HCoop / bpt / emacs.git / blame
| Commit | Line | Data |
|---|---|---|
| a1506d29 | 1 | ;;; calc-alg.el --- algebraic functions for Calc |
| 3132f345 | 2 | |
| d3896480 | 3 | ;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc. |
| 3132f345 CW |
4 | |
| 5 | ;; Author: David Gillespie <daveg@synaptics.com> | |
| a1506d29 | 6 | ;; Maintainers: D. Goel <deego@gnufans.org> |
| 6e1c888a | 7 | ;; Colin Walters <walters@debian.org> |
| 136211a9 EZ |
8 | |
| 9 | ;; This file is part of GNU Emacs. | |
| 10 | ||
| 11 | ;; GNU Emacs is distributed in the hope that it will be useful, | |
| 12 | ;; but WITHOUT ANY WARRANTY. No author or distributor | |
| 13 | ;; accepts responsibility to anyone for the consequences of using it | |
| 14 | ;; or for whether it serves any particular purpose or works at all, | |
| 15 | ;; unless he says so in writing. Refer to the GNU Emacs General Public | |
| 16 | ;; License for full details. | |
| 17 | ||
| 18 | ;; Everyone is granted permission to copy, modify and redistribute | |
| 19 | ;; GNU Emacs, but only under the conditions described in the | |
| 20 | ;; GNU Emacs General Public License. A copy of this license is | |
| 21 | ;; supposed to have been given to you along with GNU Emacs so you | |
| 22 | ;; can know your rights and responsibilities. It should be in a | |
| 23 | ;; file named COPYING. Among other things, the copyright notice | |
| 24 | ;; and this notice must be preserved on all copies. | |
| 25 | ||
| 3132f345 | 26 | ;;; Commentary: |
| 136211a9 | 27 | |
| 3132f345 | 28 | ;;; Code: |
| 136211a9 EZ |
29 | |
| 30 | ;; This file is autoloaded from calc-ext.el. | |
| 31 | (require 'calc-ext) | |
| 32 | ||
| 33 | (require 'calc-macs) | |
| 34 | ||
| 35 | (defun calc-Need-calc-alg () nil) | |
| 36 | ||
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37 | ;;; Algebra commands. |
| 38 | ||
| 39 | (defun calc-alg-evaluate (arg) | |
| 40 | (interactive "p") | |
| 41 | (calc-slow-wrapper | |
| 42 | (calc-with-default-simplification | |
| 43 | (let ((math-simplify-only nil)) | |
| 44 | (calc-modify-simplify-mode arg) | |
| d3896480 | 45 | (calc-enter-result 1 "dsmp" (calc-top 1)))))) |
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46 | |
| 47 | (defun calc-modify-simplify-mode (arg) | |
| 48 | (if (= (math-abs arg) 2) | |
| 49 | (setq calc-simplify-mode 'alg) | |
| 50 | (if (>= (math-abs arg) 3) | |
| 51 | (setq calc-simplify-mode 'ext))) | |
| 52 | (if (< arg 0) | |
| d3896480 | 53 | (setq calc-simplify-mode (list calc-simplify-mode)))) |
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54 | |
| 55 | (defun calc-simplify () | |
| 56 | (interactive) | |
| 57 | (calc-slow-wrapper | |
| 58 | (calc-with-default-simplification | |
| d3896480 | 59 | (calc-enter-result 1 "simp" (math-simplify (calc-top-n 1)))))) |
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60 | |
| 61 | (defun calc-simplify-extended () | |
| 62 | (interactive) | |
| 63 | (calc-slow-wrapper | |
| 64 | (calc-with-default-simplification | |
| d3896480 | 65 | (calc-enter-result 1 "esmp" (math-simplify-extended (calc-top-n 1)))))) |
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66 | |
| 67 | (defun calc-expand-formula (arg) | |
| 68 | (interactive "p") | |
| 69 | (calc-slow-wrapper | |
| 70 | (calc-with-default-simplification | |
| 71 | (let ((math-simplify-only nil)) | |
| 72 | (calc-modify-simplify-mode arg) | |
| a1506d29 | 73 | (calc-enter-result 1 "expf" |
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74 | (if (> arg 0) |
| 75 | (let ((math-expand-formulas t)) | |
| 76 | (calc-top-n 1)) | |
| 77 | (let ((top (calc-top-n 1))) | |
| 78 | (or (math-expand-formula top) | |
| d3896480 | 79 | top)))))))) |
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80 | |
| 81 | (defun calc-factor (arg) | |
| 82 | (interactive "P") | |
| 83 | (calc-slow-wrapper | |
| 84 | (calc-unary-op "fctr" (if (calc-is-hyperbolic) | |
| 85 | 'calcFunc-factors 'calcFunc-factor) | |
| d3896480 | 86 | arg))) |
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87 | |
| 88 | (defun calc-expand (n) | |
| 89 | (interactive "P") | |
| 90 | (calc-slow-wrapper | |
| 91 | (calc-enter-result 1 "expa" | |
| 92 | (append (list 'calcFunc-expand | |
| 93 | (calc-top-n 1)) | |
| d3896480 | 94 | (and n (list (prefix-numeric-value n))))))) |
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95 | |
| 96 | (defun calc-collect (&optional var) | |
| 97 | (interactive "sCollect terms involving: ") | |
| 98 | (calc-slow-wrapper | |
| 99 | (if (or (equal var "") (equal var "$") (null var)) | |
| 100 | (calc-enter-result 2 "clct" (cons 'calcFunc-collect | |
| 101 | (calc-top-list-n 2))) | |
| 102 | (let ((var (math-read-expr var))) | |
| 103 | (if (eq (car-safe var) 'error) | |
| 104 | (error "Bad format in expression: %s" (nth 1 var))) | |
| 105 | (calc-enter-result 1 "clct" (list 'calcFunc-collect | |
| 106 | (calc-top-n 1) | |
| d3896480 | 107 | var)))))) |
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108 | |
| 109 | (defun calc-apart (arg) | |
| 110 | (interactive "P") | |
| 111 | (calc-slow-wrapper | |
| d3896480 | 112 | (calc-unary-op "aprt" 'calcFunc-apart arg))) |
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113 | |
| 114 | (defun calc-normalize-rat (arg) | |
| 115 | (interactive "P") | |
| 116 | (calc-slow-wrapper | |
| d3896480 | 117 | (calc-unary-op "nrat" 'calcFunc-nrat arg))) |
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118 | |
| 119 | (defun calc-poly-gcd (arg) | |
| 120 | (interactive "P") | |
| 121 | (calc-slow-wrapper | |
| d3896480 | 122 | (calc-binary-op "pgcd" 'calcFunc-pgcd arg))) |
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123 | |
| 124 | (defun calc-poly-div (arg) | |
| 125 | (interactive "P") | |
| 126 | (calc-slow-wrapper | |
| 127 | (setq calc-poly-div-remainder nil) | |
| 128 | (calc-binary-op "pdiv" 'calcFunc-pdiv arg) | |
| 129 | (if (and calc-poly-div-remainder (null arg)) | |
| 130 | (progn | |
| 131 | (calc-clear-command-flag 'clear-message) | |
| 132 | (calc-record calc-poly-div-remainder "prem") | |
| 133 | (if (not (Math-zerop calc-poly-div-remainder)) | |
| 134 | (message "(Remainder was %s)" | |
| 135 | (math-format-flat-expr calc-poly-div-remainder 0)) | |
| d3896480 | 136 | (message "(No remainder)")))))) |
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137 | |
| 138 | (defun calc-poly-rem (arg) | |
| 139 | (interactive "P") | |
| 140 | (calc-slow-wrapper | |
| d3896480 | 141 | (calc-binary-op "prem" 'calcFunc-prem arg))) |
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142 | |
| 143 | (defun calc-poly-div-rem (arg) | |
| 144 | (interactive "P") | |
| 145 | (calc-slow-wrapper | |
| 146 | (if (calc-is-hyperbolic) | |
| 147 | (calc-binary-op "pdvr" 'calcFunc-pdivide arg) | |
| d3896480 | 148 | (calc-binary-op "pdvr" 'calcFunc-pdivrem arg)))) |
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149 | |
| 150 | (defun calc-substitute (&optional oldname newname) | |
| 151 | (interactive "sSubstitute old: ") | |
| 152 | (calc-slow-wrapper | |
| 153 | (let (old new (num 1) expr) | |
| 154 | (if (or (equal oldname "") (equal oldname "$") (null oldname)) | |
| 155 | (setq new (calc-top-n 1) | |
| 156 | old (calc-top-n 2) | |
| 157 | expr (calc-top-n 3) | |
| 158 | num 3) | |
| 159 | (or newname | |
| 160 | (progn (calc-unread-command ?\C-a) | |
| 161 | (setq newname (read-string (concat "Substitute old: " | |
| 162 | oldname | |
| 163 | ", new: ") | |
| 164 | oldname)))) | |
| 165 | (if (or (equal newname "") (equal newname "$") (null newname)) | |
| 166 | (setq new (calc-top-n 1) | |
| 167 | expr (calc-top-n 2) | |
| 168 | num 2) | |
| 169 | (setq new (if (stringp newname) (math-read-expr newname) newname)) | |
| 170 | (if (eq (car-safe new) 'error) | |
| 171 | (error "Bad format in expression: %s" (nth 1 new))) | |
| 172 | (setq expr (calc-top-n 1))) | |
| 173 | (setq old (if (stringp oldname) (math-read-expr oldname) oldname)) | |
| 174 | (if (eq (car-safe old) 'error) | |
| 175 | (error "Bad format in expression: %s" (nth 1 old))) | |
| 176 | (or (math-expr-contains expr old) | |
| 3132f345 | 177 | (error "No occurrences found"))) |
| d3896480 | 178 | (calc-enter-result num "sbst" (math-expr-subst expr old new))))) |
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179 | |
| 180 | ||
| 181 | (defun calc-has-rules (name) | |
| 182 | (setq name (calc-var-value name)) | |
| 183 | (and (consp name) | |
| 184 | (memq (car name) '(vec calcFunc-assign calcFunc-condition)) | |
| d3896480 | 185 | name)) |
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186 | |
| 187 | (defun math-recompile-eval-rules () | |
| 188 | (setq math-eval-rules-cache (and (calc-has-rules 'var-EvalRules) | |
| 189 | (math-compile-rewrites | |
| 190 | '(var EvalRules var-EvalRules))) | |
| 191 | math-eval-rules-cache-other (assq nil math-eval-rules-cache) | |
