HCoop / bpt / emacs.git / blame
| Commit | Line | Data |
|---|---|---|
| a1506d29 | 1 | ;;; calc-alg.el --- algebraic functions for Calc |
| 3132f345 | 2 | |
| 58ba2f8f | 3 | ;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004, |
| f0fa15c5 | 4 | ;; 2005, 2006, 2007 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 | ||
| 7c671b23 GM |
11 | ;; GNU Emacs is free software; you can redistribute it and/or modify |
| 12 | ;; it under the terms of the GNU General Public License as published by | |
| 13 | ;; the Free Software Foundation; either version 2, or (at your option) | |
| 14 | ;; any later version. | |
| 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 | |
| 22 | ;; along with GNU Emacs; see the file COPYING. If not, write to the | |
| 23 | ;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, | |
| 24 | ;; Boston, MA 02110-1301, USA. | |
| 136211a9 | 25 | |
| 3132f345 | 26 | ;;; Commentary: |
| 136211a9 | 27 | |
| 3132f345 | 28 | ;;; Code: |
| 136211a9 EZ |
29 | |
| 30 | ;; This file is autoloaded from calc-ext.el. | |
| 136211a9 | 31 | |
| 41cf648d | 32 | (require 'calc-ext) |
| 136211a9 EZ |
33 | (require 'calc-macs) |
| 34 | ||
| 136211a9 EZ |
35 | ;;; Algebra commands. |
| 36 | ||
| 37 | (defun calc-alg-evaluate (arg) | |
| 38 | (interactive "p") | |
| 39 | (calc-slow-wrapper | |
| 40 | (calc-with-default-simplification | |
| 41 | (let ((math-simplify-only nil)) | |
| 42 | (calc-modify-simplify-mode arg) | |
| d3896480 | 43 | (calc-enter-result 1 "dsmp" (calc-top 1)))))) |
| 136211a9 EZ |
44 | |
| 45 | (defun calc-modify-simplify-mode (arg) | |
| 46 | (if (= (math-abs arg) 2) | |
| 47 | (setq calc-simplify-mode 'alg) | |
| 48 | (if (>= (math-abs arg) 3) | |
| 49 | (setq calc-simplify-mode 'ext))) | |
| 50 | (if (< arg 0) | |
| d3896480 | 51 | (setq calc-simplify-mode (list calc-simplify-mode)))) |
| 136211a9 EZ |
52 | |
| 53 | (defun calc-simplify () | |
| 54 | (interactive) | |
| 55 | (calc-slow-wrapper | |
| 56 | (calc-with-default-simplification | |
| d3896480 | 57 | (calc-enter-result 1 "simp" (math-simplify (calc-top-n 1)))))) |
| 136211a9 EZ |
58 | |
| 59 | (defun calc-simplify-extended () | |
| 60 | (interactive) | |
| 61 | (calc-slow-wrapper | |
| 62 | (calc-with-default-simplification | |
| d3896480 | 63 | (calc-enter-result 1 "esmp" (math-simplify-extended (calc-top-n 1)))))) |
| 136211a9 EZ |
64 | |
| 65 | (defun calc-expand-formula (arg) | |
| 66 | (interactive "p") | |
| 67 | (calc-slow-wrapper | |
| 68 | (calc-with-default-simplification | |
| 69 | (let ((math-simplify-only nil)) | |
| 70 | (calc-modify-simplify-mode arg) | |
| a1506d29 | 71 | (calc-enter-result 1 "expf" |
| 136211a9 EZ |
72 | (if (> arg 0) |
| 73 | (let ((math-expand-formulas t)) | |
| 74 | (calc-top-n 1)) | |
| 75 | (let ((top (calc-top-n 1))) | |
| 76 | (or (math-expand-formula top) | |
| d3896480 | 77 | top)))))))) |
| 136211a9 EZ |
78 | |
| 79 | (defun calc-factor (arg) | |
| 80 | (interactive "P") | |
| 81 | (calc-slow-wrapper | |
| 82 | (calc-unary-op "fctr" (if (calc-is-hyperbolic) | |
| 83 | 'calcFunc-factors 'calcFunc-factor) | |
| d3896480 | 84 | arg))) |
| 136211a9 EZ |
85 | |
| 86 | (defun calc-expand (n) | |
| 87 | (interactive "P") | |
| 88 | (calc-slow-wrapper | |
| 89 | (calc-enter-result 1 "expa" | |
| 90 | (append (list 'calcFunc-expand | |
| 91 | (calc-top-n 1)) | |
| d3896480 | 92 | (and n (list (prefix-numeric-value n))))))) |
| 136211a9 | 93 | |
| 93e7f889 | 94 | ;;; Write out powers (a*b*...)^n as a*b*...*a*b*... |
| c431c730 JB |
95 | (defun calcFunc-powerexpand (expr) |
| 96 | (math-normalize (math-map-tree 'math-powerexpand expr))) | |
| 93e7f889 | 97 | |
| c431c730 | 98 | (defun math-powerexpand (expr) |
| 93e7f889 | 99 | (if (eq (car-safe expr) '^) |
| c431c730 JB |
100 | (let ((n (nth 2 expr))) |
| 101 | (cond ((and (integerp n) | |
| 102 | (> n 0)) | |
| 103 | (let ((i 1) | |
| 104 | (a (nth 1 expr)) | |
| 105 | (prod (nth 1 expr))) | |
| 106 | (while (< i n) | |
| 107 | (setq prod (math-mul prod a)) | |
| 108 | (setq i (1+ i))) | |
| 109 | prod)) | |
| 110 | ((and (integerp n) | |
| 111 | (< n 0)) | |
| 112 | (let ((i -1) | |
| 113 | (a (math-pow (nth 1 expr) -1)) | |
| 114 | (prod (math-pow (nth 1 expr) -1))) | |
| 115 | (while (> i n) | |
| 116 | (setq prod (math-mul a prod)) | |
| 117 | (setq i (1- i))) | |
| 118 | prod)) | |
| 119 | (t | |
| 120 | expr))) | |
| 93e7f889 JB |
121 | expr)) |
| 122 | ||
| c431c730 | 123 | (defun calc-powerexpand () |
| 93e7f889 JB |
124 | (interactive) |
| 125 | (calc-slow-wrapper | |
| c431c730 JB |
126 | (calc-enter-result 1 "pexp" |
| 127 | (calcFunc-powerexpand (calc-top-n 1))))) | |
| 93e7f889 | 128 | |
| 136211a9 EZ |
129 | (defun calc-collect (&optional var) |
| 130 | (interactive "sCollect terms involving: ") | |
| 131 | (calc-slow-wrapper | |
| 132 | (if (or (equal var "") (equal var "$") (null var)) | |
| 133 | (calc-enter-result 2 "clct" (cons 'calcFunc-collect | |
| 134 | (calc-top-list-n 2))) | |
| 135 | (let ((var (math-read-expr var))) | |
| 136 | (if (eq (car-safe var) 'error) | |
| 137 | (error "Bad format in expression: %s" (nth 1 var))) | |
| 138 | (calc-enter-result 1 "clct" (list 'calcFunc-collect | |
| 139 | (calc-top-n 1) | |
| d3896480 | 140 | var)))))) |
| 136211a9 EZ |
141 | |
| 142 | (defun calc-apart (arg) | |
| 143 | (interactive "P") | |
| 144 | (calc-slow-wrapper | |
| d3896480 | 145 | (calc-unary-op "aprt" 'calcFunc-apart arg))) |
| 136211a9 EZ |
146 | |
| 147 | (defun calc-normalize-rat (arg) | |
| 148 | (interactive "P") | |
| 149 | (calc-slow-wrapper | |
| d3896480 | 150 | (calc-unary-op "nrat" 'calcFunc-nrat arg))) |
| 136211a9 EZ |
151 | |
| 152 | (defun calc-poly-gcd (arg) | |
| 153 | (interactive "P") | |
| 154 | (calc-slow-wrapper | |
| d3896480 | 155 | (calc-binary-op "pgcd" 'calcFunc-pgcd arg))) |
| 136211a9 | 156 | |
| 0c908945 | 157 | |
| 136211a9 EZ |
158 | (defun calc-poly-div (arg) |
| 159 | (interactive "P") | |
| 160 | (calc-slow-wrapper | |
| 0c908945 JB |
161 | (let ((calc-poly-div-remainder nil)) |
| 162 | (calc-binary-op "pdiv" 'calcFunc-pdiv arg) | |
| 163 | (if (and calc-poly-div-remainder (null arg)) | |
| 164 | (progn | |
| 165 | (calc-clear-command-flag 'clear-message) | |
| 166 | (calc-record calc-poly-div-remainder "prem") | |
| 167 | (if (not (Math-zerop calc-poly-div-remainder)) | |
| 168 | (message "(Remainder was %s)" | |
| 169 | (math-format-flat-expr calc-poly-div-remainder 0)) | |
| 170 | (message "(No remainder)"))))))) | |
| 136211a9 EZ |
171 | |
| 172 | (defun calc-poly-rem (arg) | |
| 173 | (interactive "P") | |
| 174 | (calc-slow-wrapper | |
| d3896480 | 175 | (calc-binary-op "prem" 'calcFunc-prem arg))) |
| 136211a9 EZ |
176 | |
| 177 | (defun calc-poly-div-rem (arg) | |
| 178 | (interactive "P") | |
| 179 | (calc-slow-wrapper | |
| 180 | (if (calc-is-hyperbolic) | |
| 181 | (calc-binary-op "pdvr" 'calcFunc-pdivide arg) | |
| d3896480 | 182 | (calc-binary-op "pdvr" 'calcFunc-pdivrem arg)))) |
| 136211a9 EZ |
183 | |
| 184 | (defun calc-substitute (&optional oldname newname) | |
