x)),\ntrunc(select(x)) := -trunc(select(-x)),\nround(select(x)) := -round(select(-x)),\nfloor(select(x)) := -ceil(select(-x)),\nceil(select(x)) := -floor(select(-x)),\nftrunc(select(x)) := -ftrunc(select(-x)),\nfround(select(x)) := -fround(select(-x)),\nffloor(select(x)) := -fceil(select(-x)),\nfceil(select(x)) := -ffloor(select(-x)),\nexp(select(x)) := 1 / exp(select(-x)),\nsin(select(x)) := -sin(select(-x)),\ncos(select(x)) := cos(select(-x)),\ntan(select(x)) := -tan(select(-x)),\nsec(select(x)) := sec(select(-x)),\ncsc(select(x)) := -csc(select(-x)),\ncot(select(x)) := -cot(select(-x)),\narcsin(select(x)) := -arcsin(select(-x)),\narccos(select(x)) := 4 arctan(1) - arccos(select(-x)),\narctan(select(x)) := -arctan(select(-x)),\nsinh(select(x)) := -sinh(select(-x)),\ncosh(select(x)) := cosh(select(-x)),\ntanh(select(x)) := -tanh(select(-x)),\nsech(select(x)) := sech(select(-x)),\ncsch(select(x)) := -csch(select(-x)),\ncoth(select(x)) := -coth(select(-x)),\narcsinh(select(x)) := -arcsinh(select(-x)),\narctanh(select(x)) := -arctanh(select(-x)),\nselect(x) = a := select(-x) = -a,\nselect(x) != a := select(-x) != -a,\nselect(x) < a := select(-x) > -a,\nselect(x) > a := select(-x) < -a,\nselect(x) <= a := select(-x) >= -a,\nselect(x) >= a := select(-x) <= -a,\na < select(x) := -a > select(-x),\na > select(x) := -a < select(-x),\na <= select(x) := -a >= select(-x),\na >= select(x) := -a <= select(-x),\nselect(x) := -select(-x) ]"] 3 (#$ . 10312)]) #@13 InvertRules (defalias 'calc-InvertRules #[nil "\300\301\302\"\207" [calc-compile-rule-set "InvertRules" "[\niterations(1),\na * select(x) := a / select(1/x),\na / select(x) := a * select(1/x),\nselect(x) / a := 1 / (select(1/x) a),\nprod(select(x),b,c,d) := 1 / prod(select(1/x),b,c,d),\nabs(select(x)) := 1 / abs(select(1/x)),\nsqrt(select(x)) := 1 / sqrt(select(1/x)),\nln(select(x)) := -ln(select(1/x)),\nlog10(select(x)) := -log10(select(1/x)),\nlog(select(x), a) := -log(select(1/x), a),\nlog(a, select(x)) := -log(a, select(1/x)),\narctan(select(x)) := simplify(2 arctan(1))-arctan(select(1/x)),\nselect(x) = a := select(1/x) = 1/a,\nselect(x) != a := select(1/x) != 1/a,\nselect(x) < a := select(1/x) > 1/a,\nselect(x) > a := select(1/x) < 1/a,\nselect(x) <= a := select(1/x) >= 1/a,\nselect(x) >= a := select(1/x) <= 1/a,\na < select(x) := 1/a > select(1/x),\na > select(x) := 1/a < select(1/x),\na <= select(x) := 1/a >= select(1/x),\na >= select(x) := 1/a <= select(1/x),\nselect(x) := 1 / select(1/x) ]"] 3 (#$ . 12760)]) #@13 FactorRules (defalias 'calc-FactorRules #[nil "\300\301\302\"\207" [calc-compile-rule-set "FactorRules" "[\nthecoefs(x, [z, a+b, c]) := thefactors(x, [d x + d a/c, (c/d) x + (b/d)])\n :: z = a b/c :: let(d := pgcd(pcont(c), pcont(b))),\nthecoefs(x, [z, a, c]) := thefactors(x, [(r x + a/(2 r))^2])\n :: z = (a/2)^2/c :: let(r := esimplify(sqrt(c)))\n :: !matches(r, sqrt(rr)),\nthecoefs(x, [z, 0, c]) := thefactors(x, [rc x + rz, rc x - rz])\n :: negative(z)\n :: let(rz := esimplify(sqrt(-z))) :: !matches(rz, sqrt(rzz))\n :: let(rc := esimplify(sqrt(c))) :: !matches(rc, sqrt(rcc)),\nthecoefs(x, [z, 0, c]) := thefactors(x, [rz + rc x, rz - rc x])\n :: negative(c)\n :: let(rz := esimplify(sqrt(z))) :: !matches(rz, sqrt(rzz))\n :: let(rc := esimplify(sqrt(-c))) :: !matches(rc, sqrt(rcc))\n ]"] 3 (#$ . 