| d3896480 | 192 | math-eval-rules-cache-tag (calc-var-value 'var-EvalRules))) |
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193 | |
| 194 | ||
| 195 | ;;; Try to expand a formula according to its definition. | |
| 196 | (defun math-expand-formula (expr) | |
| 197 | (and (consp expr) | |
| 198 | (symbolp (car expr)) | |
| 199 | (or (get (car expr) 'calc-user-defn) | |
| 200 | (get (car expr) 'math-expandable)) | |
| 201 | (let ((res (let ((math-expand-formulas t)) | |
| 202 | (apply (car expr) (cdr expr))))) | |
| 203 | (and (not (eq (car-safe res) (car expr))) | |
| d3896480 | 204 | res)))) |
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205 | |
| 206 | ||
| 207 | ||
| 208 | ||
| 209 | ;;; True if A comes before B in a canonical ordering of expressions. [P X X] | |
| 210 | (defun math-beforep (a b) ; [Public] | |
| 211 | (cond ((and (Math-realp a) (Math-realp b)) | |
| 212 | (let ((comp (math-compare a b))) | |
| 213 | (or (eq comp -1) | |
| 214 | (and (eq comp 0) | |
| 215 | (not (equal a b)) | |
| 216 | (> (length (memq (car-safe a) | |
| 217 | '(bigneg nil bigpos frac float))) | |
| 218 | (length (memq (car-safe b) | |
| 219 | '(bigneg nil bigpos frac float)))))))) | |
| 220 | ((equal b '(neg (var inf var-inf))) nil) | |
| 221 | ((equal a '(neg (var inf var-inf))) t) | |
| 222 | ((equal a '(var inf var-inf)) nil) | |
| 223 | ((equal b '(var inf var-inf)) t) | |
| 224 | ((Math-realp a) | |
| 225 | (if (and (eq (car-safe b) 'intv) (math-intv-constp b)) | |
| 226 | (if (or (math-beforep a (nth 2 b)) (Math-equal a (nth 2 b))) | |
| 227 | t | |
| 228 | nil) | |
| 229 | t)) | |
| 230 | ((Math-realp b) | |
| 231 | (if (and (eq (car-safe a) 'intv) (math-intv-constp a)) | |
| 232 | (if (math-beforep (nth 2 a) b) | |
| 233 | t | |
| 234 | nil) | |
| 235 | nil)) | |
| 236 | ((and (eq (car a) 'intv) (eq (car b) 'intv) | |
| 237 | (math-intv-constp a) (math-intv-constp b)) | |
| 238 | (let ((comp (math-compare (nth 2 a) (nth 2 b)))) | |
| 239 | (cond ((eq comp -1) t) | |
| 240 | ((eq comp 1) nil) | |
| 241 | ((and (memq (nth 1 a) '(2 3)) (memq (nth 1 b) '(0 1))) t) | |
| 242 | ((and (memq (nth 1 a) '(0 1)) (memq (nth 1 b) '(2 3))) nil) | |
| 243 | ((eq (setq comp (math-compare (nth 3 a) (nth 3 b))) -1) t) | |
| 244 | ((eq comp 1) nil) | |
| 245 | ((and (memq (nth 1 a) '(0 2)) (memq (nth 1 b) '(1 3))) t) | |
| 246 | (t nil)))) | |
| 247 | ((not (eq (not (Math-objectp a)) (not (Math-objectp b)))) | |
| 248 | (Math-objectp a)) | |
| 249 | ((eq (car a) 'var) | |
| 250 | (if (eq (car b) 'var) | |
| 251 | (string-lessp (symbol-name (nth 1 a)) (symbol-name (nth 1 b))) | |
| 252 | (not (Math-numberp b)))) | |
| 253 | ((eq (car b) 'var) (Math-numberp a)) | |
| 254 | ((eq (car a) (car b)) | |
| 255 | (while (and (setq a (cdr a) b (cdr b)) a | |
| 256 | (equal (car a) (car b)))) | |
| 257 | (and b | |
| 258 | (or (null a) | |
| 259 | (math-beforep (car a) (car b))))) | |
| d3896480 | 260 | (t (string-lessp (symbol-name (car a)) (symbol-name (car b)))))) |
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261 | |
| 262 | ||
| d3896480 | 263 | (defsubst math-simplify-extended (a) |
| 136211a9 | 264 | (let ((math-living-dangerously t)) |
| d3896480 CW |
265 | (math-simplify a))) |
| 266 | ||
| 267 | (defalias 'calcFunc-esimplify 'math-simplify-extended) | |
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268 | |
| 269 | (defun math-simplify (top-expr) | |
| 270 | (let ((math-simplifying t) | |
| 271 | (top-only (consp calc-simplify-mode)) | |
| 272 | (simp-rules (append (and (calc-has-rules 'var-AlgSimpRules) | |
| 273 | '((var AlgSimpRules var-AlgSimpRules))) | |
| 274 | (and math-living-dangerously | |
| 275 | (calc-has-rules 'var-ExtSimpRules) | |
| 276 | '((var ExtSimpRules var-ExtSimpRules))) | |
| 277 | (and math-simplifying-units | |
| 278 | (calc-has-rules 'var-UnitSimpRules) | |
| 279 | '((var UnitSimpRules var-UnitSimpRules))) | |
| 280 | (and math-integrating | |
| 281 | (calc-has-rules 'var-IntegSimpRules) | |
| 282 | '((var IntegSimpRules var-IntegSimpRules))))) | |
| 283 | res) | |
| 284 | (if top-only | |
| 285 | (let ((r simp-rules)) | |
| 286 | (setq res (math-simplify-step (math-normalize top-expr)) | |
| 287 | calc-simplify-mode '(nil) | |
| 288 | top-expr (math-normalize res)) | |
| 289 | (while r | |
| 290 | (setq top-expr (math-rewrite top-expr (car r) | |
| 291 | '(neg (var inf var-inf))) | |
| 292 | r (cdr r)))) | |
| 293 | (calc-with-default-simplification | |
| 294 | (while (let ((r simp-rules)) | |
| 295 | (setq res (math-normalize top-expr)) | |
| 296 | (while r | |
| 297 | (setq res (math-rewrite res (car r)) | |
| 298 | r (cdr r))) | |
| 299 | (not (equal top-expr (setq res (math-simplify-step res))))) | |
| 300 | (setq top-expr res))))) | |
| d3896480 CW |
301 | top-expr) |
| 302 | ||
| 303 | (defalias 'calcFunc-simplify 'math-simplify) | |
| 136211a9 EZ |
304 | |
| 305 | ;;; The following has a "bug" in that if any recursive simplifications | |
| 306 | ;;; occur only the first handler will be tried; this doesn't really | |
| 307 | ;;; matter, since math-simplify-step is iterated to a fixed point anyway. | |
| 308 | (defun math-simplify-step (a) | |
| 309 | (if (Math-primp a) | |
| 310 | a | |
| 311 | (let ((aa (if (or top-only | |
| 312 | (memq (car a) '(calcFunc-quote calcFunc-condition | |
| 313 | calcFunc-evalto))) | |
| 314 | a | |
| 315 | (cons (car a) (mapcar 'math-simplify-step (cdr a)))))) | |
| 316 | (and (symbolp (car aa)) | |
| 317 | (let ((handler (get (car aa) 'math-simplify))) | |
| 318 | (and handler | |
| 319 | (while (and handler | |
| 320 | (equal (setq aa (or (funcall (car handler) aa) | |
| 321 | aa)) | |
| 322 | a)) | |
| 323 | (setq handler (cdr handler)))))) | |
| d3896480 | 324 | aa))) |
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325 | |
| 326 | ||
| d3896480 | 327 | ;; Placeholder, to synchronize autoloading. |
| 136211a9 | 328 | (defun math-need-std-simps () |
| d3896480 | 329 | nil) |
| 136211a9 EZ |
330 | |
| 331 | (math-defsimplify (+ -) | |
| 332 | (math-simplify-plus)) | |
| 333 | ||
| 334 | (defun math-simplify-plus () | |
| 335 | (cond ((and (memq (car-safe (nth 1 expr)) '(+ -)) | |
| 336 | (Math-numberp (nth 2 (nth 1 expr))) | |
| 337 | (not (Math-numberp (nth 2 expr)))) | |
| 338 | (let ((x (nth 2 expr)) | |
| 339 | (op (car expr))) | |
| 340 | (setcar (cdr (cdr expr)) (nth 2 (nth 1 expr))) | |
| 341 | (setcar expr (car (nth 1 expr))) | |
| 342 | (setcar (cdr (cdr (nth 1 expr))) x) | |
| 343 | (setcar (nth 1 expr) op))) | |
| 344 | ((and (eq (car expr) '+) | |
| 345 | (Math-numberp (nth 1 expr)) | |
| 346 | (not (Math-numberp (nth 2 expr)))) | |
| 347 | (let ((x (nth 2 expr))) | |
| 348 | (setcar (cdr (cdr expr)) (nth 1 expr)) | |
| 349 | (setcar (cdr expr) x)))) | |
| 350 | (let ((aa expr) | |
| 351 | aaa temp) | |
| 352 | (while (memq (car-safe (setq aaa (nth 1 aa))) '(+ -)) | |
| 353 | (if (setq temp (math-combine-sum (nth 2 aaa) (nth 2 expr) | |
| 354 | (eq (car aaa) '-) (eq (car expr) '-) t)) | |
| 355 | (progn | |
| 356 | (setcar (cdr (cdr expr)) temp) | |
| 357 | (setcar expr '+) | |
| 358 | (setcar (cdr (cdr aaa)) 0))) | |
| 359 | (setq aa (nth 1 aa))) | |
| 360 | (if (setq temp (math-combine-sum aaa (nth 2 expr) | |
| 361 | nil (eq (car expr) '-) t)) | |
| 362 | (progn | |
| 363 | (setcar (cdr (cdr expr)) temp) | |
| 364 | (setcar expr '+) | |
| 365 | (setcar (cdr aa) 0))) | |
| d3896480 | 366 | expr)) |
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367 | |
| 368 | (math-defsimplify * | |
| 369 | (math-simplify-times)) | |
| 370 | ||
| 371 | (defun math-simplify-times () | |
| 372 | (if (eq (car-safe (nth 2 expr)) '*) | |
| 373 | (and (math-beforep (nth 1 (nth 2 expr)) (nth 1 expr)) | |
| 374 | (or (math-known-scalarp (nth 1 expr) t) | |
| 375 | (math-known-scalarp (nth 1 (nth 2 expr)) t)) | |
| 376 | (let ((x (nth 1 expr))) | |
| 377 | (setcar (cdr expr) (nth 1 (nth 2 expr))) | |
| 378 | (setcar (cdr (nth 2 expr)) x))) | |
| 379 | (and (math-beforep (nth 2 expr) (nth 1 expr)) | |
| 380 | (or (math-known-scalarp (nth 1 expr) t) | |
| 381 | (math-known-scalarp (nth 2 expr) t)) | |
| 382 | (let ((x (nth 2 expr))) | |
| 383 | (setcar (cdr (cdr expr)) (nth 1 expr)) | |
| 384 | (setcar (cdr expr) x)))) | |
| 385 | (let ((aa expr) | |
| 386 | aaa temp | |
| 387 | (safe t) (scalar (math-known-scalarp (nth 1 expr)))) | |
| 388 | (if (and (Math-ratp (nth 1 expr)) | |
| 389 | (setq temp (math-common-constant-factor (nth 2 expr)))) | |
| 390 | (progn | |
| 391 | (setcar (cdr (cdr expr)) | |
| 392 | (math-cancel-common-factor (nth 2 expr) temp)) | |
| 393 | (setcar (cdr expr) (math-mul (nth 1 expr) temp)))) | |
| 394 | (while (and (eq (car-safe (setq aaa (nth 2 aa))) '*) | |
| 395 | safe) | |
| 396 | (if (setq temp (math-combine-prod (nth 1 expr) (nth 1 aaa) nil nil t)) | |
| 397 | (progn | |
| 398 | (setcar (cdr expr) temp) | |
