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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, |
114f9c96 | 4 | ;; 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc. |
3132f345 CW |
5 | |
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 | ||
662c9c64 | 11 | ;; GNU Emacs is free software: you can redistribute it and/or modify |
7c671b23 | 12 | ;; it under the terms of the GNU General Public License as published by |
662c9c64 GM |
13 | ;; the Free Software Foundation, either version 3 of the License, or |
14 | ;; (at your option) any later version. | |
7c671b23 | 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 | |
662c9c64 | 22 | ;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>. |
136211a9 | 23 | |
3132f345 | 24 | ;;; Commentary: |
136211a9 | 25 | |
3132f345 | 26 | ;;; Code: |
136211a9 EZ |
27 | |
28 | ;; This file is autoloaded from calc-ext.el. | |
136211a9 | 29 | |
51b5c91c | 30 | (require 'calc-ext) |
136211a9 EZ |
31 | (require 'calc-macs) |
32 | ||
136211a9 EZ |
33 | (defun calc-compile-rule-set (name rules) |
34 | (prog2 | |
35 | (message "Preparing rule set %s..." name) | |
36 | (math-read-plain-expr rules t) | |
bf77c646 | 37 | (message "Preparing rule set %s...done" name))) |
136211a9 EZ |
38 | |
39 | (defun calc-CommuteRules () | |
40 | "CommuteRules" | |
41 | (calc-compile-rule-set | |
42 | "CommuteRules" "[ | |
43 | iterations(1), | |
44 | select(plain(a + b)) := select(plain(b + a)), | |
45 | select(plain(a - b)) := select(plain((-b) + a)), | |
46 | select(plain((1/a) * b)) := select(b / a), | |
47 | select(plain(a * b)) := select(b * a), | |
48 | select((1/a) / b) := select((1/b) / a), | |
49 | select(a / b) := select((1/b) * a), | |
50 | select((a^b) ^ c) := select((a^c) ^ b), | |
51 | select(log(a, b)) := select(1 / log(b, a)), | |
52 | select(plain(a && b)) := select(b && a), | |
53 | select(plain(a || b)) := select(b || a), | |
54 | select(plain(a = b)) := select(b = a), | |
55 | select(plain(a != b)) := select(b != a), | |
56 | select(a < b) := select(b > a), | |
57 | select(a > b) := select(b < a), | |
58 | select(a <= b) := select(b >= a), | |
bf77c646 | 59 | select(a >= b) := select(b <= a) ]")) |
136211a9 EZ |
60 | |
61 | (defun calc-JumpRules () | |
62 | "JumpRules" | |
63 | (calc-compile-rule-set | |
64 | "JumpRules" "[ | |
65 | iterations(1), | |
66 | plain(select(x) = y) := 0 = select(-x) + y, | |
67 | plain(a + select(x) = y) := a = select(-x) + y, | |
68 | plain(a - select(x) = y) := a = select(x) + y, | |
69 | plain(select(x) + a = y) := a = select(-x) + y, | |
70 | plain(a * select(x) = y) := a = y / select(x), | |
71 | plain(a / select(x) = y) := a = select(x) * y, | |
72 | plain(select(x) / a = y) := 1/a = y / select(x), | |
73 | plain(a ^ select(2) = y) := a = select(sqrt(y)), | |
74 | plain(a ^ select(x) = y) := a = y ^ select(1/x), | |
75 | plain(select(x) ^ a = y) := a = log(y, select(x)), | |
76 | plain(log(a, select(x)) = y) := a = select(x) ^ y, | |
77 | plain(log(select(x), a) = y) := a = select(x) ^ (1/y), | |