| 185 | (interactive "sSubstitute old: ") | |
| 186 | (calc-slow-wrapper | |
| 187 | (let (old new (num 1) expr) | |
| 188 | (if (or (equal oldname "") (equal oldname "$") (null oldname)) | |
| 189 | (setq new (calc-top-n 1) | |
| 190 | old (calc-top-n 2) | |
| 191 | expr (calc-top-n 3) | |
| 192 | num 3) | |
| 193 | (or newname | |
| 194 | (progn (calc-unread-command ?\C-a) | |
| 195 | (setq newname (read-string (concat "Substitute old: " | |
| 196 | oldname | |
| 197 | ", new: ") | |
| 198 | oldname)))) | |
| 199 | (if (or (equal newname "") (equal newname "$") (null newname)) | |
| 200 | (setq new (calc-top-n 1) | |
| 201 | expr (calc-top-n 2) | |
| 202 | num 2) | |
| 203 | (setq new (if (stringp newname) (math-read-expr newname) newname)) | |
| 204 | (if (eq (car-safe new) 'error) | |
| 205 | (error "Bad format in expression: %s" (nth 1 new))) | |
| 206 | (setq expr (calc-top-n 1))) | |
| 207 | (setq old (if (stringp oldname) (math-read-expr oldname) oldname)) | |
| 208 | (if (eq (car-safe old) 'error) | |
| 209 | (error "Bad format in expression: %s" (nth 1 old))) | |
| 210 | (or (math-expr-contains expr old) | |
| 3132f345 | 211 | (error "No occurrences found"))) |
| d3896480 | 212 | (calc-enter-result num "sbst" (math-expr-subst expr old new))))) |
| 136211a9 EZ |
213 | |
| 214 | ||
| 215 | (defun calc-has-rules (name) | |
| 216 | (setq name (calc-var-value name)) | |
| 217 | (and (consp name) | |
| 218 | (memq (car name) '(vec calcFunc-assign calcFunc-condition)) | |
| d3896480 | 219 | name)) |
| 136211a9 | 220 | |
| 0c908945 JB |
221 | ;; math-eval-rules-cache and math-eval-rules-cache-other are |
| 222 | ;; declared in calc.el, but are used here by math-recompile-eval-rules. | |
| 223 | (defvar math-eval-rules-cache) | |
| 224 | (defvar math-eval-rules-cache-other) | |
| 225 | ||
| 136211a9 EZ |
226 | (defun math-recompile-eval-rules () |
| 227 | (setq math-eval-rules-cache (and (calc-has-rules 'var-EvalRules) | |
| 228 | (math-compile-rewrites | |
| 229 | '(var EvalRules var-EvalRules))) | |
| 230 | math-eval-rules-cache-other (assq nil math-eval-rules-cache) | |
| d3896480 | 231 | math-eval-rules-cache-tag (calc-var-value 'var-EvalRules))) |
| 136211a9 EZ |
232 | |
| 233 | ||
| 234 | ;;; Try to expand a formula according to its definition. | |
| 235 | (defun math-expand-formula (expr) | |
| 236 | (and (consp expr) | |
| 237 | (symbolp (car expr)) | |
| 238 | (or (get (car expr) 'calc-user-defn) | |
| 239 | (get (car expr) 'math-expandable)) | |
| 240 | (let ((res (let ((math-expand-formulas t)) | |
| 241 | (apply (car expr) (cdr expr))))) | |
| 242 | (and (not (eq (car-safe res) (car expr))) | |
| d3896480 | 243 | res)))) |
| 136211a9 EZ |
244 | |
| 245 | ||
| 246 | ||
| 247 | ||
| 248 | ;;; True if A comes before B in a canonical ordering of expressions. [P X X] | |
| 249 | (defun math-beforep (a b) ; [Public] | |
| 250 | (cond ((and (Math-realp a) (Math-realp b)) | |
| 251 | (let ((comp (math-compare a b))) | |
| 252 | (or (eq comp -1) | |
| 253 | (and (eq comp 0) | |
| 254 | (not (equal a b)) | |
| 255 | (> (length (memq (car-safe a) | |
| 256 | '(bigneg nil bigpos frac float))) | |
| 257 | (length (memq (car-safe b) | |
| 258 | '(bigneg nil bigpos frac float)))))))) | |
| 259 | ((equal b '(neg (var inf var-inf))) nil) | |
| 260 | ((equal a '(neg (var inf var-inf))) t) | |
| 261 | ((equal a '(var inf var-inf)) nil) | |
| 262 | ((equal b '(var inf var-inf)) t) | |
| 263 | ((Math-realp a) | |
| 264 | (if (and (eq (car-safe b) 'intv) (math-intv-constp b)) | |
| 265 | (if (or (math-beforep a (nth 2 b)) (Math-equal a (nth 2 b))) | |
| 266 | t | |
| 267 | nil) | |
| 268 | t)) | |
| 269 | ((Math-realp b) | |
| 270 | (if (and (eq (car-safe a) 'intv) (math-intv-constp a)) | |
| 271 | (if (math-beforep (nth 2 a) b) | |
| 272 | t | |
| 273 | nil) | |
| 274 | nil)) | |
| 275 | ((and (eq (car a) 'intv) (eq (car b) 'intv) | |
| 276 | (math-intv-constp a) (math-intv-constp b)) | |
| 277 | (let ((comp (math-compare (nth 2 a) (nth 2 b)))) | |
| 278 | (cond ((eq comp -1) t) | |
| 279 | ((eq comp 1) nil) | |
| 280 | ((and (memq (nth 1 a) '(2 3)) (memq (nth 1 b) '(0 1))) t) | |
| 281 | ((and (memq (nth 1 a) '(0 1)) (memq (nth 1 b) '(2 3))) nil) | |
| 282 | ((eq (setq comp (math-compare (nth 3 a) (nth 3 b))) -1) t) | |
| 283 | ((eq comp 1) nil) | |
| 284 | ((and (memq (nth 1 a) '(0 2)) (memq (nth 1 b) '(1 3))) t) | |
| 285 | (t nil)))) | |
| 286 | ((not (eq (not (Math-objectp a)) (not (Math-objectp b)))) | |
| 287 | (Math-objectp a)) | |
| 288 | ((eq (car a) 'var) | |
| 289 | (if (eq (car b) 'var) | |
| 290 | (string-lessp (symbol-name (nth 1 a)) (symbol-name (nth 1 b))) | |
| 291 | (not (Math-numberp b)))) | |
| 292 | ((eq (car b) 'var) (Math-numberp a)) | |
| 293 | ((eq (car a) (car b)) | |
| 294 | (while (and (setq a (cdr a) b (cdr b)) a | |
| 295 | (equal (car a) (car b)))) | |
| 296 | (and b | |
| 297 | (or (null a) | |
| 298 | (math-beforep (car a) (car b))))) | |
| d3896480 | 299 | (t (string-lessp (symbol-name (car a)) (symbol-name (car b)))))) |
| 136211a9 EZ |
300 | |
| 301 | ||
| d3896480 | 302 | (defsubst math-simplify-extended (a) |
| 136211a9 | 303 | (let ((math-living-dangerously t)) |
| d3896480 CW |
304 | (math-simplify a))) |
| 305 | ||
| 306 | (defalias 'calcFunc-esimplify 'math-simplify-extended) | |
| 136211a9 | 307 | |
| 0c908945 JB |
308 | ;; math-top-only is local to math-simplify, but is used by |
| 309 | ;; math-simplify-step, which is called by math-simplify. | |
| 310 | (defvar math-top-only) | |
| 311 | ||
| 136211a9 EZ |
312 | (defun math-simplify (top-expr) |
| 313 | (let ((math-simplifying t) | |
| 0c908945 | 314 | (math-top-only (consp calc-simplify-mode)) |
| 136211a9 EZ |
315 | (simp-rules (append (and (calc-has-rules 'var-AlgSimpRules) |
| 316 | '((var AlgSimpRules var-AlgSimpRules))) | |
| 317 | (and math-living-dangerously | |
| 318 | (calc-has-rules 'var-ExtSimpRules) | |
| 319 | '((var ExtSimpRules var-ExtSimpRules))) | |
| 320 | (and math-simplifying-units | |
| 321 | (calc-has-rules 'var-UnitSimpRules) | |
| 322 | '((var UnitSimpRules var-UnitSimpRules))) | |
| 323 | (and math-integrating | |
| 324 | (calc-has-rules 'var-IntegSimpRules) | |
| 325 | '((var IntegSimpRules var-IntegSimpRules))))) | |
| 326 | res) | |
| 0c908945 | 327 | (if math-top-only |
| 136211a9 EZ |
328 | (let ((r simp-rules)) |
| 329 | (setq res (math-simplify-step (math-normalize top-expr)) | |
| 330 | calc-simplify-mode '(nil) | |
| 331 | top-expr (math-normalize res)) | |
| 332 | (while r | |
| 333 | (setq top-expr (math-rewrite top-expr (car r) | |
| 334 | '(neg (var inf var-inf))) | |
| 335 | r (cdr r)))) | |
| 336 | (calc-with-default-simplification | |
| 337 | (while (let ((r simp-rules)) | |
| 338 | (setq res (math-normalize top-expr)) | |
| 339 | (while r | |
| 340 | (setq res (math-rewrite res (car r)) | |
| 341 | r (cdr r))) | |
| 342 | (not (equal top-expr (setq res (math-simplify-step res))))) | |
| 343 | (setq top-expr res))))) | |
| d3896480 CW |
344 | top-expr) |
| 345 | ||
| 346 | (defalias 'calcFunc-simplify 'math-simplify) | |