| 399 | (setcar (cdr aaa) 1))) | |
| 400 | (setq safe (or scalar (math-known-scalarp (nth 1 aaa) t)) | |
| 401 | aa (nth 2 aa))) | |
| 402 | (if (and (setq temp (math-combine-prod aaa (nth 1 expr) nil nil t)) | |
| 403 | safe) | |
| 404 | (progn | |
| 405 | (setcar (cdr expr) temp) | |
| 406 | (setcar (cdr (cdr aa)) 1))) | |
| 407 | (if (and (eq (car-safe (nth 1 expr)) 'frac) | |
| 408 | (memq (nth 1 (nth 1 expr)) '(1 -1))) | |
| 409 | (math-div (math-mul (nth 2 expr) (nth 1 (nth 1 expr))) | |
| 410 | (nth 2 (nth 1 expr))) | |
| d3896480 | 411 | expr))) |
| 136211a9 EZ |
412 | |
| 413 | (math-defsimplify / | |
| 414 | (math-simplify-divide)) | |
| 415 | ||
| 416 | (defun math-simplify-divide () | |
| 417 | (let ((np (cdr expr)) | |
| 418 | (nover nil) | |
| 419 | (nn (and (or (eq (car expr) '/) (not (Math-realp (nth 2 expr)))) | |
| 420 | (math-common-constant-factor (nth 2 expr)))) | |
| 421 | n op) | |
| 422 | (if nn | |
| 423 | (progn | |
| 424 | (setq n (and (or (eq (car expr) '/) (not (Math-realp (nth 1 expr)))) | |
| 425 | (math-common-constant-factor (nth 1 expr)))) | |
| 426 | (if (and (eq (car-safe nn) 'frac) (eq (nth 1 nn) 1) (not n)) | |
| 427 | (progn | |
| 428 | (setcar (cdr expr) (math-mul (nth 2 nn) (nth 1 expr))) | |
| 429 | (setcar (cdr (cdr expr)) | |
| 430 | (math-cancel-common-factor (nth 2 expr) nn)) | |
| 431 | (if (and (math-negp nn) | |
| 432 | (setq op (assq (car expr) calc-tweak-eqn-table))) | |
| 433 | (setcar expr (nth 1 op)))) | |
| 434 | (if (and n (not (eq (setq n (math-frac-gcd n nn)) 1))) | |
| 435 | (progn | |
| 436 | (setcar (cdr expr) | |
| 437 | (math-cancel-common-factor (nth 1 expr) n)) | |
| 438 | (setcar (cdr (cdr expr)) | |
| 439 | (math-cancel-common-factor (nth 2 expr) n)) | |
| 440 | (if (and (math-negp n) | |
| 441 | (setq op (assq (car expr) calc-tweak-eqn-table))) | |
| 442 | (setcar expr (nth 1 op)))))))) | |
| 443 | (if (and (eq (car-safe (car np)) '/) | |
| 444 | (math-known-scalarp (nth 2 expr) t)) | |
| 445 | (progn | |
| 446 | (setq np (cdr (nth 1 expr))) | |
| 447 | (while (eq (car-safe (setq n (car np))) '*) | |
| 448 | (and (math-known-scalarp (nth 2 n) t) | |
| 449 | (math-simplify-divisor (cdr n) (cdr (cdr expr)) nil t)) | |
| 450 | (setq np (cdr (cdr n)))) | |
| 451 | (math-simplify-divisor np (cdr (cdr expr)) nil t) | |
| 452 | (setq nover t | |
| 453 | np (cdr (cdr (nth 1 expr)))))) | |
| 454 | (while (eq (car-safe (setq n (car np))) '*) | |
| 455 | (and (math-known-scalarp (nth 2 n) t) | |
| 456 | (math-simplify-divisor (cdr n) (cdr (cdr expr)) nover t)) | |
| 457 | (setq np (cdr (cdr n)))) | |
| 458 | (math-simplify-divisor np (cdr (cdr expr)) nover t) | |
| d3896480 | 459 | expr)) |
| 136211a9 EZ |
460 | |
| 461 | (defun math-simplify-divisor (np dp nover dover) | |
| 462 | (cond ((eq (car-safe (car dp)) '/) | |
| 463 | (math-simplify-divisor np (cdr (car dp)) nover dover) | |
| 464 | (and (math-known-scalarp (nth 1 (car dp)) t) | |
| 465 | (math-simplify-divisor np (cdr (cdr (car dp))) | |
| 466 | nover (not dover)))) | |
| 467 | ((or (or (eq (car expr) '/) | |
| 468 | (let ((signs (math-possible-signs (car np)))) | |
| 469 | (or (memq signs '(1 4)) | |
| 470 | (and (memq (car expr) '(calcFunc-eq calcFunc-neq)) | |
| 471 | (eq signs 5)) | |
| 472 | math-living-dangerously))) | |
| 473 | (math-numberp (car np))) | |
| 474 | (let ((n (car np)) | |
| 475 | d dd temp op | |
| 476 | (safe t) (scalar (math-known-scalarp n))) | |
| 477 | (while (and (eq (car-safe (setq d (car dp))) '*) | |
| 478 | safe) | |
| 479 | (math-simplify-one-divisor np (cdr d)) | |
| 480 | (setq safe (or scalar (math-known-scalarp (nth 1 d) t)) | |
| 481 | dp (cdr (cdr d)))) | |
| 482 | (if safe | |
| d3896480 | 483 | (math-simplify-one-divisor np dp)))))) |
| 136211a9 EZ |
484 | |
| 485 | (defun math-simplify-one-divisor (np dp) | |
| 486 | (if (setq temp (math-combine-prod (car np) (car dp) nover dover t)) | |
| 487 | (progn | |
| 488 | (and (not (memq (car expr) '(/ calcFunc-eq calcFunc-neq))) | |
| 489 | (math-known-negp (car dp)) | |
| 490 | (setq op (assq (car expr) calc-tweak-eqn-table)) | |
| 491 | (setcar expr (nth 1 op))) | |
| 492 | (setcar np (if nover (math-div 1 temp) temp)) | |
| 493 | (setcar dp 1)) | |
| 494 | (and dover (not nover) (eq (car expr) '/) | |
| 495 | (eq (car-safe (car dp)) 'calcFunc-sqrt) | |
| 496 | (Math-integerp (nth 1 (car dp))) | |
| 497 | (progn | |
| 498 | (setcar np (math-mul (car np) | |
| 499 | (list 'calcFunc-sqrt (nth 1 (car dp))))) | |
| d3896480 | 500 | (setcar dp (nth 1 (car dp))))))) |
| 136211a9 EZ |
501 | |
| 502 | (defun math-common-constant-factor (expr) | |
| 503 | (if (Math-realp expr) | |
| 504 | (if (Math-ratp expr) | |
| 505 | (and (not (memq expr '(0 1 -1))) | |
| 506 | (math-abs expr)) | |
| 507 | (if (math-ratp (setq expr (math-to-simple-fraction expr))) | |
| 508 | (math-common-constant-factor expr))) | |
| 509 | (if (memq (car expr) '(+ - cplx sdev)) | |
| 510 | (let ((f1 (math-common-constant-factor (nth 1 expr))) | |
| 511 | (f2 (math-common-constant-factor (nth 2 expr)))) | |
| 512 | (and f1 f2 | |
| 513 | (not (eq (setq f1 (math-frac-gcd f1 f2)) 1)) | |
| 514 | f1)) | |
| 515 | (if (memq (car expr) '(* polar)) | |
| 516 | (math-common-constant-factor (nth 1 expr)) | |
| 517 | (if (eq (car expr) '/) | |
| 518 | (or (math-common-constant-factor (nth 1 expr)) | |
| 519 | (and (Math-integerp (nth 2 expr)) | |
| d3896480 | 520 | (list 'frac 1 (math-abs (nth 2 expr)))))))))) |
| 136211a9 EZ |
521 | |
| 522 | (defun math-cancel-common-factor (expr val) | |
| 523 | (if (memq (car-safe expr) '(+ - cplx sdev)) | |
| 524 | (progn | |
| 525 | (setcar (cdr expr) (math-cancel-common-factor (nth 1 expr) val)) | |
| 526 | (setcar (cdr (cdr expr)) (math-cancel-common-factor (nth 2 expr) val)) | |
| 527 | expr) | |
| 528 | (if (eq (car-safe expr) '*) | |
| 529 | (math-mul (math-cancel-common-factor (nth 1 expr) val) (nth 2 expr)) | |
| d3896480 | 530 | (math-div expr val)))) |
| 136211a9 EZ |
531 | |
| 532 | (defun math-frac-gcd (a b) | |
| 533 | (if (Math-zerop a) | |
| 534 | b | |
| 535 | (if (Math-zerop b) | |
| 536 | a | |
| 537 | (if (and (Math-integerp a) | |
| 538 | (Math-integerp b)) | |
| 539 | (math-gcd a b) | |
| 540 | (and (Math-integerp a) (setq a (list 'frac a 1))) | |
| 541 | (and (Math-integerp b) (setq b (list 'frac b 1))) | |
| 542 | (math-make-frac (math-gcd (nth 1 a) (nth 1 b)) | |
| d3896480 | 543 | (math-gcd (nth 2 a) (nth 2 b))))))) |
| 136211a9 EZ |
544 | |
| 545 | (math-defsimplify % | |
| 546 | (math-simplify-mod)) | |
| 547 | ||
| 548 | (defun math-simplify-mod () | |
| 549 | (and (Math-realp (nth 2 expr)) | |
| 550 | (Math-posp (nth 2 expr)) | |
| 551 | (let ((lin (math-is-linear (nth 1 expr))) | |
| 552 | t1 t2 t3) | |
| 553 | (or (and lin | |
| 554 | (or (math-negp (car lin)) | |
| 555 | (not (Math-lessp (car lin) (nth 2 expr)))) | |
| 556 | (list '% | |
| 557 | (list '+ | |
| 558 | (math-mul (nth 1 lin) (nth 2 lin)) | |
| 559 | (math-mod (car lin) (nth 2 expr))) | |
| 560 | (nth 2 expr))) | |
| 561 | (and lin | |
| 562 | (not (math-equal-int (nth 1 lin) 1)) | |
| 563 | (math-num-integerp (nth 1 lin)) | |
| 564 | (math-num-integerp (nth 2 expr)) | |
| 565 | (setq t1 (calcFunc-gcd (nth 1 lin) (nth 2 expr))) | |
| 566 | (not (math-equal-int t1 1)) | |
| 567 | (list '* | |
| 568 | t1 | |
| 569 | (list '% | |
| 570 | (list '+ | |
| 571 | (math-mul (math-div (nth 1 lin) t1) | |
| 572 | (nth 2 lin)) | |
| 573 | (let ((calc-prefer-frac t)) | |
| 574 | (math-div (car lin) t1))) | |
| 575 | (math-div (nth 2 expr) t1)))) | |
| 576 | (and (math-equal-int (nth 2 expr) 1) | |
| 577 | (math-known-integerp (if lin | |
| 578 | (math-mul (nth 1 lin) (nth 2 lin)) | |
| 579 | (nth 1 expr))) | |
| d3896480 | 580 | (if lin (math-mod (car lin) 1) 0)))))) |
| 136211a9 EZ |
581 | |
| 582 | (math-defsimplify (calcFunc-eq calcFunc-neq calcFunc-lt | |
| 583 | calcFunc-gt calcFunc-leq calcFunc-geq) | |
| 584 | (if (= (length expr) 3) | |
| 585 | (math-simplify-ineq))) | |
| 586 | ||
| 587 | (defun math-simplify-ineq () | |
| 588 | (let ((np (cdr expr)) | |
| 589 | n) | |
| 590 | (while (memq (car-safe (setq n (car np))) '(+ -)) | |
| 591 | (math-simplify-add-term (cdr (cdr n)) (cdr (cdr expr)) | |
| 592 | (eq (car n) '-) nil) | |
| 593 | (setq np (cdr n))) | |
| 594 | (math-simplify-add-term np (cdr (cdr expr)) nil (eq np (cdr expr))) | |
| 595 | (math-simplify-divide) | |
| 596 | (let ((signs (math-possible-signs (cons '- (cdr expr))))) | |
| 597 | (or (cond ((eq (car expr) 'calcFunc-eq) | |
| 598 | (or (and (eq signs 2) 1) | |
| 599 | (and (memq signs '(1 4 5)) 0))) | |
| 600 | ((eq (car expr) 'calcFunc-neq) | |
| 601 | (or (and (eq signs 2) 0) | |
| 602 | (and (memq signs '(1 4 5)) 1))) | |
| 603 | ((eq (car expr) 'calcFunc-lt) | |
| 604 | (or (and (eq signs 1) 1) | |
| 605 | (and (memq signs '(2 4 6)) 0))) | |