78 | plain(y = select(x)) := y - select(x) = 0, | |
79 | plain(y = a + select(x)) := y - select(x) = a, | |
80 | plain(y = a - select(x)) := y + select(x) = a, | |
81 | plain(y = select(x) + a) := y - select(x) = a, | |
82 | plain(y = a * select(x)) := y / select(x) = a, | |
83 | plain(y = a / select(x)) := y * select(x) = a, | |
84 | plain(y = select(x) / a) := y / select(x) = 1/a, | |
85 | plain(y = a ^ select(2)) := select(sqrt(y)) = a, | |
86 | plain(y = a ^ select(x)) := y ^ select(1/x) = a, | |
87 | plain(y = select(x) ^ a) := log(y, select(x)) = a, | |
88 | plain(y = log(a, select(x))) := select(x) ^ y = a, | |
bf77c646 | 89 | plain(y = log(select(x), a)) := select(x) ^ (1/y) = a ]")) |
136211a9 EZ |
90 | |
91 | (defun calc-DistribRules () | |
92 | "DistribRules" | |
93 | (calc-compile-rule-set | |
94 | "DistribRules" "[ | |
95 | iterations(1), | |
96 | x * select(a + b) := x*select(a) + x*b, | |
97 | x * select(sum(a,b,c,d)) := sum(x*select(a),b,c,d), | |
98 | x / select(a + b) := 1 / (select(a)/x + b/x), | |
99 | select(a + b) / x := select(a)/x + b/x, | |
100 | sum(select(a),b,c,d) / x := sum(select(a)/x,b,c,d), | |
101 | x ^ select(a + b) := x^select(a) * x^b, | |
102 | x ^ select(sum(a,b,c,d)) := prod(x^select(a),b,c,d), | |
103 | x ^ select(a * b) := (x^a)^select(b), | |
104 | x ^ select(a / b) := (x^a)^select(1/b), | |
105 | select(a + b) ^ n := select(x) | |
106 | :: integer(n) :: n >= 2 | |
107 | :: let(x, expandpow(a+b,n)) | |
108 | :: quote(matches(x,y+z)), | |
109 | select(a + b) ^ x := a*select(a+b)^(x-1) + b*select(a+b)^(x-1), | |
110 | select(a * b) ^ x := a^x * select(b)^x, | |
111 | select(prod(a,b,c,d)) ^ x := prod(select(a)^x,b,c,d), | |
112 | select(a / b) ^ x := select(a)^x / b^x, | |
113 | select(- a) ^ x := (-1)^x * select(a)^x, | |
114 | plain(-select(a + b)) := select(-a) - b, | |
115 | plain(-select(sum(a,b,c,d))) := sum(select(-a),b,c,d), | |
116 | plain(-select(a * b)) := select(-a) * b, | |
117 | plain(-select(a / b)) := select(-a) / b, | |
118 | sqrt(select(a * b)) := sqrt(select(a)) * sqrt(b), | |
119 | sqrt(select(prod(a,b,c,d))) := prod(sqrt(select(a)),b,c,d), | |
120 | sqrt(select(a / b)) := sqrt(select(a)) / sqrt(b), | |
121 | sqrt(select(- a)) := sqrt(-1) sqrt(select(a)), | |
122 | exp(select(a + b)) := exp(select(a)) / exp(-b) :: negative(b), | |
123 | exp(select(a + b)) := exp(select(a)) * exp(b), | |
124 | exp(select(sum(a,b,c,d))) := prod(exp(select(a)),b,c,d), | |
125 | exp(select(a * b)) := exp(select(a)) ^ b :: constant(b), | |
126 | exp(select(a * b)) := exp(select(a)) ^ b, | |
127 | exp(select(a / b)) := exp(select(a)) ^ (1/b), | |
128 | ln(select(a * b)) := ln(select(a)) + ln(b), | |
129 | ln(select(prod(a,b,c,d))) := sum(ln(select(a)),b,c,d), | |
130 | ln(select(a / b)) := ln(select(a)) - ln(b), | |
131 | ln(select(a ^ b)) := ln(select(a)) * b, | |
132 | log10(select(a * b)) := log10(select(a)) + log10(b), | |
133 | log10(select(prod(a,b,c,d))) := sum(log10(select(a)),b,c,d), | |
