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436 lines
17 KiB
EmacsLisp
436 lines
17 KiB
EmacsLisp
;; Calculator for GNU Emacs, part II [calc-rules.el]
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;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc.
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;; Written by Dave Gillespie, daveg@synaptics.com.
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;; This file is part of GNU Emacs.
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;; GNU Emacs is distributed in the hope that it will be useful,
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;; but WITHOUT ANY WARRANTY. No author or distributor
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;; accepts responsibility to anyone for the consequences of using it
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;; or for whether it serves any particular purpose or works at all,
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;; unless he says so in writing. Refer to the GNU Emacs General Public
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;; License for full details.
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;; Everyone is granted permission to copy, modify and redistribute
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;; GNU Emacs, but only under the conditions described in the
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;; GNU Emacs General Public License. A copy of this license is
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;; supposed to have been given to you along with GNU Emacs so you
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;; can know your rights and responsibilities. It should be in a
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;; file named COPYING. Among other things, the copyright notice
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;; and this notice must be preserved on all copies.
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;; This file is autoloaded from calc-ext.el.
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(require 'calc-ext)
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(require 'calc-macs)
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(defun calc-Need-calc-rules () nil)
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(defun calc-compile-rule-set (name rules)
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(prog2
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(message "Preparing rule set %s..." name)
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(math-read-plain-expr rules t)
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(message "Preparing rule set %s...done" name)))
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(defun calc-CommuteRules ()
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"CommuteRules"
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(calc-compile-rule-set
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"CommuteRules" "[
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iterations(1),
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select(plain(a + b)) := select(plain(b + a)),
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select(plain(a - b)) := select(plain((-b) + a)),
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select(plain((1/a) * b)) := select(b / a),
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select(plain(a * b)) := select(b * a),
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select((1/a) / b) := select((1/b) / a),
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select(a / b) := select((1/b) * a),
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select((a^b) ^ c) := select((a^c) ^ b),
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select(log(a, b)) := select(1 / log(b, a)),
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select(plain(a && b)) := select(b && a),
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select(plain(a || b)) := select(b || a),
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select(plain(a = b)) := select(b = a),
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select(plain(a != b)) := select(b != a),
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select(a < b) := select(b > a),
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select(a > b) := select(b < a),
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select(a <= b) := select(b >= a),
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select(a >= b) := select(b <= a) ]"))
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(defun calc-JumpRules ()
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"JumpRules"
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(calc-compile-rule-set
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"JumpRules" "[
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iterations(1),
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plain(select(x) = y) := 0 = select(-x) + y,
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plain(a + select(x) = y) := a = select(-x) + y,
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plain(a - select(x) = y) := a = select(x) + y,
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plain(select(x) + a = y) := a = select(-x) + y,
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plain(a * select(x) = y) := a = y / select(x),
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plain(a / select(x) = y) := a = select(x) * y,
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plain(select(x) / a = y) := 1/a = y / select(x),
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plain(a ^ select(2) = y) := a = select(sqrt(y)),
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plain(a ^ select(x) = y) := a = y ^ select(1/x),
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plain(select(x) ^ a = y) := a = log(y, select(x)),
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plain(log(a, select(x)) = y) := a = select(x) ^ y,
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plain(log(select(x), a) = y) := a = select(x) ^ (1/y),
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plain(y = select(x)) := y - select(x) = 0,
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plain(y = a + select(x)) := y - select(x) = a,
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plain(y = a - select(x)) := y + select(x) = a,
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plain(y = select(x) + a) := y - select(x) = a,
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plain(y = a * select(x)) := y / select(x) = a,
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plain(y = a / select(x)) := y * select(x) = a,
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plain(y = select(x) / a) := y / select(x) = 1/a,
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plain(y = a ^ select(2)) := select(sqrt(y)) = a,
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plain(y = a ^ select(x)) := y ^ select(1/x) = a,
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plain(y = select(x) ^ a) := log(y, select(x)) = a,
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plain(y = log(a, select(x))) := select(x) ^ y = a,
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plain(y = log(select(x), a)) := select(x) ^ (1/y) = a ]"))