| 606 | ((eq (car expr) 'calcFunc-gt) | |
| 607 | (or (and (eq signs 4) 1) | |
| 608 | (and (memq signs '(1 2 3)) 0))) | |
| 609 | ((eq (car expr) 'calcFunc-leq) | |
| 610 | (or (and (eq signs 4) 0) | |
| 611 | (and (memq signs '(1 2 3)) 1))) | |
| 612 | ((eq (car expr) 'calcFunc-geq) | |
| 613 | (or (and (eq signs 1) 0) | |
| 614 | (and (memq signs '(2 4 6)) 1)))) | |
| d3896480 | 615 | expr)))) |
| 136211a9 EZ |
616 | |
| 617 | (defun math-simplify-add-term (np dp minus lplain) | |
| 618 | (or (math-vectorp (car np)) | |
| 619 | (let ((rplain t) | |
| 620 | n d dd temp) | |
| 621 | (while (memq (car-safe (setq n (car np) d (car dp))) '(+ -)) | |
| 622 | (setq rplain nil) | |
| 623 | (if (setq temp (math-combine-sum n (nth 2 d) | |
| 624 | minus (eq (car d) '+) t)) | |
| 625 | (if (or lplain (eq (math-looks-negp temp) minus)) | |
| 626 | (progn | |
| 627 | (setcar np (setq n (if minus (math-neg temp) temp))) | |
| 628 | (setcar (cdr (cdr d)) 0)) | |
| 629 | (progn | |
| 630 | (setcar np 0) | |
| 631 | (setcar (cdr (cdr d)) (setq n (if (eq (car d) '+) | |
| 632 | (math-neg temp) | |
| 633 | temp)))))) | |
| 634 | (setq dp (cdr d))) | |
| 635 | (if (setq temp (math-combine-sum n d minus t t)) | |
| 636 | (if (or lplain | |
| 637 | (and (not rplain) | |
| 638 | (eq (math-looks-negp temp) minus))) | |
| 639 | (progn | |
| 640 | (setcar np (setq n (if minus (math-neg temp) temp))) | |
| 641 | (setcar dp 0)) | |
| 642 | (progn | |
| 643 | (setcar np 0) | |
| d3896480 | 644 | (setcar dp (setq n (math-neg temp))))))))) |
| 136211a9 EZ |
645 | |
| 646 | (math-defsimplify calcFunc-sin | |
| 647 | (or (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsin) | |
| 648 | (nth 1 (nth 1 expr))) | |
| 649 | (and (math-looks-negp (nth 1 expr)) | |
| 650 | (math-neg (list 'calcFunc-sin (math-neg (nth 1 expr))))) | |
| 651 | (and (eq calc-angle-mode 'rad) | |
| 652 | (let ((n (math-linear-in (nth 1 expr) '(var pi var-pi)))) | |
| 653 | (and n | |
| 654 | (math-known-sin (car n) (nth 1 n) 120 0)))) | |
| 655 | (and (eq calc-angle-mode 'deg) | |
| 656 | (let ((n (math-integer-plus (nth 1 expr)))) | |
| 657 | (and n | |
| 658 | (math-known-sin (car n) (nth 1 n) '(frac 2 3) 0)))) | |
| 659 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccos) | |
| 660 | (list 'calcFunc-sqrt (math-sub 1 (math-sqr (nth 1 (nth 1 expr)))))) | |
| 661 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctan) | |
| 662 | (math-div (nth 1 (nth 1 expr)) | |
| 663 | (list 'calcFunc-sqrt | |
| 664 | (math-add 1 (math-sqr (nth 1 (nth 1 expr))))))) | |
| 665 | (let ((m (math-should-expand-trig (nth 1 expr)))) | |
| 666 | (and m (integerp (car m)) | |
| 667 | (let ((n (car m)) (a (nth 1 m))) | |
| 668 | (list '+ | |
| 669 | (list '* (list 'calcFunc-sin (list '* (1- n) a)) | |
| 670 | (list 'calcFunc-cos a)) | |
| 671 | (list '* (list 'calcFunc-cos (list '* (1- n) a)) | |
| d3896480 | 672 | (list 'calcFunc-sin a)))))))) |
| 136211a9 EZ |
673 | |
| 674 | (math-defsimplify calcFunc-cos | |
| 675 | (or (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccos) | |
| 676 | (nth 1 (nth 1 expr))) | |
| 677 | (and (math-looks-negp (nth 1 expr)) | |
| 678 | (list 'calcFunc-cos (math-neg (nth 1 expr)))) | |
| 679 | (and (eq calc-angle-mode 'rad) | |
| 680 | (let ((n (math-linear-in (nth 1 expr) '(var pi var-pi)))) | |
| 681 | (and n | |
| 682 | (math-known-sin (car n) (nth 1 n) 120 300)))) | |
| 683 | (and (eq calc-angle-mode 'deg) | |
| 684 | (let ((n (math-integer-plus (nth 1 expr)))) | |
| 685 | (and n | |
| 686 | (math-known-sin (car n) (nth 1 n) '(frac 2 3) 300)))) | |
| 687 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsin) | |
| 688 | (list 'calcFunc-sqrt (math-sub 1 (math-sqr (nth 1 (nth 1 expr)))))) | |
| 689 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctan) | |
| 690 | (math-div 1 | |
| 691 | (list 'calcFunc-sqrt | |
| 692 | (math-add 1 (math-sqr (nth 1 (nth 1 expr))))))) | |
| 693 | (let ((m (math-should-expand-trig (nth 1 expr)))) | |
| 694 | (and m (integerp (car m)) | |
| 695 | (let ((n (car m)) (a (nth 1 m))) | |
| 696 | (list '- | |
| 697 | (list '* (list 'calcFunc-cos (list '* (1- n) a)) | |
| 698 | (list 'calcFunc-cos a)) | |
| 699 | (list '* (list 'calcFunc-sin (list '* (1- n) a)) | |
| d3896480 | 700 | (list 'calcFunc-sin a)))))))) |
| 136211a9 EZ |
701 | |
| 702 | (defun math-should-expand-trig (x &optional hyperbolic) | |
| 703 | (let ((m (math-is-multiple x))) | |
| 704 | (and math-living-dangerously | |
| 705 | m (or (and (integerp (car m)) (> (car m) 1)) | |
| 706 | (equal (car m) '(frac 1 2))) | |
| 707 | (or math-integrating | |
| 708 | (memq (car-safe (nth 1 m)) | |
| 709 | (if hyperbolic | |
| 710 | '(calcFunc-arcsinh calcFunc-arccosh calcFunc-arctanh) | |
| 711 | '(calcFunc-arcsin calcFunc-arccos calcFunc-arctan))) | |
| 712 | (and (eq (car-safe (nth 1 m)) 'calcFunc-ln) | |
| 713 | (eq hyperbolic 'exp))) | |
| d3896480 | 714 | m))) |
| 136211a9 EZ |
715 | |
| 716 | (defun math-known-sin (plus n mul off) | |
| 717 | (setq n (math-mul n mul)) | |
| 718 | (and (math-num-integerp n) | |
| 719 | (setq n (math-mod (math-add (math-trunc n) off) 240)) | |
| 720 | (if (>= n 120) | |
| 721 | (and (setq n (math-known-sin plus (- n 120) 1 0)) | |
| 722 | (math-neg n)) | |
| 723 | (if (> n 60) | |
| 724 | (setq n (- 120 n))) | |
| 725 | (if (math-zerop plus) | |
| 726 | (and (or calc-symbolic-mode | |
| 727 | (memq n '(0 20 60))) | |
| 728 | (cdr (assq n | |
| 729 | '( (0 . 0) | |
| 730 | (10 . (/ (calcFunc-sqrt | |
| 731 | (- 2 (calcFunc-sqrt 3))) 2)) | |
| 732 | (12 . (/ (- (calcFunc-sqrt 5) 1) 4)) | |
| 733 | (15 . (/ (calcFunc-sqrt | |
| 734 | (- 2 (calcFunc-sqrt 2))) 2)) | |
| 735 | (20 . (/ 1 2)) | |
| 736 | (24 . (* (^ (/ 1 2) (/ 3 2)) | |
| 737 | (calcFunc-sqrt | |
| 738 | (- 5 (calcFunc-sqrt 5))))) | |
| 739 | (30 . (/ (calcFunc-sqrt 2) 2)) | |
| 740 | (36 . (/ (+ (calcFunc-sqrt 5) 1) 4)) | |
| 741 | (40 . (/ (calcFunc-sqrt 3) 2)) | |
| 742 | (45 . (/ (calcFunc-sqrt | |
| 743 | (+ 2 (calcFunc-sqrt 2))) 2)) | |
| 744 | (48 . (* (^ (/ 1 2) (/ 3 2)) | |
| 745 | (calcFunc-sqrt | |
| 746 | (+ 5 (calcFunc-sqrt 5))))) | |
| 747 | (50 . (/ (calcFunc-sqrt | |
| 748 | (+ 2 (calcFunc-sqrt 3))) 2)) | |
| 749 | (60 . 1))))) | |
| 750 | (cond ((eq n 0) (math-normalize (list 'calcFunc-sin plus))) | |
| 751 | ((eq n 60) (math-normalize (list 'calcFunc-cos plus))) | |
| d3896480 | 752 | (t nil)))))) |
| 136211a9 EZ |
753 | |
| 754 | (math-defsimplify calcFunc-tan | |
| 755 | (or (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctan) | |
| 756 | (nth 1 (nth 1 expr))) | |
| 757 | (and (math-looks-negp (nth 1 expr)) | |
| 758 | (math-neg (list 'calcFunc-tan (math-neg (nth 1 expr))))) | |
| 759 | (and (eq calc-angle-mode 'rad) | |
| 760 | (let ((n (math-linear-in (nth 1 expr) '(var pi var-pi)))) | |
| 761 | (and n | |
| 762 | (math-known-tan (car n) (nth 1 n) 120)))) | |
| 763 | (and (eq calc-angle-mode 'deg) | |
| 764 | (let ((n (math-integer-plus (nth 1 expr)))) | |
| 765 | (and n | |
| 766 | (math-known-tan (car n) (nth 1 n) '(frac 2 3))))) | |
| 767 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsin) | |
| 768 | (math-div (nth 1 (nth 1 expr)) | |
| 769 | (list 'calcFunc-sqrt | |
| 770 | (math-sub 1 (math-sqr (nth 1 (nth 1 expr))))))) | |
| 771 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccos) | |
| 772 | (math-div (list 'calcFunc-sqrt | |
| 773 | (math-sub 1 (math-sqr (nth 1 (nth 1 expr))))) | |
| 774 | (nth 1 (nth 1 expr)))) | |
| 775 | (let ((m (math-should-expand-trig (nth 1 expr)))) | |
| 776 | (and m | |
| 777 | (if (equal (car m) '(frac 1 2)) | |
| 778 | (math-div (math-sub 1 (list 'calcFunc-cos (nth 1 m))) | |
| 779 | (list 'calcFunc-sin (nth 1 m))) | |
| 780 | (math-div (list 'calcFunc-sin (nth 1 expr)) | |
| d3896480 | 781 | (list 'calcFunc-cos (nth 1 expr)))))))) |
| 136211a9 EZ |
782 | |
| 783 | (defun math-known-tan (plus n mul) | |
| 784 | (setq n (math-mul n mul)) | |
| 785 | (and (math-num-integerp n) | |
| 786 | (setq n (math-mod (math-trunc n) 120)) | |
| 787 | (if (> n 60) | |
| 788 | (and (setq n (math-known-tan plus (- 120 n) 1)) | |
| 789 | (math-neg n)) | |
| 790 | (if (math-zerop plus) | |
| 791 | (and (or calc-symbolic-mode | |
| 792 | (memq n '(0 30 60))) | |
| 793 | (cdr (assq n '( (0 . 0) | |
| 794 | (10 . (- 2 (calcFunc-sqrt 3))) | |
| 795 | (12 . (calcFunc-sqrt | |
| 796 | (- 1 (* (/ 2 5) (calcFunc-sqrt 5))))) | |
| 797 | (15 . (- (calcFunc-sqrt 2) 1)) | |
| 798 | (20 . (/ (calcFunc-sqrt 3) 3)) | |
| 799 | (24 . (calcFunc-sqrt | |
| 800 | (- 5 (* 2 (calcFunc-sqrt 5))))) | |
| 801 | (30 . 1) | |
| 802 | (36 . (calcFunc-sqrt | |
| 803 | (+ 1 (* (/ 2 5) (calcFunc-sqrt 5))))) | |
| 804 | (40 . (calcFunc-sqrt 3)) | |
| 805 | (45 . (+ (calcFunc-sqrt 2) 1)) | |
| 806 | (48 . (calcFunc-sqrt | |
| 807 | (+ 5 (* 2 (calcFunc-sqrt 5))))) | |
| 808 | (50 . (+ 2 (calcFunc-sqrt 3))) | |
| 809 | (60 . (var uinf var-uinf)))))) | |