134 | log10(select(a / b)) := log10(select(a)) - log10(b), | |
135 | log10(select(a ^ b)) := log10(select(a)) * b, | |
136 | log(select(a * b), x) := log(select(a), x) + log(b,x), | |
137 | log(select(prod(a,b,c,d)),x) := sum(log(select(a),x),b,c,d), | |
138 | log(select(a / b), x) := log(select(a), x) - log(b,x), | |
139 | log(select(a ^ b), x) := log(select(a), x) * b, | |
140 | log(a, select(b)) := ln(a) / select(ln(b)), | |
141 | sin(select(a + b)) := sin(select(a)) cos(b) + cos(a) sin(b), | |
142 | sin(select(2 a)) := 2 sin(select(a)) cos(a), | |
143 | sin(select(n a)) := 2sin((n-1) select(a)) cos(a) - sin((n-2) a) | |
144 | :: integer(n) :: n > 2, | |
145 | cos(select(a + b)) := cos(select(a)) cos(b) - sin(a) sin(b), | |
146 | cos(select(2 a)) := 2 cos(select(a))^2 - 1, | |
147 | cos(select(n a)) := 2cos((n-1) select(a)) cos(a) - cos((n-2) a) | |
148 | :: integer(n) :: n > 2, | |
149 | tan(select(a + b)) := (tan(select(a)) + tan(b)) / | |
150 | (1 - tan(a) tan(b)), | |
151 | tan(select(2 a)) := 2 tan(select(a)) / (1 - tan(a)^2), | |
152 | tan(select(n a)) := (tan((n-1) select(a)) + tan(a)) / | |
153 | (1 - tan((n-1) a) tan(a)) | |
154 | :: integer(n) :: n > 2, | |
6fc5a7da JB |
155 | cot(select(a + b)) := (cot(select(a)) cot(b) - 1) / |
156 | (cot(a) + cot(b)), | |
136211a9 EZ |
157 | sinh(select(a + b)) := sinh(select(a)) cosh(b) + cosh(a) sinh(b), |
158 | cosh(select(a + b)) := cosh(select(a)) cosh(b) + sinh(a) sinh(b), | |
159 | tanh(select(a + b)) := (tanh(select(a)) + tanh(b)) / | |
160 | (1 + tanh(a) tanh(b)), | |
6fc5a7da JB |
161 | coth(select(a + b)) := (coth(select(a)) coth(b) + 1) / |
162 | (coth(a) + coth(b)), | |
136211a9 EZ |
163 | x && select(a || b) := (x && select(a)) || (x && b), |
164 | select(a || b) && x := (select(a) && x) || (b && x), | |
165 | ! select(a && b) := (!a) || (!b), | |
bf77c646 | 166 | ! select(a || b) := (!a) && (!b) ]")) |
136211a9 EZ |
167 | |
168 | (defun calc-MergeRules () | |
169 | "MergeRules" | |
170 | (calc-compile-rule-set | |
171 | "MergeRules" "[ | |
172 | iterations(1), | |
173 | (x*opt(a)) + select(x*b) := x * (a + select(b)), | |
174 | (x*opt(a)) - select(x*b) := x * (a - select(b)), | |
175 | sum(select(x)*a,b,c,d) := x * sum(select(a),b,c,d), | |
176 | (a/x) + select(b/x) := (a + select(b)) / x, | |
177 | (a/x) - select(b/x) := (a - select(b)) / x, | |
178 | sum(a/select(x),b,c,d) := sum(select(a),b,c,d) / x, | |
179 | (a/opt(b)) + select(c/d) := ((select(a)*d) + (b*c)) / (b*d), | |
180 | (a/opt(b)) - select(c/d) := ((select(a)*d) - (b*c)) / (b*d), | |
181 | (x^opt(a)) * select(x^b) := x ^ (a + select(b)), | |
182 | (x^opt(a)) / select(x^b) := x ^ (a - select(b)), | |
183 | select(x^a) / (x^opt(b)) := x ^ (select(a) - b), | |
184 | prod(select(x)^a,b,c,d) := x ^ sum(select(a),b,c,d), | |
185 | select(x^a) / (x^opt(b)) := x ^ (select(a) - b), | |
186 | (a^x) * select(b^x) := select((a * b) ^x), | |
187 | (a^x) / select(b^x) := select((b / b) ^ x), | |
188 | select(a^x) / (b^x) := select((a / b) ^ x), | |