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(defun calc-DistribRules ()
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"DistribRules"
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(calc-compile-rule-set
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"DistribRules" "[
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iterations(1),
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x * select(a + b) := x*select(a) + x*b,
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x * select(sum(a,b,c,d)) := sum(x*select(a),b,c,d),
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x / select(a + b) := 1 / (select(a)/x + b/x),
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select(a + b) / x := select(a)/x + b/x,
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sum(select(a),b,c,d) / x := sum(select(a)/x,b,c,d),
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x ^ select(a + b) := x^select(a) * x^b,
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x ^ select(sum(a,b,c,d)) := prod(x^select(a),b,c,d),
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x ^ select(a * b) := (x^a)^select(b),
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x ^ select(a / b) := (x^a)^select(1/b),
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select(a + b) ^ n := select(x)
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:: integer(n) :: n >= 2
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:: let(x, expandpow(a+b,n))
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:: quote(matches(x,y+z)),
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select(a + b) ^ x := a*select(a+b)^(x-1) + b*select(a+b)^(x-1),
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select(a * b) ^ x := a^x * select(b)^x,
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select(prod(a,b,c,d)) ^ x := prod(select(a)^x,b,c,d),
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select(a / b) ^ x := select(a)^x / b^x,
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select(- a) ^ x := (-1)^x * select(a)^x,
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plain(-select(a + b)) := select(-a) - b,
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plain(-select(sum(a,b,c,d))) := sum(select(-a),b,c,d),
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plain(-select(a * b)) := select(-a) * b,
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plain(-select(a / b)) := select(-a) / b,
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sqrt(select(a * b)) := sqrt(select(a)) * sqrt(b),
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sqrt(select(prod(a,b,c,d))) := prod(sqrt(select(a)),b,c,d),
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sqrt(select(a / b)) := sqrt(select(a)) / sqrt(b),
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sqrt(select(- a)) := sqrt(-1) sqrt(select(a)),
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exp(select(a + b)) := exp(select(a)) / exp(-b) :: negative(b),
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exp(select(a + b)) := exp(select(a)) * exp(b),
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exp(select(sum(a,b,c,d))) := prod(exp(select(a)),b,c,d),
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exp(select(a * b)) := exp(select(a)) ^ b :: constant(b),
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exp(select(a * b)) := exp(select(a)) ^ b,
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exp(select(a / b)) := exp(select(a)) ^ (1/b),
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ln(select(a * b)) := ln(select(a)) + ln(b),
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ln(select(prod(a,b,c,d))) := sum(ln(select(a)),b,c,d),
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ln(select(a / b)) := ln(select(a)) - ln(b),
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ln(select(a ^ b)) := ln(select(a)) * b,
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log10(select(a * b)) := log10(select(a)) + log10(b),
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log10(select(prod(a,b,c,d))) := sum(log10(select(a)),b,c,d),
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log10(select(a / b)) := log10(select(a)) - log10(b),
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log10(select(a ^ b)) := log10(select(a)) * b,
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log(select(a * b), x) := log(select(a), x) + log(b,x),
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log(select(prod(a,b,c,d)),x) := sum(log(select(a),x),b,c,d),
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log(select(a / b), x) := log(select(a), x) - log(b,x),
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log(select(a ^ b), x) := log(select(a), x) * b,
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log(a, select(b)) := ln(a) / select(ln(b)),
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sin(select(a + b)) := sin(select(a)) cos(b) + cos(a) sin(b),
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sin(select(2 a)) := 2 sin(select(a)) cos(a),
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sin(select(n a)) := 2sin((n-1) select(a)) cos(a) - sin((n-2) a)
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:: integer(n) :: n > 2,
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cos(select(a + b)) := cos(select(a)) cos(b) - sin(a) sin(b),
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cos(select(2 a)) := 2 cos(select(a))^2 - 1,
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cos(select(n a)) := 2cos((n-1) select(a)) cos(a) - cos((n-2) a)
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:: integer(n) :: n > 2,
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tan(select(a + b)) := (tan(select(a)) + tan(b)) /
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(1 - tan(a) tan(b)),
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tan(select(2 a)) := 2 tan(select(a)) / (1 - tan(a)^2),
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tan(select(n a)) := (tan((n-1) select(a)) + tan(a)) /
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(1 - tan((n-1) a) tan(a))
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:: integer(n) :: n > 2,
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sinh(select(a + b)) := sinh(select(a)) cosh(b) + cosh(a) sinh(b),
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cosh(select(a + b)) := cosh(select(a)) cosh(b) + sinh(a) sinh(b),
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tanh(select(a + b)) := (tanh(select(a)) + tanh(b)) /
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(1 + tanh(a) tanh(b)),
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x && select(a || b) := (x && select(a)) || (x && b),
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select(a || b) && x := (select(a) && x) || (b && x),
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! select(a && b) := (!a) || (!b),
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! select(a || b) := (!a) && (!b) ]"))
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(defun calc-MergeRules ()
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"MergeRules"
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(calc-compile-rule-set
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"MergeRules" "[