| 810 | (cond ((eq n 0) (math-normalize (list 'calcFunc-tan plus))) | |
| 811 | ((eq n 60) (math-normalize (list '/ -1 | |
| 812 | (list 'calcFunc-tan plus)))) | |
| d3896480 | 813 | (t nil)))))) |
| 136211a9 EZ |
814 | |
| 815 | (math-defsimplify calcFunc-sinh | |
| 816 | (or (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsinh) | |
| 817 | (nth 1 (nth 1 expr))) | |
| 818 | (and (math-looks-negp (nth 1 expr)) | |
| 819 | (math-neg (list 'calcFunc-sinh (math-neg (nth 1 expr))))) | |
| 820 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccosh) | |
| 821 | math-living-dangerously | |
| 822 | (list 'calcFunc-sqrt (math-sub (math-sqr (nth 1 (nth 1 expr))) 1))) | |
| 823 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctanh) | |
| 824 | math-living-dangerously | |
| 825 | (math-div (nth 1 (nth 1 expr)) | |
| 826 | (list 'calcFunc-sqrt | |
| 827 | (math-sub 1 (math-sqr (nth 1 (nth 1 expr))))))) | |
| 828 | (let ((m (math-should-expand-trig (nth 1 expr) t))) | |
| 829 | (and m (integerp (car m)) | |
| 830 | (let ((n (car m)) (a (nth 1 m))) | |
| 831 | (if (> n 1) | |
| 832 | (list '+ | |
| 833 | (list '* (list 'calcFunc-sinh (list '* (1- n) a)) | |
| 834 | (list 'calcFunc-cosh a)) | |
| 835 | (list '* (list 'calcFunc-cosh (list '* (1- n) a)) | |
| d3896480 | 836 | (list 'calcFunc-sinh a))))))))) |
| 136211a9 EZ |
837 | |
| 838 | (math-defsimplify calcFunc-cosh | |
| 839 | (or (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccosh) | |
| 840 | (nth 1 (nth 1 expr))) | |
| 841 | (and (math-looks-negp (nth 1 expr)) | |
| 842 | (list 'calcFunc-cosh (math-neg (nth 1 expr)))) | |
| 843 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsinh) | |
| 844 | math-living-dangerously | |
| 845 | (list 'calcFunc-sqrt (math-add (math-sqr (nth 1 (nth 1 expr))) 1))) | |
| 846 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctanh) | |
| 847 | math-living-dangerously | |
| 848 | (math-div 1 | |
| 849 | (list 'calcFunc-sqrt | |
| 850 | (math-sub 1 (math-sqr (nth 1 (nth 1 expr))))))) | |
| 851 | (let ((m (math-should-expand-trig (nth 1 expr) t))) | |
| 852 | (and m (integerp (car m)) | |
| 853 | (let ((n (car m)) (a (nth 1 m))) | |
| 854 | (if (> n 1) | |
| 855 | (list '+ | |
| 856 | (list '* (list 'calcFunc-cosh (list '* (1- n) a)) | |
| 857 | (list 'calcFunc-cosh a)) | |
| 858 | (list '* (list 'calcFunc-sinh (list '* (1- n) a)) | |
| d3896480 | 859 | (list 'calcFunc-sinh a))))))))) |
| 136211a9 EZ |
860 | |
| 861 | (math-defsimplify calcFunc-tanh | |
| 862 | (or (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctanh) | |
| 863 | (nth 1 (nth 1 expr))) | |
| 864 | (and (math-looks-negp (nth 1 expr)) | |
| 865 | (math-neg (list 'calcFunc-tanh (math-neg (nth 1 expr))))) | |
| 866 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsinh) | |
| 867 | math-living-dangerously | |
| 868 | (math-div (nth 1 (nth 1 expr)) | |
| 869 | (list 'calcFunc-sqrt | |
| 870 | (math-add (math-sqr (nth 1 (nth 1 expr))) 1)))) | |
| 871 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccosh) | |
| 872 | math-living-dangerously | |
| 873 | (math-div (list 'calcFunc-sqrt | |
| 874 | (math-sub (math-sqr (nth 1 (nth 1 expr))) 1)) | |
| 875 | (nth 1 (nth 1 expr)))) | |
| 876 | (let ((m (math-should-expand-trig (nth 1 expr) t))) | |
| 877 | (and m | |
| 878 | (if (equal (car m) '(frac 1 2)) | |
| 879 | (math-div (math-sub (list 'calcFunc-cosh (nth 1 m)) 1) | |
| 880 | (list 'calcFunc-sinh (nth 1 m))) | |
| 881 | (math-div (list 'calcFunc-sinh (nth 1 expr)) | |
| d3896480 | 882 | (list 'calcFunc-cosh (nth 1 expr)))))))) |
| 136211a9 EZ |
883 | |
| 884 | (math-defsimplify calcFunc-arcsin | |
| 885 | (or (and (math-looks-negp (nth 1 expr)) | |
| 886 | (math-neg (list 'calcFunc-arcsin (math-neg (nth 1 expr))))) | |
| 887 | (and (eq (nth 1 expr) 1) | |
| 888 | (math-quarter-circle t)) | |
| 889 | (and (equal (nth 1 expr) '(frac 1 2)) | |
| 890 | (math-div (math-half-circle t) 6)) | |
| 891 | (and math-living-dangerously | |
| 892 | (eq (car-safe (nth 1 expr)) 'calcFunc-sin) | |
| 893 | (nth 1 (nth 1 expr))) | |
| 894 | (and math-living-dangerously | |
| 895 | (eq (car-safe (nth 1 expr)) 'calcFunc-cos) | |
| 896 | (math-sub (math-quarter-circle t) | |
| d3896480 | 897 | (nth 1 (nth 1 expr)))))) |
| 136211a9 EZ |
898 | |
| 899 | (math-defsimplify calcFunc-arccos | |
| 900 | (or (and (eq (nth 1 expr) 0) | |
| 901 | (math-quarter-circle t)) | |
| 902 | (and (eq (nth 1 expr) -1) | |
| 903 | (math-half-circle t)) | |
| 904 | (and (equal (nth 1 expr) '(frac 1 2)) | |
| 905 | (math-div (math-half-circle t) 3)) | |
| 906 | (and (equal (nth 1 expr) '(frac -1 2)) | |
| 907 | (math-div (math-mul (math-half-circle t) 2) 3)) | |
| 908 | (and math-living-dangerously | |
| 909 | (eq (car-safe (nth 1 expr)) 'calcFunc-cos) | |
| 910 | (nth 1 (nth 1 expr))) | |
| 911 | (and math-living-dangerously | |
| 912 | (eq (car-safe (nth 1 expr)) 'calcFunc-sin) | |
| 913 | (math-sub (math-quarter-circle t) | |
| d3896480 | 914 | (nth 1 (nth 1 expr)))))) |
| 136211a9 EZ |
915 | |
| 916 | (math-defsimplify calcFunc-arctan | |
| 917 | (or (and (math-looks-negp (nth 1 expr)) | |
| 918 | (math-neg (list 'calcFunc-arctan (math-neg (nth 1 expr))))) | |
| 919 | (and (eq (nth 1 expr) 1) | |
| 920 | (math-div (math-half-circle t) 4)) | |
| 921 | (and math-living-dangerously | |
| 922 | (eq (car-safe (nth 1 expr)) 'calcFunc-tan) | |
| d3896480 | 923 | (nth 1 (nth 1 expr))))) |
| 136211a9 EZ |
924 | |
| 925 | (math-defsimplify calcFunc-arcsinh | |
| 926 | (or (and (math-looks-negp (nth 1 expr)) | |
| 927 | (math-neg (list 'calcFunc-arcsinh (math-neg (nth 1 expr))))) | |
| 928 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-sinh) | |
| 929 | (or math-living-dangerously | |
| 930 | (math-known-realp (nth 1 (nth 1 expr)))) | |
| d3896480 | 931 | (nth 1 (nth 1 expr))))) |
| 136211a9 EZ |
932 | |
| 933 | (math-defsimplify calcFunc-arccosh | |
| 934 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-cosh) | |
| 935 | (or math-living-dangerously | |
| 936 | (math-known-realp (nth 1 (nth 1 expr)))) | |
| d3896480 | 937 | (nth 1 (nth 1 expr)))) |
| 136211a9 EZ |
938 | |
| 939 | (math-defsimplify calcFunc-arctanh | |
| 940 | (or (and (math-looks-negp (nth 1 expr)) | |
| 941 | (math-neg (list 'calcFunc-arctanh (math-neg (nth 1 expr))))) | |
| 942 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-tanh) | |
| 943 | (or math-living-dangerously | |
| 944 | (math-known-realp (nth 1 (nth 1 expr)))) | |
| d3896480 | 945 | (nth 1 (nth 1 expr))))) |
| 136211a9 EZ |
946 | |
| 947 | (math-defsimplify calcFunc-sqrt | |
| d3896480 | 948 | (math-simplify-sqrt)) |
| 136211a9 EZ |
949 | |
| 950 | (defun math-simplify-sqrt () | |
| 951 | (or (and (eq (car-safe (nth 1 expr)) 'frac) | |
| 952 | (math-div (list 'calcFunc-sqrt (math-mul (nth 1 (nth 1 expr)) | |
| 953 | (nth 2 (nth 1 expr)))) | |
| 954 | (nth 2 (nth 1 expr)))) | |
| 955 | (let ((fac (if (math-objectp (nth 1 expr)) | |
| 956 | (math-squared-factor (nth 1 expr)) | |
| 957 | (math-common-constant-factor (nth 1 expr))))) | |
| 958 | (and fac (not (eq fac 1)) | |
| 959 | (math-mul (math-normalize (list 'calcFunc-sqrt fac)) | |
| 960 | (math-normalize | |
| 961 | (list 'calcFunc-sqrt | |
| 962 | (math-cancel-common-factor (nth 1 expr) fac)))))) | |
| 963 | (and math-living-dangerously | |
| 964 | (or (and (eq (car-safe (nth 1 expr)) '-) | |
| 965 | (math-equal-int (nth 1 (nth 1 expr)) 1) | |
| 966 | (eq (car-safe (nth 2 (nth 1 expr))) '^) | |
| 967 | (math-equal-int (nth 2 (nth 2 (nth 1 expr))) 2) | |
| 968 | (or (and (eq (car-safe (nth 1 (nth 2 (nth 1 expr)))) | |
| 969 | 'calcFunc-sin) | |
| 970 | (list 'calcFunc-cos | |
| 971 | (nth 1 (nth 1 (nth 2 (nth 1 expr)))))) | |
| 972 | (and (eq (car-safe (nth 1 (nth 2 (nth 1 expr)))) | |
| 973 | 'calcFunc-cos) | |
| 974 | (list 'calcFunc-sin | |
| 975 | (nth 1 (nth 1 (nth 2 (nth 1 expr)))))))) | |
| 976 | (and (eq (car-safe (nth 1 expr)) '-) | |
| 977 | (math-equal-int (nth 2 (nth 1 expr)) 1) | |
| 978 | (eq (car-safe (nth 1 (nth 1 expr))) '^) | |
| 979 | (math-equal-int (nth 2 (nth 1 (nth 1 expr))) 2) | |
| 980 | (and (eq (car-safe (nth 1 (nth 1 (nth 1 expr)))) | |
| 981 | 'calcFunc-cosh) | |
| 982 | (list 'calcFunc-sinh | |
| 983 | (nth 1 (nth 1 (nth 1 (nth 1 expr))))))) | |
| 984 | (and (eq (car-safe (nth 1 expr)) '+) | |
| 985 | (let ((a (nth 1 (nth 1 expr))) | |
| 986 | (b (nth 2 (nth 1 expr)))) | |
| 987 | (and (or (and (math-equal-int a 1) | |
| 988 | (setq a b b (nth 1 (nth 1 expr)))) | |
| 989 | (math-equal-int b 1)) | |
| 990 | (eq (car-safe a) '^) | |
| 991 | (math-equal-int (nth 2 a) 2) | |
| 992 | (or (and (eq (car-safe (nth 1 a)) 'calcFunc-sinh) | |
| 993 | (list 'calcFunc-cosh (nth 1 (nth 1 a)))) | |
| 994 | (and (eq (car-safe (nth 1 a)) 'calcFunc-tan) | |
| 995 | (list '/ 1 (list 'calcFunc-cos | |
| 996 | (nth 1 (nth 1 a))))))))) | |
| 997 | (and (eq (car-safe (nth 1 expr)) '^) | |