189 | prod(a^select(x),b,c,d) := select(prod(a,b,c,d) ^ x), | |
190 | (a^x) * select(b^y) := select((a * b^(y-x)) ^x), | |
191 | (a^x) / select(b^y) := select((b / b^(y-x)) ^ x), | |
192 | select(a^x) / (b^y) := select((a / b^(y-x)) ^ x), | |
193 | select(x^a) ^ b := x ^ select(a * b), | |
194 | (x^a) ^ select(b) := x ^ select(a * b), | |
195 | select(sqrt(a)) ^ b := select(a ^ (b / 2)), | |
196 | sqrt(a) ^ select(b) := select(a ^ (b / 2)), | |
197 | sqrt(select(a) ^ b) := select(a ^ (b / 2)), | |
198 | sqrt(a ^ select(b)) := select(a ^ (b / 2)), | |
199 | sqrt(a) * select(sqrt(b)) := select(sqrt(a * b)), | |
200 | sqrt(a) / select(sqrt(b)) := select(sqrt(a / b)), | |
201 | select(sqrt(a)) / sqrt(b) := select(sqrt(a / b)), | |
202 | prod(select(sqrt(a)),b,c,d) := select(sqrt(prod(a,b,c,d))), | |
203 | exp(a) * select(exp(b)) := select(exp(a + b)), | |
204 | exp(a) / select(exp(b)) := select(exp(a - b)), | |
205 | select(exp(a)) / exp(b) := select(exp(a - b)), | |
206 | prod(select(exp(a)),b,c,d) := select(exp(sum(a,b,c,d))), | |
207 | select(exp(a)) ^ b := select(exp(a * b)), | |
208 | exp(a) ^ select(b) := select(exp(a * b)), | |
209 | ln(a) + select(ln(b)) := select(ln(a * b)), | |
210 | ln(a) - select(ln(b)) := select(ln(a / b)), | |
211 | select(ln(a)) - ln(b) := select(ln(a / b)), | |
212 | sum(select(ln(a)),b,c,d) := select(ln(prod(a,b,c,d))), | |
213 | b * select(ln(a)) := select(ln(a ^ b)), | |
214 | select(b) * ln(a) := select(ln(a ^ b)), | |
215 | select(ln(a)) / ln(b) := select(log(a, b)), | |
216 | ln(a) / select(ln(b)) := select(log(a, b)), | |
217 | select(ln(a)) / b := select(ln(a ^ (1/b))), | |
218 | ln(a) / select(b) := select(ln(a ^ (1/b))), | |
219 | log10(a) + select(log10(b)) := select(log10(a * b)), | |
220 | log10(a) - select(log10(b)) := select(log10(a / b)), | |
221 | select(log10(a)) - log10(b) := select(log10(a / b)), | |
222 | sum(select(log10(a)),b,c,d) := select(log10(prod(a,b,c,d))), | |
223 | b * select(log10(a)) := select(log10(a ^ b)), | |
224 | select(b) * log10(a) := select(log10(a ^ b)), | |
225 | select(log10(a)) / log10(b) := select(log(a, b)), | |
226 | log10(a) / select(log10(b)) := select(log(a, b)), | |
227 | select(log10(a)) / b := select(log10(a ^ (1/b))), | |
228 | log10(a) / select(b) := select(log10(a ^ (1/b))), | |
229 | log(a,x) + select(log(b,x)) := select(log(a * b,x)), | |
230 | log(a,x) - select(log(b,x)) := select(log(a / b,x)), | |
231 | select(log(a,x)) - log(b,x) := select(log(a / b,x)), | |
232 | sum(select(log(a,x)),b,c,d) := select(log(prod(a,b,c,d),x)), | |
233 | b * select(log(a,x)) := select(log(a ^ b,x)), | |
234 | select(b) * log(a,x) := select(log(a ^ b,x)), | |
235 | select(log(a,x)) / log(b,x) := select(log(a, b)), | |
236 | log(a,x) / select(log(b,x)) := select(log(a, b)), | |
237 | select(log(a,x)) / b := select(log(a ^ (1/b),x)), | |
238 | log(a,x) / select(b) := select(log(a ^ (1/b),x)), | |
bf77c646 | 239 | select(x && a) || (x && opt(b)) := x && (select(a) || b) ]")) |
136211a9 EZ |
240 | |