13873)]) #@17 IntegAfterRules (defalias 'calc-IntegAfterRules #[nil "\300\301\302\"\207" [calc-compile-rule-set "IntegAfterRules" "[\n opt(a) ln(x) + opt(b) ln(y) := 2 a esimplify(arctanh(x-1))\n :: a + b = 0 :: nrat(x + y) = 2 || nrat(x - y) = 2,\n a * (b + c) := a b + a c :: constant(a)\n ]"] 3 (#$ . 14757)]) #@10 FitRules (defalias 'calc-FitRules #[nil "\300\301\302\"\207" [calc-compile-rule-set "FitRules" "[\n\nschedule(1,2,3,4),\niterations(inf),\n\nphase(1),\ne^x := exp(x),\nx^y := exp(y ln(x)) :: !istrue(constant(y)),\nx/y := x fitinv(y),\nfitinv(x y) := fitinv(x) fitinv(y),\nexp(a) exp(b) := exp(a + b),\na exp(b) := exp(ln(a) + b) :: !hasfitvars(a),\nfitinv(exp(a)) := exp(-a),\nln(a b) := ln(a) + ln(b),\nln(fitinv(a)) := -ln(a),\nlog10(a b) := log10(a) + log10(b),\nlog10(fitinv(a)) := -log10(a),\nlog(a,b) := ln(a)/ln(b),\nln(exp(a)) := a,\na*(b+c) := a*b + a*c,\n(a+b)^n := x :: integer(n) :: n >= 2\n :: let(x, expandpow(a+b,n))\n :: quote(matches(x,y+z)),\n\nphase(1,2),\nfitmodel(y = x) := fitmodel(0, y - x),\nfitmodel(y, x+c) := fitmodel(y-c, x) :: !hasfitparams(c),\nfitmodel(y, x c) := fitmodel(y/c, x) :: !hasfitparams(c),\nfitmodel(y, x/(c opt(d))) := fitmodel(y c, x/d) :: !hasfitparams(c),\nfitmodel(y, apply(f,[x])) := fitmodel(yy, x)\n :: hasfitparams(x)\n :: let(FTemp() = yy,\n solve(apply(f,[FTemp()]) = y,\n FTemp())),\nfitmodel(y, apply(f,[x,c])) := fitmodel(yy, x)\n :: !hasfitparams(c)\n :: let(FTemp() = yy,\n solve(apply(f,[FTemp(),c]) = y,\n FTemp())),\nfitmodel(y, apply(f,[c,x])) := fitmodel(yy, x)\n :: !hasfitparams(c)\n :: let(FTemp() = yy,\n solve(apply(f,[c,FTemp()]) = y,\n FTemp())),\n\nphase(2,3),\nfitmodel(y, x) := fitsystem(y, [], [], fitpart(1,1,x)),\nfitpart(a,b,plain(x + y)) := fitpart(a,b,x) + fitpart(a,b,y),\nfitpart(a,b,plain(x - y)) := fitpart(a,b,x) + fitpart(-a,b,y),\nfitpart(a,b,plain(-x)) := fitpart(-a,b,x),\nfitpart(a,b,x opt(c)) := fitpart(a,x b,c) :: !hasfitvars(x),\nfitpart(a,x opt(b),c) := fitpart(x a,b,c) :: !hasfitparams(x),\nfitpart(a,x y + x opt(z),c) := fitpart(a,x*(y+z),c),\nfitpart(a,b,c) := fitpart2(a,b,c),\n\nphase(3),\nfitpart2(a1,b1,x) + fitpart2(a2,b2,x) := fitpart(1, a1 b1 + a2 b2, x),\nfitpart2(a1,x,c1) + fitpart2(a2,x,c2) := fitpart2(1, x, a1 c1 + a2 c2),\n\nphase(4),\nfitinv(x) := 1 / x,\nexp(x + ln(y)) := y exp(x),\nexp(x ln(y)) := y^x,\nln(x) + ln(y) := ln(x y),\nln(x) - ln(y) := ln(x/y),\nx*y + x*z := x*(y+z),\nfitsystem(y, xv, pv, fitpart2(a,fitparam(b),c) + opt(d))\n := fitsystem(y, rcons(xv, a c),\n rcons(pv, fitdummy(b) = fitparam(b)), d)\n :: b = vlen(pv)+1,\nfitsystem(y, xv, pv, fitpart2(a,b,c) + opt(d))\n := fitsystem(y, rcons(xv, a c),\n rcons(pv, fitdummy(vlen(pv)+1) = b), d),\nfitsystem(y, xv, pv, 0) := fitsystem(y, xv, cons(fvh,fvt))\n :: !hasfitparams(xv)\n :: let(cons(fvh,fvt),\n solve(pv, table(fitparam(j), j, 1,\n hasfitparams(pv)))),\nfitparam(n) = x := x ]"] 3 (#$ . 15066)]) (provide 'calc-rules)