| 998 | (list '^ | |
| 999 | (nth 1 (nth 1 expr)) | |
| 1000 | (math-div (nth 2 (nth 1 expr)) 2))) | |
| 1001 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-sqrt) | |
| 1002 | (list '^ (nth 1 (nth 1 expr)) (math-div 1 4))) | |
| 1003 | (and (memq (car-safe (nth 1 expr)) '(* /)) | |
| 1004 | (list (car (nth 1 expr)) | |
| 1005 | (list 'calcFunc-sqrt (nth 1 (nth 1 expr))) | |
| 1006 | (list 'calcFunc-sqrt (nth 2 (nth 1 expr))))) | |
| 1007 | (and (memq (car-safe (nth 1 expr)) '(+ -)) | |
| 1008 | (not (math-any-floats (nth 1 expr))) | |
| 1009 | (let ((f (calcFunc-factors (calcFunc-expand | |
| 1010 | (nth 1 expr))))) | |
| 1011 | (and (math-vectorp f) | |
| 1012 | (or (> (length f) 2) | |
| 1013 | (> (nth 2 (nth 1 f)) 1)) | |
| 1014 | (let ((out 1) (rest 1) (sums 1) fac pow) | |
| 1015 | (while (setq f (cdr f)) | |
| 1016 | (setq fac (nth 1 (car f)) | |
| 1017 | pow (nth 2 (car f))) | |
| 1018 | (if (> pow 1) | |
| 1019 | (setq out (math-mul out (math-pow | |
| 1020 | fac (/ pow 2))) | |
| 1021 | pow (% pow 2))) | |
| 1022 | (if (> pow 0) | |
| 1023 | (if (memq (car-safe fac) '(+ -)) | |
| 1024 | (setq sums (math-mul-thru sums fac)) | |
| 1025 | (setq rest (math-mul rest fac))))) | |
| 1026 | (and (not (and (eq out 1) (memq rest '(1 -1)))) | |
| 1027 | (math-mul | |
| 1028 | out | |
| 1029 | (list 'calcFunc-sqrt | |
| d3896480 | 1030 | (math-mul sums rest)))))))))))) |
| 136211a9 EZ |
1031 | |
| 1032 | ;;; Rather than factoring x into primes, just check for the first ten primes. | |
| 1033 | (defun math-squared-factor (x) | |
| 1034 | (if (Math-integerp x) | |
| 1035 | (let ((prsqr '(4 9 25 49 121 169 289 361 529 841)) | |
| 1036 | (fac 1) | |
| 1037 | res) | |
| 1038 | (while prsqr | |
| 1039 | (if (eq (cdr (setq res (math-idivmod x (car prsqr)))) 0) | |
| 1040 | (setq x (car res) | |
| 1041 | fac (math-mul fac (car prsqr))) | |
| 1042 | (setq prsqr (cdr prsqr)))) | |
| d3896480 | 1043 | fac))) |
| 136211a9 EZ |
1044 | |
| 1045 | (math-defsimplify calcFunc-exp | |
| d3896480 | 1046 | (math-simplify-exp (nth 1 expr))) |
| 136211a9 EZ |
1047 | |
| 1048 | (defun math-simplify-exp (x) | |
| 1049 | (or (and (eq (car-safe x) 'calcFunc-ln) | |
| 1050 | (nth 1 x)) | |
| 1051 | (and math-living-dangerously | |
| 1052 | (or (and (eq (car-safe x) 'calcFunc-arcsinh) | |
| 1053 | (math-add (nth 1 x) | |
| 1054 | (list 'calcFunc-sqrt | |
| 1055 | (math-add (math-sqr (nth 1 x)) 1)))) | |
| 1056 | (and (eq (car-safe x) 'calcFunc-arccosh) | |
| 1057 | (math-add (nth 1 x) | |
| 1058 | (list 'calcFunc-sqrt | |
| 1059 | (math-sub (math-sqr (nth 1 x)) 1)))) | |
| 1060 | (and (eq (car-safe x) 'calcFunc-arctanh) | |
| 1061 | (math-div (list 'calcFunc-sqrt (math-add 1 (nth 1 x))) | |
| 1062 | (list 'calcFunc-sqrt (math-sub 1 (nth 1 x))))) | |
| 1063 | (let ((m (math-should-expand-trig x 'exp))) | |
| 1064 | (and m (integerp (car m)) | |
| 1065 | (list '^ (list 'calcFunc-exp (nth 1 m)) (car m)))))) | |
| 1066 | (and calc-symbolic-mode | |
| 1067 | (math-known-imagp x) | |
| 1068 | (let* ((ip (calcFunc-im x)) | |
| 1069 | (n (math-linear-in ip '(var pi var-pi))) | |
| 1070 | s c) | |
| 1071 | (and n | |
| 1072 | (setq s (math-known-sin (car n) (nth 1 n) 120 0)) | |
| 1073 | (setq c (math-known-sin (car n) (nth 1 n) 120 300)) | |
| d3896480 | 1074 | (list '+ c (list '* s '(var i var-i)))))))) |
| 136211a9 EZ |
1075 | |
| 1076 | (math-defsimplify calcFunc-ln | |
| 1077 | (or (and (eq (car-safe (nth 1 expr)) 'calcFunc-exp) | |
| 1078 | (or math-living-dangerously | |
| 1079 | (math-known-realp (nth 1 (nth 1 expr)))) | |
| 1080 | (nth 1 (nth 1 expr))) | |
| 1081 | (and (eq (car-safe (nth 1 expr)) '^) | |
| 1082 | (equal (nth 1 (nth 1 expr)) '(var e var-e)) | |
| 1083 | (or math-living-dangerously | |
| 1084 | (math-known-realp (nth 2 (nth 1 expr)))) | |
| 1085 | (nth 2 (nth 1 expr))) | |
| 1086 | (and calc-symbolic-mode | |
| 1087 | (math-known-negp (nth 1 expr)) | |
| 1088 | (math-add (list 'calcFunc-ln (math-neg (nth 1 expr))) | |
| 2c6dfebb | 1089 | '(* (var pi var-pi) (var i var-i)))) |
| 136211a9 EZ |
1090 | (and calc-symbolic-mode |
| 1091 | (math-known-imagp (nth 1 expr)) | |
| 1092 | (let* ((ip (calcFunc-im (nth 1 expr))) | |
| 1093 | (ips (math-possible-signs ip))) | |
| 1094 | (or (and (memq ips '(4 6)) | |
| 1095 | (math-add (list 'calcFunc-ln ip) | |
| 1096 | '(/ (* (var pi var-pi) (var i var-i)) 2))) | |
| 1097 | (and (memq ips '(1 3)) | |
| 1098 | (math-sub (list 'calcFunc-ln (math-neg ip)) | |
| d3896480 | 1099 | '(/ (* (var pi var-pi) (var i var-i)) 2)))))))) |
| 136211a9 EZ |
1100 | |
| 1101 | (math-defsimplify ^ | |
| 1102 | (math-simplify-pow)) | |
| 1103 | ||
| 1104 | (defun math-simplify-pow () | |
| 1105 | (or (and math-living-dangerously | |
| 1106 | (or (and (eq (car-safe (nth 1 expr)) '^) | |
| 1107 | (list '^ | |
| 1108 | (nth 1 (nth 1 expr)) | |
| 1109 | (math-mul (nth 2 expr) (nth 2 (nth 1 expr))))) | |
| 1110 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-sqrt) | |
| 1111 | (list '^ | |
| 1112 | (nth 1 (nth 1 expr)) | |
| 1113 | (math-div (nth 2 expr) 2))) | |
| 1114 | (and (memq (car-safe (nth 1 expr)) '(* /)) | |
| 1115 | (list (car (nth 1 expr)) | |
| 1116 | (list '^ (nth 1 (nth 1 expr)) (nth 2 expr)) | |
| 1117 | (list '^ (nth 2 (nth 1 expr)) (nth 2 expr)))))) | |
| 1118 | (and (math-equal-int (nth 1 expr) 10) | |
| 1119 | (eq (car-safe (nth 2 expr)) 'calcFunc-log10) | |
| 1120 | (nth 1 (nth 2 expr))) | |
| 1121 | (and (equal (nth 1 expr) '(var e var-e)) | |
| 1122 | (math-simplify-exp (nth 2 expr))) | |
| 1123 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-exp) | |
| 1124 | (not math-integrating) | |
| 1125 | (list 'calcFunc-exp (math-mul (nth 1 (nth 1 expr)) (nth 2 expr)))) | |
| 1126 | (and (equal (nth 1 expr) '(var i var-i)) | |
| 1127 | (math-imaginary-i) | |
| 1128 | (math-num-integerp (nth 2 expr)) | |
| 1129 | (let ((x (math-mod (math-trunc (nth 2 expr)) 4))) | |
| 1130 | (cond ((eq x 0) 1) | |
| 1131 | ((eq x 1) (nth 1 expr)) | |
| 1132 | ((eq x 2) -1) | |
| 1133 | ((eq x 3) (math-neg (nth 1 expr)))))) | |
| 1134 | (and math-integrating | |
| 1135 | (integerp (nth 2 expr)) | |
| 1136 | (>= (nth 2 expr) 2) | |
| 1137 | (or (and (eq (car-safe (nth 1 expr)) 'calcFunc-cos) | |
| 1138 | (math-mul (math-pow (nth 1 expr) (- (nth 2 expr) 2)) | |
| 1139 | (math-sub 1 | |
| 1140 | (math-sqr | |
| 1141 | (list 'calcFunc-sin | |
| 1142 | (nth 1 (nth 1 expr))))))) | |
| 1143 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-cosh) | |
| 1144 | (math-mul (math-pow (nth 1 expr) (- (nth 2 expr) 2)) | |
| 1145 | (math-add 1 | |
| 1146 | (math-sqr | |
| 1147 | (list 'calcFunc-sinh | |
| 1148 | (nth 1 (nth 1 expr))))))))) | |
| 1149 | (and (eq (car-safe (nth 2 expr)) 'frac) | |
| 1150 | (Math-ratp (nth 1 expr)) | |
| 1151 | (Math-posp (nth 1 expr)) | |
| 1152 | (if (equal (nth 2 expr) '(frac 1 2)) | |
| 1153 | (list 'calcFunc-sqrt (nth 1 expr)) | |
| 1154 | (let ((flr (math-floor (nth 2 expr)))) | |
| 1155 | (and (not (Math-zerop flr)) | |
| 1156 | (list '* (list '^ (nth 1 expr) flr) | |
| 1157 | (list '^ (nth 1 expr) | |
| 1158 | (math-sub (nth 2 expr) flr))))))) | |
| 1159 | (and (eq (math-quarter-integer (nth 2 expr)) 2) | |
| 1160 | (let ((temp (math-simplify-sqrt))) | |
| 1161 | (and temp | |
| d3896480 | 1162 | (list '^ temp (math-mul (nth 2 expr) 2))))))) |
| 136211a9 EZ |
1163 | |
| 1164 | (math-defsimplify calcFunc-log10 | |
| 1165 | (and (eq (car-safe (nth 1 expr)) '^) | |
| 1166 | (math-equal-int (nth 1 (nth 1 expr)) 10) | |
| 1167 | (or math-living-dangerously | |
| 1168 | (math-known-realp (nth 2 (nth 1 expr)))) | |
| d3896480 | 1169 | (nth 2 (nth 1 expr)))) |
| 136211a9 EZ |
1170 | |
| 1171 | ||
| 1172 | (math-defsimplify calcFunc-erf | |
| 1173 | (or (and (math-looks-negp (nth 1 expr)) | |
| 1174 | (math-neg (list 'calcFunc-erf (math-neg (nth 1 expr))))) | |
| 1175 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-conj) | |
| d3896480 | 1176 | (list 'calcFunc-conj (list 'calcFunc-erf (nth 1 (nth 1 expr))))))) |
| 136211a9 EZ |
1177 | |
| 1178 | (math-defsimplify calcFunc-erfc | |
| 1179 | (or (and (math-looks-negp (nth 1 expr)) | |
| 1180 | (math-sub 2 (list 'calcFunc-erfc (math-neg (nth 1 expr))))) | |
| 1181 | (and (eq (car-safe (nth 1 expr)) 'calcFunc-conj) | |
| d3896480 | 1182 | (list 'calcFunc-conj (list 'calcFunc-erfc (nth 1 (nth 1 expr))))))) |
| 136211a9 EZ |
1183 | |
| 1184 | ||
| 1185 | (defun math-linear-in (expr term &optional always) | |
| 1186 | (if (math-expr-contains expr term) | |
| 1187 | (let* ((calc-prefer-frac t) | |
| 1188 | (p (math-is-polynomial expr term 1))) | |
| 1189 | (and (cdr p) | |
| 1190 | p)) | |
| d3896480 | 1191 | (and always (list expr 0)))) |
| 136211a9 EZ |
1192 | |
| 1193 | (defun math-multiple-of (expr term) | |
| 1194 | (let ((p (math-linear-in expr term))) | |
| 1195 | (and p | |
| 1196 | (math-zerop (car p)) | |