241 | (defun calc-NegateRules () | |
242 | "NegateRules" | |
243 | (calc-compile-rule-set | |
244 | "NegateRules" "[ | |
245 | iterations(1), | |
246 | a + select(x) := a - select(-x), | |
247 | a - select(x) := a + select(-x), | |
248 | sum(select(x),b,c,d) := -sum(select(-x),b,c,d), | |
249 | a * select(x) := -a * select(-x), | |
250 | a / select(x) := -a / select(-x), | |
251 | select(x) / a := -select(-x) / a, | |
252 | prod(select(x),b,c,d) := (-1)^(d-c+1) * prod(select(-x),b,c,d), | |
253 | select(x) ^ n := select(-x) ^ a :: integer(n) :: n%2 = 0, | |
254 | select(x) ^ n := -(select(-x) ^ a) :: integer(n) :: n%2 = 1, | |
255 | select(x) ^ a := (-select(-x)) ^ a, | |
256 | a ^ select(x) := (1 / a)^select(-x), | |
257 | abs(select(x)) := abs(select(-x)), | |
258 | i sqrt(select(x)) := -sqrt(select(-x)), | |
259 | sqrt(select(x)) := i sqrt(select(-x)), | |
260 | re(select(x)) := -re(select(-x)), | |
261 | im(select(x)) := -im(select(-x)), | |
262 | conj(select(x)) := -conj(select(-x)), | |
263 | trunc(select(x)) := -trunc(select(-x)), | |
264 | round(select(x)) := -round(select(-x)), | |
265 | floor(select(x)) := -ceil(select(-x)), | |
266 | ceil(select(x)) := -floor(select(-x)), | |
267 | ftrunc(select(x)) := -ftrunc(select(-x)), | |
268 | fround(select(x)) := -fround(select(-x)), | |
269 | ffloor(select(x)) := -fceil(select(-x)), | |
270 | fceil(select(x)) := -ffloor(select(-x)), | |
271 | exp(select(x)) := 1 / exp(select(-x)), | |
272 | sin(select(x)) := -sin(select(-x)), | |
273 | cos(select(x)) := cos(select(-x)), | |
274 | tan(select(x)) := -tan(select(-x)), | |
6fc5a7da JB |
275 | sec(select(x)) := sec(select(-x)), |
276 | csc(select(x)) := -csc(select(-x)), | |
277 | cot(select(x)) := -cot(select(-x)), | |
136211a9 EZ |
278 | arcsin(select(x)) := -arcsin(select(-x)), |
279 | arccos(select(x)) := 4 arctan(1) - arccos(select(-x)), | |
280 | arctan(select(x)) := -arctan(select(-x)), | |
281 | sinh(select(x)) := -sinh(select(-x)), | |
282 | cosh(select(x)) := cosh(select(-x)), | |
283 | tanh(select(x)) := -tanh(select(-x)), | |
6fc5a7da JB |
284 | sech(select(x)) := sech(select(-x)), |
285 | csch(select(x)) := -csch(select(-x)), | |
286 | coth(select(x)) := -coth(select(-x)), | |
136211a9 EZ |
287 | arcsinh(select(x)) := -arcsinh(select(-x)), |
288 | arctanh(select(x)) := -arctanh(select(-x)), | |
289 | select(x) = a := select(-x) = -a, | |
290 | select(x) != a := select(-x) != -a, | |
291 | select(x) < a := select(-x) > -a, | |
292 | select(x) > a := select(-x) < -a, | |
293 | select(x) <= a := select(-x) >= -a, | |
294 | select(x) >= a := select(-x) <= -a, | |
295 | a < select(x) := -a > select(-x), | |
296 | a > select(x) := -a < select(-x), | |
297 | a <= select(x) := -a >= select(-x), | |
298 | a >= select(x) := -a <= select(-x), | |
bf77c646 | 299 | select(x) := -select(-x) ]")) |
136211a9 EZ |
300 | |
301 | (defun calc-InvertRules () | |
302 | "InvertRules" | |
303 | (calc-compile-rule-set | |
304 | "InvertRules" "[ | |
305 | iterations(1), | |