| 136211a9 EZ |
347 | |
| 348 | ;;; The following has a "bug" in that if any recursive simplifications | |
| 349 | ;;; occur only the first handler will be tried; this doesn't really | |
| 350 | ;;; matter, since math-simplify-step is iterated to a fixed point anyway. | |
| 351 | (defun math-simplify-step (a) | |
| 352 | (if (Math-primp a) | |
| 353 | a | |
| 0c908945 | 354 | (let ((aa (if (or math-top-only |
| 136211a9 EZ |
355 | (memq (car a) '(calcFunc-quote calcFunc-condition |
| 356 | calcFunc-evalto))) | |
| 357 | a | |
| 358 | (cons (car a) (mapcar 'math-simplify-step (cdr a)))))) | |
| 359 | (and (symbolp (car aa)) | |
| 360 | (let ((handler (get (car aa) 'math-simplify))) | |
| 361 | (and handler | |
| 362 | (while (and handler | |
| 363 | (equal (setq aa (or (funcall (car handler) aa) | |
| 364 | aa)) | |
| 365 | a)) | |
| 366 | (setq handler (cdr handler)))))) | |
| d3896480 | 367 | aa))) |
| 136211a9 EZ |
368 | |
| 369 | ||
| 41cf648d JB |
370 | (defmacro math-defsimplify (funcs &rest code) |
| 371 | (append '(progn) | |
| 372 | (mapcar (function | |
| 373 | (lambda (func) | |
| 374 | (list 'put (list 'quote func) ''math-simplify | |
| 375 | (list 'nconc | |
| 376 | (list 'get (list 'quote func) ''math-simplify) | |
| 377 | (list 'list | |
| 378 | (list 'function | |
| 379 | (append '(lambda (math-simplify-expr)) | |
| 380 | code))))))) | |
| 381 | (if (symbolp funcs) (list funcs) funcs)))) | |
| 382 | (put 'math-defsimplify 'lisp-indent-hook 1) | |
| 136211a9 | 383 | |
| 0c908945 JB |
384 | ;; The function created by math-defsimplify uses the variable |
| 385 | ;; math-simplify-expr, and so is used by functions in math-defsimplify | |
| 386 | (defvar math-simplify-expr) | |
| 387 | ||
| 136211a9 EZ |
388 | (math-defsimplify (+ -) |
| 389 | (math-simplify-plus)) | |
| 390 | ||
| 391 | (defun math-simplify-plus () | |
| 0c908945 JB |
392 | (cond ((and (memq (car-safe (nth 1 math-simplify-expr)) '(+ -)) |
| 393 | (Math-numberp (nth 2 (nth 1 math-simplify-expr))) | |
| 394 | (not (Math-numberp (nth 2 math-simplify-expr)))) | |
| 395 | (let ((x (nth 2 math-simplify-expr)) | |
| 396 | (op (car math-simplify-expr))) | |
| 397 | (setcar (cdr (cdr math-simplify-expr)) (nth 2 (nth 1 math-simplify-expr))) | |
| 398 | (setcar math-simplify-expr (car (nth 1 math-simplify-expr))) | |
| 399 | (setcar (cdr (cdr (nth 1 math-simplify-expr))) x) | |
| 400 | (setcar (nth 1 math-simplify-expr) op))) | |
| 401 | ((and (eq (car math-simplify-expr) '+) | |
| 402 | (Math-numberp (nth 1 math-simplify-expr)) | |
| 403 | (not (Math-numberp (nth 2 math-simplify-expr)))) | |
| 404 | (let ((x (nth 2 math-simplify-expr))) | |
| 405 | (setcar (cdr (cdr math-simplify-expr)) (nth 1 math-simplify-expr)) | |
| 406 | (setcar (cdr math-simplify-expr) x)))) | |
| 407 | (let ((aa math-simplify-expr) | |
| 136211a9 EZ |
408 | aaa temp) |
| 409 | (while (memq (car-safe (setq aaa (nth 1 aa))) '(+ -)) | |
| 0c908945 JB |
410 | (if (setq temp (math-combine-sum (nth 2 aaa) (nth 2 math-simplify-expr) |
| 411 | (eq (car aaa) '-) | |
| 412 | (eq (car math-simplify-expr) '-) t)) | |
| 136211a9 | 413 | (progn |
| 0c908945 JB |
414 | (setcar (cdr (cdr math-simplify-expr)) temp) |
| 415 | (setcar math-simplify-expr '+) | |
| 136211a9 EZ |
416 | (setcar (cdr (cdr aaa)) 0))) |
| 417 | (setq aa (nth 1 aa))) | |
| 0c908945 JB |
418 | (if (setq temp (math-combine-sum aaa (nth 2 math-simplify-expr) |
| 419 | nil (eq (car math-simplify-expr) '-) t)) | |
| 136211a9 | 420 | (progn |
| 0c908945 JB |
421 | (setcar (cdr (cdr math-simplify-expr)) temp) |
| 422 | (setcar math-simplify-expr '+) | |
| 136211a9 | 423 | (setcar (cdr aa) 0))) |
| 0c908945 | 424 | math-simplify-expr)) |
| 136211a9 EZ |
425 | |
| 426 | (math-defsimplify * | |
| 427 | (math-simplify-times)) | |
| 428 | ||
| 429 | (defun math-simplify-times () | |
| 0c908945 JB |
430 | (if (eq (car-safe (nth 2 math-simplify-expr)) '*) |
| 431 | (and (math-beforep (nth 1 (nth 2 math-simplify-expr)) (nth 1 math-simplify-expr)) | |
| 432 | (or (math-known-scalarp (nth 1 math-simplify-expr) t) | |
| 433 | (math-known-scalarp (nth 1 (nth 2 math-simplify-expr)) t)) | |
| 434 | (let ((x (nth 1 math-simplify-expr))) | |
| 435 | (setcar (cdr math-simplify-expr) (nth 1 (nth 2 math-simplify-expr))) | |
| 436 | (setcar (cdr (nth 2 math-simplify-expr)) x))) | |
| 437 | (and (math-beforep (nth 2 math-simplify-expr) (nth 1 math-simplify-expr)) | |
| 438 | (or (math-known-scalarp (nth 1 math-simplify-expr) t) | |
| 439 | (math-known-scalarp (nth 2 math-simplify-expr) t)) | |
| 440 | (let ((x (nth 2 math-simplify-expr))) | |
| 441 | (setcar (cdr (cdr math-simplify-expr)) (nth 1 math-simplify-expr)) | |
| 442 | (setcar (cdr math-simplify-expr) x)))) | |
| 443 | (let ((aa math-simplify-expr) | |
| 136211a9 | 444 | aaa temp |
| 0c908945 JB |
445 | (safe t) (scalar (math-known-scalarp (nth 1 math-simplify-expr)))) |
| 446 | (if (and (Math-ratp (nth 1 math-simplify-expr)) | |
| 447 | (setq temp (math-common-constant-factor (nth 2 math-simplify-expr)))) | |
| 136211a9 | 448 | (progn |
| 0c908945 JB |
449 | (setcar (cdr (cdr math-simplify-expr)) |
| 450 | (math-cancel-common-factor (nth 2 math-simplify-expr) temp)) | |
| 451 | (setcar (cdr math-simplify-expr) (math-mul (nth 1 math-simplify-expr) temp)))) | |
| 136211a9 EZ |
452 | (while (and (eq (car-safe (setq aaa (nth 2 aa))) '*) |
| 453 | safe) | |
| 0c908945 JB |
454 | (if (setq temp (math-combine-prod (nth 1 math-simplify-expr) |
| 455 | (nth 1 aaa) nil nil t)) | |
| 136211a9 | 456 | (progn |
| 0c908945 | 457 | (setcar (cdr math-simplify-expr) temp) |
| 136211a9 EZ |
458 | (setcar (cdr aaa) 1))) |
| 459 | (setq safe (or scalar (math-known-scalarp (nth 1 aaa) t)) | |
| 460 | aa (nth 2 aa))) | |
| 0c908945 | 461 | (if (and (setq temp (math-combine-prod aaa (nth 1 math-simplify-expr) nil nil t)) |
| 136211a9 EZ |
462 | safe) |
| 463 | (progn | |
| 0c908945 | 464 | (setcar (cdr math-simplify-expr) temp) |
| 136211a9 | 465 | (setcar (cdr (cdr aa)) 1))) |
| 0c908945 JB |
466 | (if (and (eq (car-safe (nth 1 math-simplify-expr)) 'frac) |
| 467 | (memq (nth 1 (nth 1 math-simplify-expr)) '(1 -1))) | |
| 468 | (math-div (math-mul (nth 2 math-simplify-expr) | |
| 469 | (nth 1 (nth 1 math-simplify-expr))) | |
| 470 | (nth 2 (nth 1 math-simplify-expr))) | |
| 471 | math-simplify-expr))) | |
| 136211a9 EZ |
472 | |
| 473 | (math-defsimplify / | |
| 474 | (math-simplify-divide)) | |
| 475 | ||
| 476 | (defun math-simplify-divide () | |
| 0c908945 | 477 | (let ((np (cdr math-simplify-expr)) |
| 136211a9 | 478 | (nover nil) |
| 0c908945 JB |
479 | (nn (and (or (eq (car math-simplify-expr) '/) |
| 480 | (not (Math-realp (nth 2 math-simplify-expr)))) | |
| 481 | (math-common-constant-factor (nth 2 math-simplify-expr)))) | |
| 136211a9 EZ |
482 | n op) |
| 483 | (if nn | |
| 484 | (progn | |
| 0c908945 JB |
485 | (setq n (and (or (eq (car math-simplify-expr) '/) |
| 486 | (not (Math-realp (nth 1 math-simplify-expr)))) | |
| 487 | (math-common-constant-factor (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