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iterations(1),
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(x*opt(a)) + select(x*b) := x * (a + select(b)),
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(x*opt(a)) - select(x*b) := x * (a - select(b)),
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sum(select(x)*a,b,c,d) := x * sum(select(a),b,c,d),
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(a/x) + select(b/x) := (a + select(b)) / x,
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(a/x) - select(b/x) := (a - select(b)) / x,
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sum(a/select(x),b,c,d) := sum(select(a),b,c,d) / x,
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(a/opt(b)) + select(c/d) := ((select(a)*d) + (b*c)) / (b*d),
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(a/opt(b)) - select(c/d) := ((select(a)*d) - (b*c)) / (b*d),
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(x^opt(a)) * select(x^b) := x ^ (a + select(b)),
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(x^opt(a)) / select(x^b) := x ^ (a - select(b)),
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select(x^a) / (x^opt(b)) := x ^ (select(a) - b),
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prod(select(x)^a,b,c,d) := x ^ sum(select(a),b,c,d),
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select(x^a) / (x^opt(b)) := x ^ (select(a) - b),
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(a^x) * select(b^x) := select((a * b) ^x),
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(a^x) / select(b^x) := select((b / b) ^ x),
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select(a^x) / (b^x) := select((a / b) ^ x),
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prod(a^select(x),b,c,d) := select(prod(a,b,c,d) ^ x),
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(a^x) * select(b^y) := select((a * b^(y-x)) ^x),
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(a^x) / select(b^y) := select((b / b^(y-x)) ^ x),
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select(a^x) / (b^y) := select((a / b^(y-x)) ^ x),
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select(x^a) ^ b := x ^ select(a * b),
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(x^a) ^ select(b) := x ^ select(a * b),
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select(sqrt(a)) ^ b := select(a ^ (b / 2)),
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sqrt(a) ^ select(b) := select(a ^ (b / 2)),
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sqrt(select(a) ^ b) := select(a ^ (b / 2)),
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sqrt(a ^ select(b)) := select(a ^ (b / 2)),
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sqrt(a) * select(sqrt(b)) := select(sqrt(a * b)),
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sqrt(a) / select(sqrt(b)) := select(sqrt(a / b)),
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select(sqrt(a)) / sqrt(b) := select(sqrt(a / b)),
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prod(select(sqrt(a)),b,c,d) := select(sqrt(prod(a,b,c,d))),
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exp(a) * select(exp(b)) := select(exp(a + b)),
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exp(a) / select(exp(b)) := select(exp(a - b)),
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select(exp(a)) / exp(b) := select(exp(a - b)),
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prod(select(exp(a)),b,c,d) := select(exp(sum(a,b,c,d))),
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select(exp(a)) ^ b := select(exp(a * b)),
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exp(a) ^ select(b) := select(exp(a * b)),
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ln(a) + select(ln(b)) := select(ln(a * b)),
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ln(a) - select(ln(b)) := select(ln(a / b)),
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select(ln(a)) - ln(b) := select(ln(a / b)),
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sum(select(ln(a)),b,c,d) := select(ln(prod(a,b,c,d))),
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b * select(ln(a)) := select(ln(a ^ b)),
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select(b) * ln(a) := select(ln(a ^ b)),
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select(ln(a)) / ln(b) := select(log(a, b)),
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ln(a) / select(ln(b)) := select(log(a, b)),
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select(ln(a)) / b := select(ln(a ^ (1/b))),
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ln(a) / select(b) := select(ln(a ^ (1/b))),
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log10(a) + select(log10(b)) := select(log10(a * b)),
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log10(a) - select(log10(b)) := select(log10(a / b)),
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select(log10(a)) - log10(b) := select(log10(a / b)),
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sum(select(log10(a)),b,c,d) := select(log10(prod(a,b,c,d))),
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b * select(log10(a)) := select(log10(a ^ b)),
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select(b) * log10(a) := select(log10(a ^ b)),
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select(log10(a)) / log10(b) := select(log(a, b)),
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log10(a) / select(log10(b)) := select(log(a, b)),
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select(log10(a)) / b := select(log10(a ^ (1/b))),
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log10(a) / select(b) := select(log10(a ^ (1/b))),
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log(a,x) + select(log(b,x)) := select(log(a * b,x)),
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log(a,x) - select(log(b,x)) := select(log(a / b,x)),
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select(log(a,x)) - log(b,x) := select(log(a / b,x)),
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sum(select(log(a,x)),b,c,d) := select(log(prod(a,b,c,d),x)),
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b * select(log(a,x)) := select(log(a ^ b,x)),
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select(b) * log(a,x) := select(log(a ^ b,x)),
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select(log(a,x)) / log(b,x) := select(log(a, b)),
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log(a,x) / select(log(b,x)) := select(log(a, b)),
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select(log(a,x)) / b := select(log(a ^ (1/b),x)),
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log(a,x) / select(b) := select(log(a ^ (1/b),x)),
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select(x && a) || (x && opt(b)) := x && (select(a) || b) ]"))
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(defun calc-NegateRules ()
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"NegateRules"
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(calc-compile-rule-set
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"NegateRules" "[
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iterations(1),
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a + select(x) := a - select(-x),