306 | a * select(x) := a / select(1/x), | |
307 | a / select(x) := a * select(1/x), | |
308 | select(x) / a := 1 / (select(1/x) a), | |
309 | prod(select(x),b,c,d) := 1 / prod(select(1/x),b,c,d), | |
310 | abs(select(x)) := 1 / abs(select(1/x)), | |
311 | sqrt(select(x)) := 1 / sqrt(select(1/x)), | |
312 | ln(select(x)) := -ln(select(1/x)), | |
313 | log10(select(x)) := -log10(select(1/x)), | |
314 | log(select(x), a) := -log(select(1/x), a), | |
315 | log(a, select(x)) := -log(a, select(1/x)), | |
316 | arctan(select(x)) := simplify(2 arctan(1))-arctan(select(1/x)), | |
317 | select(x) = a := select(1/x) = 1/a, | |
318 | select(x) != a := select(1/x) != 1/a, | |
319 | select(x) < a := select(1/x) > 1/a, | |
320 | select(x) > a := select(1/x) < 1/a, | |
321 | select(x) <= a := select(1/x) >= 1/a, | |
322 | select(x) >= a := select(1/x) <= 1/a, | |
323 | a < select(x) := 1/a > select(1/x), | |
324 | a > select(x) := 1/a < select(1/x), | |
325 | a <= select(x) := 1/a >= select(1/x), | |
326 | a >= select(x) := 1/a <= select(1/x), | |
bf77c646 | 327 | select(x) := 1 / select(1/x) ]")) |
136211a9 EZ |
328 | |
329 | ||
330 | (defun calc-FactorRules () | |
331 | "FactorRules" | |
332 | (calc-compile-rule-set | |
333 | "FactorRules" "[ | |
334 | thecoefs(x, [z, a+b, c]) := thefactors(x, [d x + d a/c, (c/d) x + (b/d)]) | |
335 | :: z = a b/c :: let(d := pgcd(pcont(c), pcont(b))), | |
336 | thecoefs(x, [z, a, c]) := thefactors(x, [(r x + a/(2 r))^2]) | |
337 | :: z = (a/2)^2/c :: let(r := esimplify(sqrt(c))) | |
338 | :: !matches(r, sqrt(rr)), | |
339 | thecoefs(x, [z, 0, c]) := thefactors(x, [rc x + rz, rc x - rz]) | |
340 | :: negative(z) | |
341 | :: let(rz := esimplify(sqrt(-z))) :: !matches(rz, sqrt(rzz)) | |
342 | :: let(rc := esimplify(sqrt(c))) :: !matches(rc, sqrt(rcc)), | |
343 | thecoefs(x, [z, 0, c]) := thefactors(x, [rz + rc x, rz - rc x]) | |
344 | :: negative(c) | |
345 | :: let(rz := esimplify(sqrt(z))) :: !matches(rz, sqrt(rzz)) | |
346 | :: let(rc := esimplify(sqrt(-c))) :: !matches(rc, sqrt(rcc)) | |
bf77c646 | 347 | ]")) |
136211a9 EZ |
348 | ;;(setq var-FactorRules 'calc-FactorRules) |
349 | ||
350 | ||
351 | (defun calc-IntegAfterRules () | |
352 | "IntegAfterRules" | |
353 | (calc-compile-rule-set | |
354 | "IntegAfterRules" "[ | |
355 | opt(a) ln(x) + opt(b) ln(y) := 2 a esimplify(arctanh(x-1)) | |
356 | :: a + b = 0 :: nrat(x + y) = 2 || nrat(x - y) = 2, | |
357 | a * (b + c) := a b + a c :: constant(a) | |
bf77c646 | 358 | ]")) |
136211a9 EZ |
359 | |
360 | ;;(setq var-IntegAfterRules 'calc-IntegAfterRules) | |
361 | ||
362 | ||
363 | (defun calc-FitRules () | |
364 | "FitRules" | |
365 | (calc-compile-rule-set | |
366 | "FitRules" "[ | |
367 | ||
368 | schedule(1,2,3,4), | |
369 | iterations(inf), | |
370 | ||
371 | phase(1), | |
372 | e^x := exp(x), | |
373 | x^y := exp(y ln(x)) :: !istrue(constant(y)), | |
374 | x/y := x fitinv(y), | |
375 | fitinv(x y) := fitinv(x) fitinv(y), | |
376 | exp(a) exp(b) := exp(a + b), | |
377 | a exp(b) := exp(ln(a) + b) :: !hasfitvars(a), | |