488 | (if (and (eq (car-safe nn) 'frac) (eq (nth 1 nn) 1) (not n)) |
| 489 | (progn | |
| 0c908945 JB |
490 | (setcar (cdr math-simplify-expr) |
| 491 | (math-mul (nth 2 nn) (nth 1 math-simplify-expr))) | |
| 492 | (setcar (cdr (cdr math-simplify-expr)) | |
| 493 | (math-cancel-common-factor (nth 2 math-simplify-expr) nn)) | |
| 136211a9 | 494 | (if (and (math-negp nn) |
| 0c908945 JB |
495 | (setq op (assq (car math-simplify-expr) calc-tweak-eqn-table))) |
| 496 | (setcar math-simplify-expr (nth 1 op)))) | |
| 136211a9 EZ |
497 | (if (and n (not (eq (setq n (math-frac-gcd n nn)) 1))) |
| 498 | (progn | |
| 0c908945 JB |
499 | (setcar (cdr math-simplify-expr) |
| 500 | (math-cancel-common-factor (nth 1 math-simplify-expr) n)) | |
| 501 | (setcar (cdr (cdr math-simplify-expr)) | |
| 502 | (math-cancel-common-factor (nth 2 math-simplify-expr) n)) | |
| 136211a9 | 503 | (if (and (math-negp n) |
| 0c908945 JB |
504 | (setq op (assq (car math-simplify-expr) |
| 505 | calc-tweak-eqn-table))) | |
| 506 | (setcar math-simplify-expr (nth 1 op)))))))) | |
| 136211a9 | 507 | (if (and (eq (car-safe (car np)) '/) |
| 0c908945 | 508 | (math-known-scalarp (nth 2 math-simplify-expr) t)) |
| 136211a9 | 509 | (progn |
| 0c908945 | 510 | (setq np (cdr (nth 1 math-simplify-expr))) |
| 136211a9 EZ |
511 | (while (eq (car-safe (setq n (car np))) '*) |
| 512 | (and (math-known-scalarp (nth 2 n) t) | |
| 0c908945 | 513 | (math-simplify-divisor (cdr n) (cdr (cdr math-simplify-expr)) nil t)) |
| 136211a9 | 514 | (setq np (cdr (cdr n)))) |
| 0c908945 | 515 | (math-simplify-divisor np (cdr (cdr math-simplify-expr)) nil t) |
| 136211a9 | 516 | (setq nover t |
| 0c908945 | 517 | np (cdr (cdr (nth 1 math-simplify-expr)))))) |
| 136211a9 EZ |
518 | (while (eq (car-safe (setq n (car np))) '*) |
| 519 | (and (math-known-scalarp (nth 2 n) t) | |
| 0c908945 | 520 | (math-simplify-divisor (cdr n) (cdr (cdr math-simplify-expr)) nover t)) |
| 136211a9 | 521 | (setq np (cdr (cdr n)))) |
| 0c908945 JB |
522 | (math-simplify-divisor np (cdr (cdr math-simplify-expr)) nover t) |
| 523 | math-simplify-expr)) | |
| 524 | ||
| 525 | ;; The variables math-simplify-divisor-nover and math-simplify-divisor-dover | |
| 526 | ;; are local variables for math-simplify-divisor, but are used by | |
| 527 | ;; math-simplify-one-divisor. | |
| 528 | (defvar math-simplify-divisor-nover) | |
| 529 | (defvar math-simplify-divisor-dover) | |
| 136211a9 | 530 | |
| 0c908945 JB |
531 | (defun math-simplify-divisor (np dp math-simplify-divisor-nover |
| 532 | math-simplify-divisor-dover) | |
| 136211a9 | 533 | (cond ((eq (car-safe (car dp)) '/) |
| 0c908945 JB |
534 | (math-simplify-divisor np (cdr (car dp)) |
| 535 | math-simplify-divisor-nover | |
| 536 | math-simplify-divisor-dover) | |
| 136211a9 EZ |
537 | (and (math-known-scalarp (nth 1 (car dp)) t) |
| 538 | (math-simplify-divisor np (cdr (cdr (car dp))) | |
| 0c908945 JB |
539 | math-simplify-divisor-nover |
| 540 | (not math-simplify-divisor-dover)))) | |
| 541 | ((or (or (eq (car math-simplify-expr) '/) | |
| 136211a9 EZ |
542 | (let ((signs (math-possible-signs (car np)))) |
| 543 | (or (memq signs '(1 4)) | |
| 0c908945 | 544 | (and (memq (car math-simplify-expr) '(calcFunc-eq calcFunc-neq)) |
| 136211a9 EZ |
545 | (eq signs 5)) |
| 546 | math-living-dangerously))) | |
| 547 | (math-numberp (car np))) | |
| 358c90f4 JB |
548 | (let (d |
| 549 | (safe t) | |
| 550 | (scalar (math-known-scalarp (car np)))) | |
| 136211a9 EZ |
551 | (while (and (eq (car-safe (setq d (car dp))) '*) |
| 552 | safe) | |
| 553 | (math-simplify-one-divisor np (cdr d)) | |
| 554 | (setq safe (or scalar (math-known-scalarp (nth 1 d) t)) | |
| 555 | dp (cdr (cdr d)))) | |
| 556 | (if safe | |
| d3896480 | 557 | (math-simplify-one-divisor np dp)))))) |
| 136211a9 EZ |
558 | |
| 559 | (defun math-simplify-one-divisor (np dp) | |
| 0c908945 JB |
560 | (let ((temp (math-combine-prod (car np) (car dp) math-simplify-divisor-nover |
| 561 | math-simplify-divisor-dover t)) | |
| 562 | op) | |
| 563 | (if temp | |
| 564 | (progn | |
| 565 | (and (not (memq (car math-simplify-expr) '(/ calcFunc-eq calcFunc-neq))) | |
| 566 | (math-known-negp (car dp)) | |
| 567 | (setq op (assq (car math-simplify-expr) calc-tweak-eqn-table)) | |
| 568 | (setcar math-simplify-expr (nth 1 op))) | |
| 569 | (setcar np (if math-simplify-divisor-nover (math-div 1 temp) temp)) | |
| 570 | (setcar dp 1)) | |
| 571 | (and math-simplify-divisor-dover (not math-simplify-divisor-nover) | |
| 572 | (eq (car math-simplify-expr) '/) | |
| 573 | (eq (car-safe (car dp)) 'calcFunc-sqrt) | |
| 574 | (Math-integerp (nth 1 (car dp))) | |
| 575 | (progn | |
| 576 | (setcar np (math-mul (car np) | |
| 577 | (list 'calcFunc-sqrt (nth 1 (car dp))))) | |
| 578 | (setcar dp (nth 1 (car dp)))))))) | |
| 136211a9 EZ |
579 | |
| 580 | (defun math-common-constant-factor (expr) | |
| 581 | (if (Math-realp expr) | |
| 582 | (if (Math-ratp expr) | |
| 583 | (and (not (memq expr '(0 1 -1))) | |
| 584 | (math-abs expr)) | |
| 585 | (if (math-ratp (setq expr (math-to-simple-fraction expr))) | |
| 586 | (math-common-constant-factor expr))) | |
| 587 | (if (memq (car expr) '(+ - cplx sdev)) | |
| 588 | (let ((f1 (math-common-constant-factor (nth 1 expr))) | |
| 589 | (f2 (math-common-constant-factor (nth 2 expr)))) | |
| 590 | (and f1 f2 | |
| 591 | (not (eq (setq f1 (math-frac-gcd f1 f2)) 1)) | |
| 592 | f1)) | |
| 593 | (if (memq (car expr) '(* polar)) | |
| 594 | (math-common-constant-factor (nth 1 expr)) | |
| 595 | (if (eq (car expr) '/) | |
| 596 | (or (math-common-constant-factor (nth 1 expr)) | |
| 597 | (and (Math-integerp (nth 2 expr)) | |
| d3896480 | 598 | (list 'frac 1 (math-abs (nth 2 expr)))))))))) |
| 136211a9 EZ |
599 | |
| 600 | (defun math-cancel-common-factor (expr val) | |
| 601 | (if (memq (car-safe expr) '(+ - cplx sdev)) | |
| 602 | (progn | |
| 603 | (setcar (cdr expr) (math-cancel-common-factor (nth 1 expr) val)) | |
| 604 | (setcar (cdr (cdr expr)) (math-cancel-common-factor (nth 2 expr) val)) | |
| 605 | expr) | |
| 606 | (if (eq (car-safe expr) '*) | |
| 607 | (math-mul (math-cancel-common-factor (nth 1 expr) val) (nth 2 expr)) | |
| d3896480 | 608 | (math-div expr val)))) |
| 136211a9 EZ |
609 | |
| 610 | (defun math-frac-gcd (a b) | |
| 611 | (if (Math-zerop a) | |
| 612 | b | |
| 613 | (if (Math-zerop b) | |
| 614 | a | |
| 615 | (if (and (Math-integerp a) | |
| 616 | (Math-integerp b)) | |
| 617 | (math-gcd a b) | |
| 618 | (and (Math-integerp a) (setq a (list 'frac a 1))) | |
| 619 | (and (Math-integerp b) (setq b (list 'frac b 1))) | |
| 620 | (math-make-frac (math-gcd (nth 1 a) (nth 1 b)) | |
| d3896480 | 621 | (math-gcd (nth 2 a) (nth 2 b))))))) |
| 136211a9 EZ |
622 | |
| 623 | (math-defsimplify % | |
| 624 | (math-simplify-mod)) | |
| 625 | ||
| 626 | (defun math-simplify-mod () | |
| 0c908945 JB |
627 | (and (Math-realp (nth 2 math-simplify-expr)) |
| 628 | (Math-posp (nth 2 math-simplify-expr)) | |
| 629 | (let ((lin (math-is-linear (nth 1 math-simplify-expr))) | |
| 136211a9 EZ |
630 | t1 t2 t3) |