| d3896480 | 1197 | (nth 1 p)))) |
| 136211a9 | 1198 | |
| d3896480 | 1199 | ; not perfect, but it'll do |
| 136211a9 EZ |
1200 | (defun math-integer-plus (expr) |
| 1201 | (cond ((Math-integerp expr) | |
| 1202 | (list 0 expr)) | |
| 1203 | ((and (memq (car expr) '(+ -)) | |
| 1204 | (Math-integerp (nth 1 expr))) | |
| 1205 | (list (if (eq (car expr) '+) (nth 2 expr) (math-neg (nth 2 expr))) | |
| 1206 | (nth 1 expr))) | |
| 1207 | ((and (memq (car expr) '(+ -)) | |
| 1208 | (Math-integerp (nth 2 expr))) | |
| 1209 | (list (nth 1 expr) | |
| 1210 | (if (eq (car expr) '+) (nth 2 expr) (math-neg (nth 2 expr))))) | |
| d3896480 | 1211 | (t nil))) |
| 136211a9 EZ |
1212 | |
| 1213 | (defun math-is-linear (expr &optional always) | |
| 1214 | (let ((offset nil) | |
| 1215 | (coef nil)) | |
| 1216 | (if (eq (car-safe expr) '+) | |
| 1217 | (if (Math-objectp (nth 1 expr)) | |
| 1218 | (setq offset (nth 1 expr) | |
| 1219 | expr (nth 2 expr)) | |
| 1220 | (if (Math-objectp (nth 2 expr)) | |
| 1221 | (setq offset (nth 2 expr) | |
| 1222 | expr (nth 1 expr)))) | |
| 1223 | (if (eq (car-safe expr) '-) | |
| 1224 | (if (Math-objectp (nth 1 expr)) | |
| 1225 | (setq offset (nth 1 expr) | |
| 1226 | expr (math-neg (nth 2 expr))) | |
| 1227 | (if (Math-objectp (nth 2 expr)) | |
| 1228 | (setq offset (math-neg (nth 2 expr)) | |
| 1229 | expr (nth 1 expr)))))) | |
| 1230 | (setq coef (math-is-multiple expr always)) | |
| 1231 | (if offset | |
| 1232 | (list offset (or (car coef) 1) (or (nth 1 coef) expr)) | |
| 1233 | (if coef | |
| d3896480 | 1234 | (cons 0 coef))))) |
| 136211a9 EZ |
1235 | |
| 1236 | (defun math-is-multiple (expr &optional always) | |
| 1237 | (or (if (eq (car-safe expr) '*) | |
| 1238 | (if (Math-objectp (nth 1 expr)) | |
| 1239 | (list (nth 1 expr) (nth 2 expr))) | |
| 1240 | (if (eq (car-safe expr) '/) | |
| 1241 | (if (and (Math-objectp (nth 1 expr)) | |
| 1242 | (not (math-equal-int (nth 1 expr) 1))) | |
| 1243 | (list (nth 1 expr) (math-div 1 (nth 2 expr))) | |
| 1244 | (if (Math-objectp (nth 2 expr)) | |
| 1245 | (list (math-div 1 (nth 2 expr)) (nth 1 expr)) | |
| 1246 | (let ((res (math-is-multiple (nth 1 expr)))) | |
| 1247 | (if res | |
| 1248 | (list (car res) | |
| 1249 | (math-div (nth 2 (nth 1 expr)) (nth 2 expr))) | |
| 1250 | (setq res (math-is-multiple (nth 2 expr))) | |
| 1251 | (if res | |
| 1252 | (list (math-div 1 (car res)) | |
| 1253 | (math-div (nth 1 expr) | |
| 1254 | (nth 2 (nth 2 expr))))))))) | |
| 1255 | (if (eq (car-safe expr) 'neg) | |
| 1256 | (list -1 (nth 1 expr))))) | |
| 1257 | (if (Math-objvecp expr) | |
| 1258 | (and (eq always 1) | |
| 1259 | (list expr 1)) | |
| a1506d29 | 1260 | (and always |
| d3896480 | 1261 | (list 1 expr))))) |
| 136211a9 EZ |
1262 | |
| 1263 | (defun calcFunc-lin (expr &optional var) | |
| 1264 | (if var | |
| 1265 | (let ((res (math-linear-in expr var t))) | |
| 1266 | (or res (math-reject-arg expr "Linear term expected")) | |
| 1267 | (list 'vec (car res) (nth 1 res) var)) | |
| 1268 | (let ((res (math-is-linear expr t))) | |
| 1269 | (or res (math-reject-arg expr "Linear term expected")) | |
| d3896480 | 1270 | (cons 'vec res)))) |
| 136211a9 EZ |
1271 | |
| 1272 | (defun calcFunc-linnt (expr &optional var) | |
| 1273 | (if var | |
| 1274 | (let ((res (math-linear-in expr var))) | |
| 1275 | (or res (math-reject-arg expr "Linear term expected")) | |
| 1276 | (list 'vec (car res) (nth 1 res) var)) | |
| 1277 | (let ((res (math-is-linear expr))) | |
| 1278 | (or res (math-reject-arg expr "Linear term expected")) | |
| d3896480 | 1279 | (cons 'vec res)))) |
| 136211a9 EZ |
1280 | |
| 1281 | (defun calcFunc-islin (expr &optional var) | |
| 1282 | (if (and (Math-objvecp expr) (not var)) | |
| 1283 | 0 | |
| 1284 | (calcFunc-lin expr var) | |
| d3896480 | 1285 | 1)) |
| 136211a9 EZ |
1286 | |
| 1287 | (defun calcFunc-islinnt (expr &optional var) | |
| 1288 | (if (Math-objvecp expr) | |
| 1289 | 0 | |
| 1290 | (calcFunc-linnt expr var) | |
| d3896480 | 1291 | 1)) |
| 136211a9 EZ |
1292 | |
| 1293 | ||
| 1294 | ||
| 1295 | ||
| 1296 | ;;; Simple operations on expressions. | |
| 1297 | ||
| 6f826971 | 1298 | ;;; Return number of occurrences of thing in expr, or nil if none. |
| 136211a9 EZ |
1299 | (defun math-expr-contains-count (expr thing) |
| 1300 | (cond ((equal expr thing) 1) | |
| 1301 | ((Math-primp expr) nil) | |
| 1302 | (t | |
| 1303 | (let ((num 0)) | |
| 1304 | (while (setq expr (cdr expr)) | |
| 1305 | (setq num (+ num (or (math-expr-contains-count | |
| 1306 | (car expr) thing) 0)))) | |
| 1307 | (and (> num 0) | |
| d3896480 | 1308 | num))))) |
| 136211a9 EZ |
1309 | |
| 1310 | (defun math-expr-contains (expr thing) | |
| 1311 | (cond ((equal expr thing) 1) | |
| 1312 | ((Math-primp expr) nil) | |
| 1313 | (t | |
| 1314 | (while (and (setq expr (cdr expr)) | |
| 1315 | (not (math-expr-contains (car expr) thing)))) | |
| d3896480 | 1316 | expr))) |
| 136211a9 EZ |
1317 | |
| 1318 | ;;; Return non-nil if any variable of thing occurs in expr. | |
| 1319 | (defun math-expr-depends (expr thing) | |
| 1320 | (if (Math-primp thing) | |
| 1321 | (and (eq (car-safe thing) 'var) | |
| 1322 | (math-expr-contains expr thing)) | |
| 1323 | (while (and (setq thing (cdr thing)) | |
| 1324 | (not (math-expr-depends expr (car thing))))) | |
| d3896480 | 1325 | thing)) |
| 136211a9 EZ |
1326 | |
| 1327 | ;;; Substitute all occurrences of old for new in expr (non-destructive). | |
| 1328 | (defun math-expr-subst (expr old new) | |
| d3896480 CW |
1329 | (math-expr-subst-rec expr)) |
| 1330 | ||
| 1331 | (defalias 'calcFunc-subst 'math-expr-subst) | |
| 136211a9 EZ |
1332 | |
| 1333 | (defun math-expr-subst-rec (expr) | |
| 1334 | (cond ((equal expr old) new) | |
| 1335 | ((Math-primp expr) expr) | |
| 1336 | ((memq (car expr) '(calcFunc-deriv | |
| 1337 | calcFunc-tderiv)) | |
| 1338 | (if (= (length expr) 2) | |
| 1339 | (if (equal (nth 1 expr) old) | |
| 1340 | (append expr (list new)) | |
| 1341 | expr) | |
| 1342 | (list (car expr) (nth 1 expr) | |
| 1343 | (math-expr-subst-rec (nth 2 expr))))) | |
| 1344 | (t | |
| 1345 | (cons (car expr) | |
| d3896480 | 1346 | (mapcar 'math-expr-subst-rec (cdr expr)))))) |
| 136211a9 EZ |
1347 | |
| 1348 | ;;; Various measures of the size of an expression. | |
| 1349 | (defun math-expr-weight (expr) | |
| 1350 | (if (Math-primp expr) | |
| 1351 | 1 | |
| 1352 | (let ((w 1)) | |
| 1353 | (while (setq expr (cdr expr)) | |
| 1354 | (setq w (+ w (math-expr-weight (car expr))))) | |
| d3896480 | 1355 | w))) |
| 136211a9 EZ |
1356 | |
| 1357 | (defun math-expr-height (expr) | |
| 1358 | (if (Math-primp expr) | |
| 1359 | 0 | |
| 1360 | (let ((h 0)) | |
| 1361 | (while (setq expr (cdr expr)) | |
| 1362 | (setq h (max h (math-expr-height (car expr))))) | |
| d3896480 | 1363 | (1+ h)))) |
| 136211a9 EZ |
1364 | |
| 1365 | ||
| 1366 | ||
| 1367 | ||
| 1368 | ;;; Polynomial operations (to support the integrator and solve-for). | |
| 1369 | ||
| 1370 | (defun calcFunc-collect (expr base) | |
| 1371 | (let ((p (math-is-polynomial expr base 50 t))) | |
| 1372 | (if (cdr p) | |
| 1373 | (math-normalize ; fix selection bug | |
| 1374 | (math-build-polynomial-expr p base)) | |
| d3896480 | 1375 | expr))) |
| 136211a9 EZ |
1376 | |
| 1377 | ;;; If expr is of the form "a + bx + cx^2 + ...", return the list (a b c ...), | |
| 1378 | ;;; else return nil if not in polynomial form. If "loose", coefficients | |
| 1379 | ;;; may contain x, e.g., sin(x) + cos(x) x^2 is a loose polynomial in x. | |
| 1380 | (defun math-is-polynomial (expr var &optional degree loose) | |
| 1381 | (let* ((math-poly-base-variable (if loose | |
| 1382 | (if (eq loose 'gen) var '(var XXX XXX)) | |
| 1383 | math-poly-base-variable)) | |
| 1384 | (poly (math-is-poly-rec expr math-poly-neg-powers))) | |
| 1385 | (and (or (null degree) | |
| 1386 | (<= (length poly) (1+ degree))) | |
| d3896480 | 1387 | poly))) |
| 136211a9 EZ |
1388 | |
| 1389 | (defun math-is-poly-rec (expr negpow) | |
| 1390 | (math-poly-simplify | |
| 1391 | (or (cond ((or (equal expr var) | |
| 1392 | (eq (car-safe expr) '^)) | |
| 1393 | (let ((pow 1) | |
| 1394 | (expr expr)) | |
| 1395 | (or (equal expr var) | |
| 1396 | (setq pow (nth 2 expr) | |
| 1397 | expr (nth 1 expr))) | |
| 1398 | (or (eq math-poly-mult-powers 1) | |
| 1399 | (setq pow (let ((m (math-is-multiple pow 1))) | |
| 1400 | (and (eq (car-safe (car m)) 'cplx) | |
| 1401 | (Math-zerop (nth 1 (car m))) | |
| 1402 | (setq m (list (nth 2 (car m)) | |
| 1403 | (math-mul (nth 1 m) | |
| 1404 | '(var i var-i))))) | |
| 1405 | (and (if math-poly-mult-powers | |
| 1406 | (equal math-poly-mult-powers | |
| 1407 | (nth 1 m)) | |
| 1408 | (setq math-poly-mult-powers (nth 1 m))) | |
| 1409 | (or (equal expr var) | |
| 1410 | (eq math-poly-mult-powers 1)) | |
| 1411 | (car m))))) | |
| 1412 | (if (consp pow) | |
| 1413 | (progn | |