378 | fitinv(exp(a)) := exp(-a), | |
379 | ln(a b) := ln(a) + ln(b), | |
380 | ln(fitinv(a)) := -ln(a), | |
381 | log10(a b) := log10(a) + log10(b), | |
382 | log10(fitinv(a)) := -log10(a), | |
383 | log(a,b) := ln(a)/ln(b), | |
384 | ln(exp(a)) := a, | |
385 | a*(b+c) := a*b + a*c, | |
386 | (a+b)^n := x :: integer(n) :: n >= 2 | |
387 | :: let(x, expandpow(a+b,n)) | |
388 | :: quote(matches(x,y+z)), | |
389 | ||
390 | phase(1,2), | |
391 | fitmodel(y = x) := fitmodel(0, y - x), | |
392 | fitmodel(y, x+c) := fitmodel(y-c, x) :: !hasfitparams(c), | |
393 | fitmodel(y, x c) := fitmodel(y/c, x) :: !hasfitparams(c), | |
394 | fitmodel(y, x/(c opt(d))) := fitmodel(y c, x/d) :: !hasfitparams(c), | |
395 | fitmodel(y, apply(f,[x])) := fitmodel(yy, x) | |
396 | :: hasfitparams(x) | |
397 | :: let(FTemp() = yy, | |
398 | solve(apply(f,[FTemp()]) = y, | |
399 | FTemp())), | |
400 | fitmodel(y, apply(f,[x,c])) := fitmodel(yy, x) | |
401 | :: !hasfitparams(c) | |
402 | :: let(FTemp() = yy, | |
403 | solve(apply(f,[FTemp(),c]) = y, | |
404 | FTemp())), | |
405 | fitmodel(y, apply(f,[c,x])) := fitmodel(yy, x) | |
406 | :: !hasfitparams(c) | |
407 | :: let(FTemp() = yy, | |
408 | solve(apply(f,[c,FTemp()]) = y, | |
409 | FTemp())), | |
410 | ||
411 | phase(2,3), | |
412 | fitmodel(y, x) := fitsystem(y, [], [], fitpart(1,1,x)), | |
413 | fitpart(a,b,plain(x + y)) := fitpart(a,b,x) + fitpart(a,b,y), | |
414 | fitpart(a,b,plain(x - y)) := fitpart(a,b,x) + fitpart(-a,b,y), | |
415 | fitpart(a,b,plain(-x)) := fitpart(-a,b,x), | |
416 | fitpart(a,b,x opt(c)) := fitpart(a,x b,c) :: !hasfitvars(x), | |
417 | fitpart(a,x opt(b),c) := fitpart(x a,b,c) :: !hasfitparams(x), | |
418 | fitpart(a,x y + x opt(z),c) := fitpart(a,x*(y+z),c), | |
419 | fitpart(a,b,c) := fitpart2(a,b,c), | |
420 | ||
421 | phase(3), | |
422 | fitpart2(a1,b1,x) + fitpart2(a2,b2,x) := fitpart(1, a1 b1 + a2 b2, x), | |
423 | fitpart2(a1,x,c1) + fitpart2(a2,x,c2) := fitpart2(1, x, a1 c1 + a2 c2), | |
424 | ||
425 | phase(4), | |
426 | fitinv(x) := 1 / x, | |
427 | exp(x + ln(y)) := y exp(x), | |
428 | exp(x ln(y)) := y^x, | |
429 | ln(x) + ln(y) := ln(x y), | |
430 | ln(x) - ln(y) := ln(x/y), | |
431 | x*y + x*z := x*(y+z), | |
432 | fitsystem(y, xv, pv, fitpart2(a,fitparam(b),c) + opt(d)) | |
433 | := fitsystem(y, rcons(xv, a c), | |
434 | rcons(pv, fitdummy(b) = fitparam(b)), d) | |
435 | :: b = vlen(pv)+1, | |
436 | fitsystem(y, xv, pv, fitpart2(a,b,c) + opt(d)) | |
437 | := fitsystem(y, rcons(xv, a c), | |
438 | rcons(pv, fitdummy(vlen(pv)+1) = b), d), | |
439 | fitsystem(y, xv, pv, 0) := fitsystem(y, xv, cons(fvh,fvt)) | |
440 | :: !hasfitparams(xv) | |
441 | :: let(cons(fvh,fvt), | |
442 | solve(pv, table(fitparam(j), j, 1, | |
443 | hasfitparams(pv)))), | |
bf77c646 | 444 | fitparam(n) = x := x ]")) |
136211a9 | 445 | |
51b5c91c JB |
446 | (provide 'calc-rules) |
447 | ||
cbee283d | 448 | ;; arch-tag: 0ed54a52-38f3-4ed7-9ca7-b8ecf8f2febe |
bf77c646 | 449 | ;;; calc-rules.el ends here |