| 631 | (or (and lin | |
| 632 | (or (math-negp (car lin)) | |
| 0c908945 | 633 | (not (Math-lessp (car lin) (nth 2 math-simplify-expr)))) |
| 136211a9 EZ |
634 | (list '% |
| 635 | (list '+ | |
| 636 | (math-mul (nth 1 lin) (nth 2 lin)) | |
| 0c908945 JB |
637 | (math-mod (car lin) (nth 2 math-simplify-expr))) |
| 638 | (nth 2 math-simplify-expr))) | |
| 136211a9 EZ |
639 | (and lin |
| 640 | (not (math-equal-int (nth 1 lin) 1)) | |
| 641 | (math-num-integerp (nth 1 lin)) | |
| 0c908945 JB |
642 | (math-num-integerp (nth 2 math-simplify-expr)) |
| 643 | (setq t1 (calcFunc-gcd (nth 1 lin) (nth 2 math-simplify-expr))) | |
| 136211a9 EZ |
644 | (not (math-equal-int t1 1)) |
| 645 | (list '* | |
| 646 | t1 | |
| 647 | (list '% | |
| 648 | (list '+ | |
| 649 | (math-mul (math-div (nth 1 lin) t1) | |
| 650 | (nth 2 lin)) | |
| 651 | (let ((calc-prefer-frac t)) | |
| 652 | (math-div (car lin) t1))) | |
| 0c908945 JB |
653 | (math-div (nth 2 math-simplify-expr) t1)))) |
| 654 | (and (math-equal-int (nth 2 math-simplify-expr) 1) | |
| 136211a9 EZ |
655 | (math-known-integerp (if lin |
| 656 | (math-mul (nth 1 lin) (nth 2 lin)) | |
| 0c908945 | 657 | (nth 1 math-simplify-expr))) |
| d3896480 | 658 | (if lin (math-mod (car lin) 1) 0)))))) |
| 136211a9 EZ |
659 | |
| 660 | (math-defsimplify (calcFunc-eq calcFunc-neq calcFunc-lt | |
| 661 | calcFunc-gt calcFunc-leq calcFunc-geq) | |
| 0c908945 | 662 | (if (= (length math-simplify-expr) 3) |
| 136211a9 EZ |
663 | (math-simplify-ineq))) |
| 664 | ||
| 665 | (defun math-simplify-ineq () | |
| 0c908945 | 666 | (let ((np (cdr math-simplify-expr)) |
| 136211a9 EZ |
667 | n) |
| 668 | (while (memq (car-safe (setq n (car np))) '(+ -)) | |
| 0c908945 | 669 | (math-simplify-add-term (cdr (cdr n)) (cdr (cdr math-simplify-expr)) |
| 136211a9 EZ |
670 | (eq (car n) '-) nil) |
| 671 | (setq np (cdr n))) | |
| 0c908945 JB |
672 | (math-simplify-add-term np (cdr (cdr math-simplify-expr)) nil |
| 673 | (eq np (cdr math-simplify-expr))) | |
| 136211a9 | 674 | (math-simplify-divide) |
| 0c908945 JB |
675 | (let ((signs (math-possible-signs (cons '- (cdr math-simplify-expr))))) |
| 676 | (or (cond ((eq (car math-simplify-expr) 'calcFunc-eq) | |
| 136211a9 EZ |
677 | (or (and (eq signs 2) 1) |
| 678 | (and (memq signs '(1 4 5)) 0))) | |
| 0c908945 | 679 | ((eq (car math-simplify-expr) 'calcFunc-neq) |
| 136211a9 EZ |
680 | (or (and (eq signs 2) 0) |
| 681 | (and (memq signs '(1 4 5)) 1))) | |
| 0c908945 | 682 | ((eq (car math-simplify-expr) 'calcFunc-lt) |
| 136211a9 EZ |
683 | (or (and (eq signs 1) 1) |
| 684 | (and (memq signs '(2 4 6)) 0))) | |
| 0c908945 | 685 | ((eq (car math-simplify-expr) 'calcFunc-gt) |
| 136211a9 EZ |
686 | (or (and (eq signs 4) 1) |
| 687 | (and (memq signs '(1 2 3)) 0))) | |
| 0c908945 | 688 | ((eq (car math-simplify-expr) 'calcFunc-leq) |
| 136211a9 EZ |
689 | (or (and (eq signs 4) 0) |
| 690 | (and (memq signs '(1 2 3)) 1))) | |
| 0c908945 | 691 | ((eq (car math-simplify-expr) 'calcFunc-geq) |
| 136211a9 EZ |
692 | (or (and (eq signs 1) 0) |
| 693 | (and (memq signs '(2 4 6)) 1)))) | |
| 0c908945 | 694 | math-simplify-expr)))) |
| 136211a9 EZ |
695 | |
| 696 | (defun math-simplify-add-term (np dp minus lplain) | |
| 697 | (or (math-vectorp (car np)) | |
| 698 | (let ((rplain t) | |
| 699 | n d dd temp) | |
| 700 | (while (memq (car-safe (setq n (car np) d (car dp))) '(+ -)) | |
| 701 | (setq rplain nil) | |
| 702 | (if (setq temp (math-combine-sum n (nth 2 d) | |
| 703 | minus (eq (car d) '+) t)) | |
| 704 | (if (or lplain (eq (math-looks-negp temp) minus)) | |
| 705 | (progn | |
| 706 | (setcar np (setq n (if minus (math-neg temp) temp))) | |
| 707 | (setcar (cdr (cdr d)) 0)) | |
| 708 | (progn | |
| 709 | (setcar np 0) | |
| 710 | (setcar (cdr (cdr d)) (setq n (if (eq (car d) '+) | |
| 711 | (math-neg temp) | |
| 712 | temp)))))) | |
| 713 | (setq dp (cdr d))) | |
| 714 | (if (setq temp (math-combine-sum n d minus t t)) | |
| 715 | (if (or lplain | |
| 716 | (and (not rplain) | |
| 717 | (eq (math-looks-negp temp) minus))) | |
| 718 | (progn | |
| 719 | (setcar np (setq n (if minus (math-neg temp) temp))) | |
| 720 | (setcar dp 0)) | |
| 721 | (progn | |
| 722 | (setcar np 0) | |
| d3896480 | 723 | (setcar dp (setq n (math-neg temp))))))))) |
| 136211a9 EZ |
724 | |
| 725 | (math-defsimplify calcFunc-sin | |
| 0c908945 JB |
726 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin) |
| 727 | (nth 1 (nth 1 math-simplify-expr))) | |
| 728 | (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 729 | (math-neg (list 'calcFunc-sin (math-neg (nth 1 math-simplify-expr))))) | |
| 136211a9 | 730 | (and (eq calc-angle-mode 'rad) |
| 0c908945 | 731 | (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi)))) |
| 136211a9 EZ |
732 | (and n |
| 733 | (math-known-sin (car n) (nth 1 n) 120 0)))) | |
| 734 | (and (eq calc-angle-mode 'deg) | |
| 0c908945 | 735 | (let ((n (math-integer-plus (nth 1 math-simplify-expr)))) |
| 136211a9 EZ |
736 | (and n |
| 737 | (math-known-sin (car n) (nth 1 n) '(frac 2 3) 0)))) | |
| 0c908945 JB |
738 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos) |
| 739 | (list 'calcFunc-sqrt (math-sub 1 (math-sqr | |
| 740 | (nth 1 (nth 1 math-simplify-expr)))))) | |
| 741 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctan) | |
| 742 | (math-div (nth 1 (nth 1 math-simplify-expr)) | |
| 136211a9 | 743 | (list 'calcFunc-sqrt |
| 0c908945 JB |
744 | (math-add 1 (math-sqr |
| 745 | (nth 1 (nth 1 math-simplify-expr))))))) | |
| 746 | (let ((m (math-should-expand-trig (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
747 | (and m (integerp (car m)) |
| 748 | (let ((n (car m)) (a (nth 1 m))) | |
| 749 | (list '+ | |
| 750 | (list '* (list 'calcFunc-sin (list '* (1- n) a)) | |
| 751 | (list 'calcFunc-cos a)) | |
| 752 | (list '* (list 'calcFunc-cos (list '* (1- n) a)) | |
| d3896480 | 753 | (list 'calcFunc-sin a)))))))) |
| 136211a9 EZ |
754 | |
| 755 | (math-defsimplify calcFunc-cos | |
| 0c908945 JB |
756 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos) |
| 757 | (nth 1 (nth 1 math-simplify-expr))) | |
| 758 | (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 759 | (list 'calcFunc-cos (math-neg (nth 1 math-simplify-expr)))) | |
| 136211a9 | 760 | (and (eq calc-angle-mode 'rad) |
| 0c908945 | 761 | (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi)))) |
| 136211a9 EZ |
762 | (and n |
| 763 | (math-known-sin (car n) (nth 1 n) 120 300)))) | |
| 764 | (and (eq calc-angle-mode 'deg) | |
| 0c908945 | 765 | (let ((n (math-integer-plus (nth 1 math-simplify-expr)))) |
| 136211a9 EZ |
766 | (and n |
| 767 | (math-known-sin (car n) (nth 1 n) '(frac 2 3) 300)))) | |
| 0c908945 JB |
768 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin) |
| 769 | (list 'calcFunc-sqrt | |
| 770 | (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr)))))) | |
| 771 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctan) | |
| 136211a9 EZ |
772 | (math-div 1 |
| 773 | (list 'calcFunc-sqrt | |
| 0c908945 JB |
774 | (math-add 1 |
| 775 | (math-sqr (nth 1 (nth 1 math-simplify-expr))))))) | |