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a - select(x) := a + select(-x),
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sum(select(x),b,c,d) := -sum(select(-x),b,c,d),
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a * select(x) := -a * select(-x),
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a / select(x) := -a / select(-x),
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select(x) / a := -select(-x) / a,
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prod(select(x),b,c,d) := (-1)^(d-c+1) * prod(select(-x),b,c,d),
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select(x) ^ n := select(-x) ^ a :: integer(n) :: n%2 = 0,
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select(x) ^ n := -(select(-x) ^ a) :: integer(n) :: n%2 = 1,
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select(x) ^ a := (-select(-x)) ^ a,
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a ^ select(x) := (1 / a)^select(-x),
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abs(select(x)) := abs(select(-x)),
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i sqrt(select(x)) := -sqrt(select(-x)),
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sqrt(select(x)) := i sqrt(select(-x)),
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re(select(x)) := -re(select(-x)),
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im(select(x)) := -im(select(-x)),
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conj(select(x)) := -conj(select(-x)),
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trunc(select(x)) := -trunc(select(-x)),
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round(select(x)) := -round(select(-x)),
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floor(select(x)) := -ceil(select(-x)),
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ceil(select(x)) := -floor(select(-x)),
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ftrunc(select(x)) := -ftrunc(select(-x)),
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fround(select(x)) := -fround(select(-x)),
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ffloor(select(x)) := -fceil(select(-x)),
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fceil(select(x)) := -ffloor(select(-x)),
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exp(select(x)) := 1 / exp(select(-x)),
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sin(select(x)) := -sin(select(-x)),
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cos(select(x)) := cos(select(-x)),
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tan(select(x)) := -tan(select(-x)),
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arcsin(select(x)) := -arcsin(select(-x)),
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arccos(select(x)) := 4 arctan(1) - arccos(select(-x)),
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arctan(select(x)) := -arctan(select(-x)),
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sinh(select(x)) := -sinh(select(-x)),
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cosh(select(x)) := cosh(select(-x)),
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tanh(select(x)) := -tanh(select(-x)),
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arcsinh(select(x)) := -arcsinh(select(-x)),
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arctanh(select(x)) := -arctanh(select(-x)),
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select(x) = a := select(-x) = -a,
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select(x) != a := select(-x) != -a,
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select(x) < a := select(-x) > -a,
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select(x) > a := select(-x) < -a,
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select(x) <= a := select(-x) >= -a,
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select(x) >= a := select(-x) <= -a,
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a < select(x) := -a > select(-x),
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a > select(x) := -a < select(-x),
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a <= select(x) := -a >= select(-x),
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a >= select(x) := -a <= select(-x),
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select(x) := -select(-x) ]"))
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(defun calc-InvertRules ()
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"InvertRules"
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(calc-compile-rule-set
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"InvertRules" "[
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iterations(1),
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a * select(x) := a / select(1/x),
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a / select(x) := a * select(1/x),
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select(x) / a := 1 / (select(1/x) a),
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prod(select(x),b,c,d) := 1 / prod(select(1/x),b,c,d),
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abs(select(x)) := 1 / abs(select(1/x)),
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sqrt(select(x)) := 1 / sqrt(select(1/x)),
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ln(select(x)) := -ln(select(1/x)),
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log10(select(x)) := -log10(select(1/x)),
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log(select(x), a) := -log(select(1/x), a),
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log(a, select(x)) := -log(a, select(1/x)),
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arctan(select(x)) := simplify(2 arctan(1))-arctan(select(1/x)),
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select(x) = a := select(1/x) = 1/a,
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select(x) != a := select(1/x) != 1/a,
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select(x) < a := select(1/x) > 1/a,
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select(x) > a := select(1/x) < 1/a,
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select(x) <= a := select(1/x) >= 1/a,
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select(x) >= a := select(1/x) <= 1/a,
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a < select(x) := 1/a > select(1/x),
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a > select(x) := 1/a < select(1/x),
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a <= select(x) := 1/a >= select(1/x),
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a >= select(x) := 1/a <= select(1/x),
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select(x) := 1 / select(1/x) ]"))
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(defun calc-FactorRules ()
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"FactorRules"
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(calc-compile-rule-set
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"FactorRules" "[
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thecoefs(x, [z, a+b, c]) := thefactors(x, [d x + d a/c, (c/d) x + (b/d)])
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:: 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 ]"))
|
|
|
|
;;; calc-rules.el ends here
|