| 1414 | (setq pow (math-to-simple-fraction pow)) | |
| 1415 | (and (eq (car-safe pow) 'frac) | |
| 1416 | math-poly-frac-powers | |
| 1417 | (equal expr var) | |
| 1418 | (setq math-poly-frac-powers | |
| 1419 | (calcFunc-lcm math-poly-frac-powers | |
| 1420 | (nth 2 pow)))))) | |
| 1421 | (or (memq math-poly-frac-powers '(1 nil)) | |
| 1422 | (setq pow (math-mul pow math-poly-frac-powers))) | |
| 1423 | (if (integerp pow) | |
| 1424 | (if (and (= pow 1) | |
| 1425 | (equal expr var)) | |
| 1426 | (list 0 1) | |
| 1427 | (if (natnump pow) | |
| 1428 | (let ((p1 (if (equal expr var) | |
| 1429 | (list 0 1) | |
| 1430 | (math-is-poly-rec expr nil))) | |
| 1431 | (n pow) | |
| 1432 | (accum (list 1))) | |
| 1433 | (and p1 | |
| 1434 | (or (null degree) | |
| 1435 | (<= (* (1- (length p1)) n) degree)) | |
| 1436 | (progn | |
| 1437 | (while (>= n 1) | |
| 1438 | (setq accum (math-poly-mul accum p1) | |
| 1439 | n (1- n))) | |
| 1440 | accum))) | |
| 1441 | (and negpow | |
| 1442 | (math-is-poly-rec expr nil) | |
| 1443 | (setq math-poly-neg-powers | |
| 1444 | (cons (math-pow expr (- pow)) | |
| 1445 | math-poly-neg-powers)) | |
| 1446 | (list (list '^ expr pow)))))))) | |
| 1447 | ((Math-objectp expr) | |
| 1448 | (list expr)) | |
| 1449 | ((memq (car expr) '(+ -)) | |
| 1450 | (let ((p1 (math-is-poly-rec (nth 1 expr) negpow))) | |
| 1451 | (and p1 | |
| 1452 | (let ((p2 (math-is-poly-rec (nth 2 expr) negpow))) | |
| 1453 | (and p2 | |
| 1454 | (math-poly-mix p1 1 p2 | |
| 1455 | (if (eq (car expr) '+) 1 -1))))))) | |
| 1456 | ((eq (car expr) 'neg) | |
| 1457 | (mapcar 'math-neg (math-is-poly-rec (nth 1 expr) negpow))) | |
| 1458 | ((eq (car expr) '*) | |
| 1459 | (let ((p1 (math-is-poly-rec (nth 1 expr) negpow))) | |
| 1460 | (and p1 | |
| 1461 | (let ((p2 (math-is-poly-rec (nth 2 expr) negpow))) | |
| 1462 | (and p2 | |
| 1463 | (or (null degree) | |
| 1464 | (<= (- (+ (length p1) (length p2)) 2) degree)) | |
| 1465 | (math-poly-mul p1 p2)))))) | |
| 1466 | ((eq (car expr) '/) | |
| 1467 | (and (or (not (math-poly-depends (nth 2 expr) var)) | |
| 1468 | (and negpow | |
| 1469 | (math-is-poly-rec (nth 2 expr) nil) | |
| 1470 | (setq math-poly-neg-powers | |
| 1471 | (cons (nth 2 expr) math-poly-neg-powers)))) | |
| 1472 | (not (Math-zerop (nth 2 expr))) | |
| 1473 | (let ((p1 (math-is-poly-rec (nth 1 expr) negpow))) | |
| 1474 | (mapcar (function (lambda (x) (math-div x (nth 2 expr)))) | |
| 1475 | p1)))) | |
| 1476 | ((and (eq (car expr) 'calcFunc-exp) | |
| 1477 | (equal var '(var e var-e))) | |
| 1478 | (math-is-poly-rec (list '^ var (nth 1 expr)) negpow)) | |
| 1479 | ((and (eq (car expr) 'calcFunc-sqrt) | |
| 1480 | math-poly-frac-powers) | |
| 1481 | (math-is-poly-rec (list '^ (nth 1 expr) '(frac 1 2)) negpow)) | |
| 1482 | (t nil)) | |
| 1483 | (and (or (not (math-poly-depends expr var)) | |
| 1484 | loose) | |
| 1485 | (not (eq (car expr) 'vec)) | |
| d3896480 | 1486 | (list expr))))) |
| 136211a9 EZ |
1487 | |
| 1488 | ;;; Check if expr is a polynomial in var; if so, return its degree. | |
| 1489 | (defun math-polynomial-p (expr var) | |
| 1490 | (cond ((equal expr var) 1) | |
| 1491 | ((Math-primp expr) 0) | |
| 1492 | ((memq (car expr) '(+ -)) | |
| 1493 | (let ((p1 (math-polynomial-p (nth 1 expr) var)) | |
| 1494 | p2) | |
| 1495 | (and p1 (setq p2 (math-polynomial-p (nth 2 expr) var)) | |
| 1496 | (max p1 p2)))) | |
| 1497 | ((eq (car expr) '*) | |
| 1498 | (let ((p1 (math-polynomial-p (nth 1 expr) var)) | |
| 1499 | p2) | |
| 1500 | (and p1 (setq p2 (math-polynomial-p (nth 2 expr) var)) | |
| 1501 | (+ p1 p2)))) | |
| 1502 | ((eq (car expr) 'neg) | |
| 1503 | (math-polynomial-p (nth 1 expr) var)) | |
| 1504 | ((and (eq (car expr) '/) | |
| 1505 | (not (math-poly-depends (nth 2 expr) var))) | |
| 1506 | (math-polynomial-p (nth 1 expr) var)) | |
| 1507 | ((and (eq (car expr) '^) | |
| 1508 | (natnump (nth 2 expr))) | |
| 1509 | (let ((p1 (math-polynomial-p (nth 1 expr) var))) | |
| 1510 | (and p1 (* p1 (nth 2 expr))))) | |
| 1511 | ((math-poly-depends expr var) nil) | |
| d3896480 | 1512 | (t 0))) |
| 136211a9 EZ |
1513 | |
| 1514 | (defun math-poly-depends (expr var) | |
| 1515 | (if math-poly-base-variable | |
| 1516 | (math-expr-contains expr math-poly-base-variable) | |
| d3896480 | 1517 | (math-expr-depends expr var))) |
| 136211a9 EZ |
1518 | |
| 1519 | ;;; Find the variable (or sub-expression) which is the base of polynomial expr. | |
| 1520 | (defun math-polynomial-base (mpb-top-expr &optional mpb-pred) | |
| 1521 | (or mpb-pred | |
| 1522 | (setq mpb-pred (function (lambda (base) (math-polynomial-p | |
| 1523 | mpb-top-expr base))))) | |
| 1524 | (or (let ((const-ok nil)) | |
| 1525 | (math-polynomial-base-rec mpb-top-expr)) | |
| 1526 | (let ((const-ok t)) | |
| d3896480 | 1527 | (math-polynomial-base-rec mpb-top-expr)))) |
| 136211a9 EZ |
1528 | |
| 1529 | (defun math-polynomial-base-rec (mpb-expr) | |
| 1530 | (and (not (Math-objvecp mpb-expr)) | |
| 1531 | (or (and (memq (car mpb-expr) '(+ - *)) | |
| 1532 | (or (math-polynomial-base-rec (nth 1 mpb-expr)) | |
| 1533 | (math-polynomial-base-rec (nth 2 mpb-expr)))) | |
| 1534 | (and (memq (car mpb-expr) '(/ neg)) | |
| 1535 | (math-polynomial-base-rec (nth 1 mpb-expr))) | |
| 1536 | (and (eq (car mpb-expr) '^) | |
| 1537 | (math-polynomial-base-rec (nth 1 mpb-expr))) | |
| 1538 | (and (eq (car mpb-expr) 'calcFunc-exp) | |
| 1539 | (math-polynomial-base-rec '(var e var-e))) | |
| 1540 | (and (or const-ok (math-expr-contains-vars mpb-expr)) | |
| 1541 | (funcall mpb-pred mpb-expr) | |
| d3896480 | 1542 | mpb-expr)))) |
| 136211a9 EZ |
1543 | |
| 1544 | ;;; Return non-nil if expr refers to any variables. | |
| 1545 | (defun math-expr-contains-vars (expr) | |
| 1546 | (or (eq (car-safe expr) 'var) | |
| 1547 | (and (not (Math-primp expr)) | |
| 1548 | (progn | |
| 1549 | (while (and (setq expr (cdr expr)) | |
| 1550 | (not (math-expr-contains-vars (car expr))))) | |
| d3896480 | 1551 | expr)))) |
| 136211a9 EZ |
1552 | |
| 1553 | ;;; Simplify a polynomial in list form by stripping off high-end zeros. | |
| 1554 | ;;; This always leaves the constant part, i.e., nil->nil and nonnil->nonnil. | |
| 1555 | (defun math-poly-simplify (p) | |
| 1556 | (and p | |
| 1557 | (if (Math-zerop (nth (1- (length p)) p)) | |
| 1558 | (let ((pp (copy-sequence p))) | |
| 1559 | (while (and (cdr pp) | |
| 1560 | (Math-zerop (nth (1- (length pp)) pp))) | |
| 1561 | (setcdr (nthcdr (- (length pp) 2) pp) nil)) | |
| 1562 | pp) | |
| d3896480 | 1563 | p))) |
| 136211a9 EZ |
1564 | |
| 1565 | ;;; Compute ac*a + bc*b for polynomials in list form a, b and | |
| 1566 | ;;; coefficients ac, bc. Result may be unsimplified. | |
| 1567 | (defun math-poly-mix (a ac b bc) | |
| 1568 | (and (or a b) | |
| 1569 | (cons (math-add (math-mul (or (car a) 0) ac) | |
| 1570 | (math-mul (or (car b) 0) bc)) | |
| d3896480 | 1571 | (math-poly-mix (cdr a) ac (cdr b) bc)))) |
| 136211a9 EZ |
1572 | |
| 1573 | (defun math-poly-zerop (a) | |
| 1574 | (or (null a) | |
| d3896480 | 1575 | (and (null (cdr a)) (Math-zerop (car a))))) |
| 136211a9 EZ |
1576 | |
| 1577 | ;;; Multiply two polynomials in list form. | |
| 1578 | (defun math-poly-mul (a b) | |
| 1579 | (and a b | |
| 1580 | (math-poly-mix b (car a) | |
| d3896480 | 1581 | (math-poly-mul (cdr a) (cons 0 b)) 1))) |
| 136211a9 EZ |
1582 | |
| 1583 | ;;; Build an expression from a polynomial list. | |
| 1584 | (defun math-build-polynomial-expr (p var) | |
| 1585 | (if p | |
| 1586 | (if (Math-numberp var) | |
| 1587 | (math-with-extra-prec 1 | |
| 1588 | (let* ((rp (reverse p)) | |
| 1589 | (accum (car rp))) | |
| 1590 | (while (setq rp (cdr rp)) | |
| 1591 | (setq accum (math-add (car rp) (math-mul accum var)))) | |
| 1592 | accum)) | |
| 1593 | (let* ((rp (reverse p)) | |
| 1594 | (n (1- (length rp))) | |
| 1595 | (accum (math-mul (car rp) (math-pow var n))) | |
| 1596 | term) | |
| 1597 | (while (setq rp (cdr rp)) | |
| 1598 | (setq n (1- n)) | |
| 1599 | (or (math-zerop (car rp)) | |
| 1600 | (setq accum (list (if (math-looks-negp (car rp)) '- '+) | |
| 1601 | accum | |
| 1602 | (math-mul (if (math-looks-negp (car rp)) | |
| 1603 | (math-neg (car rp)) | |
| 1604 | (car rp)) | |
| 1605 | (math-pow var n)))))) | |
| 1606 | accum)) | |
| d3896480 | 1607 | 0)) |
| 136211a9 EZ |
1608 | |
| 1609 | ||
| 1610 | (defun math-to-simple-fraction (f) | |
| 1611 | (or (and (eq (car-safe f) 'float) | |
| 1612 | (or (and (>= (nth 2 f) 0) | |
| 1613 | (math-scale-int (nth 1 f) (nth 2 f))) | |
| 1614 | (and (integerp (nth 1 f)) | |
| 1615 | (> (nth 1 f) -1000) | |
| 1616 | (< (nth 1 f) 1000) | |
| 1617 | (math-make-frac (nth 1 f) | |
| 1618 | (math-scale-int 1 (- (nth 2 f))))))) | |
| d3896480 | 1619 | f)) |
| 136211a9 | 1620 | |
| 6b61353c | 1621 | ;;; arch-tag: 52e7dcdf-9688-464d-a02b-4bbe789348d0 |
| d3896480 | 1622 | ;;; calc-alg.el ends here |