| 776 | (let ((m (math-should-expand-trig (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
777 | (and m (integerp (car m)) |
| 778 | (let ((n (car m)) (a (nth 1 m))) | |
| 779 | (list '- | |
| 780 | (list '* (list 'calcFunc-cos (list '* (1- n) a)) | |
| 781 | (list 'calcFunc-cos a)) | |
| 782 | (list '* (list 'calcFunc-sin (list '* (1- n) a)) | |
| d3896480 | 783 | (list 'calcFunc-sin a)))))))) |
| 136211a9 | 784 | |
| 6a5412e4 JB |
785 | (math-defsimplify calcFunc-sec |
| 786 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 787 | (list 'calcFunc-sec (math-neg (nth 1 math-simplify-expr)))) | |
| 788 | (and (eq calc-angle-mode 'rad) | |
| 789 | (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi)))) | |
| 790 | (and n | |
| 791 | (math-div 1 (math-known-sin (car n) (nth 1 n) 120 300))))) | |
| 792 | (and (eq calc-angle-mode 'deg) | |
| 793 | (let ((n (math-integer-plus (nth 1 math-simplify-expr)))) | |
| 794 | (and n | |
| 795 | (math-div 1 (math-known-sin (car n) (nth 1 n) '(frac 2 3) 300))))) | |
| 796 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin) | |
| 797 | (math-div | |
| 798 | 1 | |
| 799 | (list 'calcFunc-sqrt | |
| 800 | (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr))))))) | |
| 801 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos) | |
| 802 | (math-div | |
| 803 | 1 | |
| 804 | (nth 1 (nth 1 math-simplify-expr)))) | |
| 805 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctan) | |
| 806 | (list 'calcFunc-sqrt | |
| 807 | (math-add 1 | |
| 808 | (math-sqr (nth 1 (nth 1 math-simplify-expr)))))))) | |
| 809 | ||
| 810 | (math-defsimplify calcFunc-csc | |
| 811 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 812 | (math-neg (list 'calcFunc-csc (math-neg (nth 1 math-simplify-expr))))) | |
| 813 | (and (eq calc-angle-mode 'rad) | |
| 814 | (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi)))) | |
| 815 | (and n | |
| 816 | (math-div 1 (math-known-sin (car n) (nth 1 n) 120 0))))) | |
| 817 | (and (eq calc-angle-mode 'deg) | |
| 818 | (let ((n (math-integer-plus (nth 1 math-simplify-expr)))) | |
| 819 | (and n | |
| 820 | (math-div 1 (math-known-sin (car n) (nth 1 n) '(frac 2 3) 0))))) | |
| 821 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin) | |
| 822 | (math-div 1 (nth 1 (nth 1 math-simplify-expr)))) | |
| 823 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos) | |
| 824 | (math-div | |
| 825 | 1 | |
| 826 | (list 'calcFunc-sqrt (math-sub 1 (math-sqr | |
| 827 | (nth 1 (nth 1 math-simplify-expr))))))) | |
| 828 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctan) | |
| 829 | (math-div (list 'calcFunc-sqrt | |
| 830 | (math-add 1 (math-sqr | |
| 831 | (nth 1 (nth 1 math-simplify-expr))))) | |
| 832 | (nth 1 (nth 1 math-simplify-expr)))))) | |
| 833 | ||
| 136211a9 EZ |
834 | (defun math-should-expand-trig (x &optional hyperbolic) |
| 835 | (let ((m (math-is-multiple x))) | |
| 836 | (and math-living-dangerously | |
| 837 | m (or (and (integerp (car m)) (> (car m) 1)) | |
| 838 | (equal (car m) '(frac 1 2))) | |
| 839 | (or math-integrating | |
| 840 | (memq (car-safe (nth 1 m)) | |
| 841 | (if hyperbolic | |
| 842 | '(calcFunc-arcsinh calcFunc-arccosh calcFunc-arctanh) | |
| 843 | '(calcFunc-arcsin calcFunc-arccos calcFunc-arctan))) | |
| 844 | (and (eq (car-safe (nth 1 m)) 'calcFunc-ln) | |
| 845 | (eq hyperbolic 'exp))) | |
| d3896480 | 846 | m))) |
| 136211a9 EZ |
847 | |
| 848 | (defun math-known-sin (plus n mul off) | |
| 849 | (setq n (math-mul n mul)) | |
| 850 | (and (math-num-integerp n) | |
| 851 | (setq n (math-mod (math-add (math-trunc n) off) 240)) | |
| 852 | (if (>= n 120) | |
| 853 | (and (setq n (math-known-sin plus (- n 120) 1 0)) | |
| 854 | (math-neg n)) | |
| 855 | (if (> n 60) | |
| 856 | (setq n (- 120 n))) | |
| 857 | (if (math-zerop plus) | |
| 858 | (and (or calc-symbolic-mode | |
| 859 | (memq n '(0 20 60))) | |
| 860 | (cdr (assq n | |
| 861 | '( (0 . 0) | |
| 862 | (10 . (/ (calcFunc-sqrt | |
| 863 | (- 2 (calcFunc-sqrt 3))) 2)) | |
| 864 | (12 . (/ (- (calcFunc-sqrt 5) 1) 4)) | |
| 865 | (15 . (/ (calcFunc-sqrt | |
| 866 | (- 2 (calcFunc-sqrt 2))) 2)) | |
| 867 | (20 . (/ 1 2)) | |
| 868 | (24 . (* (^ (/ 1 2) (/ 3 2)) | |
| 869 | (calcFunc-sqrt | |
| 870 | (- 5 (calcFunc-sqrt 5))))) | |
| 871 | (30 . (/ (calcFunc-sqrt 2) 2)) | |
| 872 | (36 . (/ (+ (calcFunc-sqrt 5) 1) 4)) | |
| 873 | (40 . (/ (calcFunc-sqrt 3) 2)) | |
| 874 | (45 . (/ (calcFunc-sqrt | |
| 875 | (+ 2 (calcFunc-sqrt 2))) 2)) | |
| 876 | (48 . (* (^ (/ 1 2) (/ 3 2)) | |
| 877 | (calcFunc-sqrt | |
| 878 | (+ 5 (calcFunc-sqrt 5))))) | |
| 879 | (50 . (/ (calcFunc-sqrt | |
| 880 | (+ 2 (calcFunc-sqrt 3))) 2)) | |
| 881 | (60 . 1))))) | |
| 882 | (cond ((eq n 0) (math-normalize (list 'calcFunc-sin plus))) | |
| 883 | ((eq n 60) (math-normalize (list 'calcFunc-cos plus))) | |
| d3896480 | 884 | (t nil)))))) |
| 136211a9 EZ |
885 | |
| 886 | (math-defsimplify calcFunc-tan | |
| 0c908945 JB |
887 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctan) |
| 888 | (nth 1 (nth 1 math-simplify-expr))) | |
| 889 | (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 890 | (math-neg (list 'calcFunc-tan (math-neg (nth 1 math-simplify-expr))))) | |
| 136211a9 | 891 | (and (eq calc-angle-mode 'rad) |
| 0c908945 | 892 | (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi)))) |
| 136211a9 EZ |
893 | (and n |
| 894 | (math-known-tan (car n) (nth 1 n) 120)))) | |
| 895 | (and (eq calc-angle-mode 'deg) | |
| 0c908945 | 896 | (let ((n (math-integer-plus (nth 1 math-simplify-expr)))) |
| 136211a9 EZ |
897 | (and n |
| 898 | (math-known-tan (car n) (nth 1 n) '(frac 2 3))))) | |
| 0c908945 JB |
899 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin) |
| 900 | (math-div (nth 1 (nth 1 math-simplify-expr)) | |
| 136211a9 | 901 | (list 'calcFunc-sqrt |
| 0c908945 JB |
902 | (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr))))))) |
| 903 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos) | |
| 136211a9 | 904 | (math-div (list 'calcFunc-sqrt |
| 0c908945 JB |
905 | (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr))))) |
| 906 | (nth 1 (nth 1 math-simplify-expr)))) | |
| 907 | (let ((m (math-should-expand-trig (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
908 | (and m |
| 909 | (if (equal (car m) '(frac 1 2)) | |
| 910 | (math-div (math-sub 1 (list 'calcFunc-cos (nth 1 m))) | |
| 911 | (list 'calcFunc-sin (nth 1 m))) | |
| 0c908945 JB |
912 | (math-div (list 'calcFunc-sin (nth 1 math-simplify-expr)) |
| 913 | (list 'calcFunc-cos (nth 1 math-simplify-expr)))))))) | |
| 136211a9 | 914 | |
| 6a5412e4 JB |
915 | (math-defsimplify calcFunc-cot |
| 916 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 917 | (math-neg (list 'calcFunc-cot (math-neg (nth 1 math-simplify-expr))))) | |
| 918 | (and (eq calc-angle-mode 'rad) | |
| 919 | (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi)))) | |
| 920 | (and n | |
| 921 | (math-div 1 (math-known-tan (car n) (nth 1 n) 120))))) | |
| 922 | (and (eq calc-angle-mode 'deg) | |
| 923 | (let ((n (math-integer-plus (nth 1 math-simplify-expr)))) | |
| 924 | (and n | |
| 925 | (math-div 1 (math-known-tan (car n) (nth 1 n) '(frac 2 3)))))) | |
| 926 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin) | |
| 927 | (math-div (list 'calcFunc-sqrt | |
| 928 | (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr))))) | |
| 929 | (nth 1 (nth 1 math-simplify-expr)))) | |
| 930 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos) | |
| 931 | (math-div (nth 1 (nth 1 math-simplify-expr)) | |
| 932 | (list 'calcFunc-sqrt | |
| 933 | (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr))))))) | |
| 934 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctan) | |
| 935 | (math-div 1 (nth 1 (nth 1 math-simplify-expr)))))) | |
| 936 | ||
| 136211a9 EZ |
937 | (defun math-known-tan (plus n mul) |
| 938 | (setq n (math-mul n mul)) | |
| 939 | (and (math-num-integerp n) | |
| 940 | (setq n (math-mod (math-trunc n) 120)) | |
| 941 | (if (> n 60) | |
| 942 | (and (setq n (math-known-tan plus (- 120 n) 1)) | |
| 943 | (math-neg n)) | |
| 944 | (if (math-zerop plus) | |
| 945 | (and (or calc-symbolic-mode | |
| 946 | (memq n '(0 30 60))) | |
| 947 | (cdr (assq n '( (0 . 0) | |
| 948 | (10 . (- 2 (calcFunc-sqrt 3))) | |
| 949 | (12 . (calcFunc-sqrt | |
| 950 | (- 1 (* (/ 2 5) (calcFunc-sqrt 5))))) | |
| 951 | (15 . (- (calcFunc-sqrt 2) 1)) | |
| 952 | (20 . (/ (calcFunc-sqrt 3) 3)) | |
| 953 | (24 . (calcFunc-sqrt | |
| 954 | (- 5 (* 2 (calcFunc-sqrt 5))))) | |
| 955 | (30 . 1) | |
| 956 | (36 . (calcFunc-sqrt | |
| 957 | (+ 1 (* (/ 2 5) (calcFunc-sqrt 5))))) | |
| 958 | (40 . (calcFunc-sqrt 3)) | |
| 959 | (45 . (+ (calcFunc-sqrt 2) 1)) | |
| 960 | (48 . (calcFunc-sqrt | |
| 961 | (+ 5 (* 2 (calcFunc-sqrt 5))))) | |
| 962 | (50 . (+ 2 (calcFunc-sqrt 3))) | |
| 963 | (60 . (var uinf var-uinf)))))) | |
| 964 | (cond ((eq n 0) (math-normalize (list 'calcFunc-tan plus))) | |
| 965 | ((eq n 60) (math-normalize (list '/ -1 | |
| 966 | (list 'calcFunc-tan plus)))) | |
| d3896480 | 967 | (t nil)))))) |
| 136211a9 EZ |
968 | |
| 969 | (math-defsimplify calcFunc-sinh | |
| 0c908945 JB |
970 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh) |
| 971 | (nth 1 (nth 1 math-simplify-expr))) | |
| 972 | (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 973 | (math-neg (list 'calcFunc-sinh (math-neg (nth 1 math-simplify-expr))))) | |
| 974 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccosh) | |
| 136211a9 | 975 | math-living-dangerously |
| 0c908945 JB |
976 | (list 'calcFunc-sqrt |
| 977 | (math-sub (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1))) | |
| 978 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh) | |
| 136211a9 | 979 | math-living-dangerously |
| 0c908945 | 980 | (math-div (nth 1 (nth 1 math-simplify-expr)) |
| 136211a9 | 981 | (list 'calcFunc-sqrt |
| 0c908945 JB |
982 | (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr))))))) |
| 983 | (let ((m (math-should-expand-trig (nth 1 math-simplify-expr) t))) | |
| 136211a9 EZ |
984 | (and m (integerp (car m)) |
| 985 | (let ((n (car m)) (a (nth 1 m))) | |
| 986 | (if (> n 1) | |
| 987 | (list '+ | |
| 988 | (list '* (list 'calcFunc-sinh (list '* (1- n) a)) | |
| 989 | (list 'calcFunc-cosh a)) | |
| 990 | (list '* (list 'calcFunc-cosh (list '* (1- n) a)) | |
| d3896480 | 991 | (list 'calcFunc-sinh a))))))))) |
| 136211a9 EZ |
992 | |
| 993 | (math-defsimplify calcFunc-cosh | |
| 0c908945 JB |
994 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccosh) |
| 995 | (nth 1 (nth 1 math-simplify-expr))) | |
| 996 | (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 997 | (list 'calcFunc-cosh (math-neg (nth 1 math-simplify-expr)))) | |
| 998 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh) | |
| 136211a9 | 999 | math-living-dangerously |
| 0c908945 JB |
1000 | (list 'calcFunc-sqrt |
| 1001 | (math-add (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1))) | |
| 1002 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh) | |
| 136211a9 EZ |
1003 | math-living-dangerously |
| 1004 | (math-div 1 | |
| 1005 | (list 'calcFunc-sqrt | |
| 0c908945 JB |
1006 | (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr))))))) |
| 1007 | (let ((m (math-should-expand-trig (nth 1 math-simplify-expr) t))) | |
| 136211a9 EZ |
1008 | (and m (integerp (car m)) |
| 1009 | (let ((n (car m)) (a (nth 1 m))) | |
| 1010 | (if (> n 1) | |
| 1011 | (list '+ | |
| 1012 | (list '* (list 'calcFunc-cosh (list '* (1- n) a)) | |
| 1013 | (list 'calcFunc-cosh a)) | |
| 1014 | (list '* (list 'calcFunc-sinh (list '* (1- n) a)) | |
| d3896480 | 1015 | (list 'calcFunc-sinh a))))))))) |
| 136211a9 EZ |
1016 | |
| 1017 | (math-defsimplify calcFunc-tanh | |
| 0c908945 JB |
1018 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh) |
| 1019 | (nth 1 (nth 1 math-simplify-expr))) | |
| 1020 | (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 1021 | (math-neg (list 'calcFunc-tanh (math-neg (nth 1 math-simplify-expr))))) | |
| 1022 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh) | |
| 136211a9 | 1023 | math-living-dangerously |
| 0c908945 | 1024 | (math-div (nth 1 (nth 1 math-simplify-expr)) |
| 136211a9 | 1025 | (list 'calcFunc-sqrt |
| 0c908945 JB |
1026 | (math-add (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1)))) |
| 1027 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccosh) | |
| 136211a9 EZ |
1028 | math-living-dangerously |
| 1029 | (math-div (list 'calcFunc-sqrt | |
| 0c908945 JB |
1030 | (math-sub (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1)) |
| 1031 | (nth 1 (nth 1 math-simplify-expr)))) | |
| 1032 | (let ((m (math-should-expand-trig (nth 1 math-simplify-expr) t))) | |
| 136211a9 EZ |
1033 | (and m |
| 1034 | (if (equal (car m) '(frac 1 2)) | |
| 1035 | (math-div (math-sub (list 'calcFunc-cosh (nth 1 m)) 1) | |
| 1036 | (list 'calcFunc-sinh (nth 1 m))) | |
| 0c908945 JB |
1037 | (math-div (list 'calcFunc-sinh (nth 1 math-simplify-expr)) |
| 1038 | (list 'calcFunc-cosh (nth 1 math-simplify-expr)))))))) | |
| 136211a9 | 1039 | |
| 6a5412e4 JB |
1040 | (math-defsimplify calcFunc-sech |
| 1041 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 1042 | (list 'calcFunc-sech (math-neg (nth 1 math-simplify-expr)))) | |
| 1043 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh) | |
| 1044 | math-living-dangerously | |
| 1045 | (math-div | |
| 1046 | 1 | |
| 1047 | (list 'calcFunc-sqrt | |
| 1048 | (math-add (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1)))) | |
| 1049 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccosh) | |
| 1050 | math-living-dangerously | |
| 1051 | (math-div 1 (nth 1 (nth 1 math-simplify-expr))) 1) | |
| 1052 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh) | |
| 1053 | math-living-dangerously | |
| 1054 | (list 'calcFunc-sqrt | |
| 1055 | (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr)))))))) | |
| 1056 | ||
| 1057 | (math-defsimplify calcFunc-csch | |
| 1058 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 1059 | (math-neg (list 'calcFunc-csch (math-neg (nth 1 math-simplify-expr))))) | |
| 1060 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh) | |
| 1061 | math-living-dangerously | |
| 1062 | (math-div 1 (nth 1 (nth 1 math-simplify-expr)))) | |
| 1063 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccosh) | |
| 1064 | math-living-dangerously | |
| 1065 | (math-div | |
| 1066 | 1 | |
| 1067 | (list 'calcFunc-sqrt | |
| 1068 | (math-sub (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1)))) | |
| 1069 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh) | |
| 1070 | math-living-dangerously | |
| 1071 | (math-div (list 'calcFunc-sqrt | |
| 1072 | (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr))))) | |
| 1073 | (nth 1 (nth 1 math-simplify-expr)))))) | |
| 1074 | ||
| 1075 | (math-defsimplify calcFunc-coth | |
| 1076 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 1077 | (math-neg (list 'calcFunc-coth (math-neg (nth 1 math-simplify-expr))))) | |
| 1078 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh) | |
| 1079 | math-living-dangerously | |
| 1080 | (math-div (list 'calcFunc-sqrt | |
| 1081 | (math-add (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1)) | |
| 1082 | (nth 1 (nth 1 math-simplify-expr)))) | |
| 1083 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccosh) | |
| 1084 | math-living-dangerously | |
| 1085 | (math-div (nth 1 (nth 1 math-simplify-expr)) | |
| 1086 | (list 'calcFunc-sqrt | |
| 1087 | (math-sub (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1)))) | |
| 1088 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh) | |
| 1089 | math-living-dangerously | |
| 1090 | (math-div 1 (nth 1 (nth 1 math-simplify-expr)))))) | |
| 1091 | ||
| 136211a9 | 1092 | (math-defsimplify calcFunc-arcsin |
| 0c908945 JB |
1093 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) |
| 1094 | (math-neg (list 'calcFunc-arcsin (math-neg (nth 1 math-simplify-expr))))) | |
| 1095 | (and (eq (nth 1 math-simplify-expr) 1) | |
| 136211a9 | 1096 | (math-quarter-circle t)) |
| 0c908945 | 1097 | (and (equal (nth 1 math-simplify-expr) '(frac 1 2)) |
| 136211a9 EZ |
1098 | (math-div (math-half-circle t) 6)) |
| 1099 | (and math-living-dangerously | |
| 0c908945 JB |
1100 | (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sin) |
| 1101 | (nth 1 (nth 1 math-simplify-expr))) | |
| 136211a9 | 1102 | (and math-living-dangerously |
| 0c908945 | 1103 | (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cos) |
| 136211a9 | 1104 | (math-sub (math-quarter-circle t) |
| 0c908945 | 1105 | (nth 1 (nth 1 math-simplify-expr)))))) |
| 136211a9 EZ |
1106 | |
| 1107 | (math-defsimplify calcFunc-arccos | |
| 0c908945 | 1108 | (or (and (eq (nth 1 math-simplify-expr) 0) |
| 136211a9 | 1109 | (math-quarter-circle t)) |
| 0c908945 | 1110 | (and (eq (nth 1 math-simplify-expr) -1) |
| 136211a9 | 1111 | (math-half-circle t)) |
| 0c908945 | 1112 | (and (equal (nth 1 math-simplify-expr) '(frac 1 2)) |
| 136211a9 | 1113 | (math-div (math-half-circle t) 3)) |
| 0c908945 | 1114 | (and (equal (nth 1 math-simplify-expr) '(frac -1 2)) |
| 136211a9 EZ |
1115 | (math-div (math-mul (math-half-circle t) 2) 3)) |
| 1116 | (and math-living-dangerously | |
| 0c908945 JB |
1117 | (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cos) |
| 1118 | (nth 1 (nth 1 math-simplify-expr))) | |
| 136211a9 | 1119 | (and math-living-dangerously |
| 0c908945 | 1120 | (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sin) |
| 136211a9 | 1121 | (math-sub (math-quarter-circle t) |
| 0c908945 | 1122 | (nth 1 (nth 1 math-simplify-expr)))))) |
| 136211a9 EZ |
1123 | |
| 1124 | (math-defsimplify calcFunc-arctan | |
| 0c908945 JB |
1125 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) |
| 1126 | (math-neg (list 'calcFunc-arctan (math-neg (nth 1 math-simplify-expr))))) | |
| 1127 | (and (eq (nth 1 math-simplify-expr) 1) | |
| 136211a9 EZ |
1128 | (math-div (math-half-circle t) 4)) |
| 1129 | (and math-living-dangerously | |
| 0c908945 JB |
1130 | (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-tan) |
| 1131 | (nth 1 (nth 1 math-simplify-expr))))) | |
| 136211a9 EZ |
1132 | |
| 1133 | (math-defsimplify calcFunc-arcsinh | |
| 0c908945 JB |
1134 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) |
| 1135 | (math-neg (list 'calcFunc-arcsinh (math-neg (nth 1 math-simplify-expr))))) | |
| 1136 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sinh) | |
| 136211a9 | 1137 | (or math-living-dangerously |
| 0c908945 JB |
1138 | (math-known-realp (nth 1 (nth 1 math-simplify-expr)))) |
| 1139 | (nth 1 (nth 1 math-simplify-expr))))) | |
| 136211a9 EZ |
1140 | |
| 1141 | (math-defsimplify calcFunc-arccosh | |
| 0c908945 | 1142 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cosh) |
| 136211a9 | 1143 | (or math-living-dangerously |
| 0c908945 JB |
1144 | (math-known-realp (nth 1 (nth 1 math-simplify-expr)))) |
| 1145 | (nth 1 (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
1146 | |
| 1147 | (math-defsimplify calcFunc-arctanh | |
| 0c908945 JB |
1148 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) |
| 1149 | (math-neg (list 'calcFunc-arctanh (math-neg (nth 1 math-simplify-expr))))) | |
| 1150 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-tanh) | |
| 136211a9 | 1151 | (or math-living-dangerously |
| 0c908945 JB |
1152 | (math-known-realp (nth 1 (nth 1 math-simplify-expr)))) |
| 1153 | (nth 1 (nth 1 math-simplify-expr))))) | |
| 136211a9 EZ |
1154 | |
| 1155 | (math-defsimplify calcFunc-sqrt | |
| d3896480 | 1156 | (math-simplify-sqrt)) |
| 136211a9 EZ |
1157 | |
| 1158 | (defun math-simplify-sqrt () | |
| 0c908945 JB |
1159 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'frac) |
| 1160 | (math-div (list 'calcFunc-sqrt | |
| 1161 | (math-mul (nth 1 (nth 1 math-simplify-expr)) | |
| 1162 | (nth 2 (nth 1 math-simplify-expr)))) | |
| 1163 | (nth 2 (nth 1 math-simplify-expr)))) | |
| 1164 | (let ((fac (if (math-objectp (nth 1 math-simplify-expr)) | |
| 1165 | (math-squared-factor (nth 1 math-simplify-expr)) | |
| 1166 | (math-common-constant-factor (nth 1 math-simplify-expr))))) | |
| 136211a9 EZ |
1167 | (and fac (not (eq fac 1)) |
| 1168 | (math-mul (math-normalize (list 'calcFunc-sqrt fac)) | |
| 1169 | (math-normalize | |
| 1170 | (list 'calcFunc-sqrt | |
| 0c908945 JB |
1171 | (math-cancel-common-factor |
| 1172 | (nth 1 math-simplify-expr) fac)))))) | |
| 136211a9 | 1173 | (and math-living-dangerously |
| 0c908945 JB |
1174 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) '-) |
| 1175 | (math-equal-int (nth 1 (nth 1 math-simplify-expr)) 1) | |
| 1176 | (eq (car-safe (nth 2 (nth 1 math-simplify-expr))) '^) | |
| 1177 | (math-equal-int (nth 2 (nth 2 (nth 1 math-simplify-expr))) 2) | |
| 1178 | (or (and (eq (car-safe (nth 1 (nth 2 (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
1179 | 'calcFunc-sin) |
| 1180 | (list 'calcFunc-cos | |
| 0c908945 JB |
1181 | (nth 1 (nth 1 (nth 2 (nth 1 math-simplify-expr)))))) |
| 1182 | (and (eq (car-safe (nth 1 (nth 2 (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
1183 | 'calcFunc-cos) |
| 1184 | (list 'calcFunc-sin | |
| 0c908945 JB |
1185 | (nth 1 (nth 1 (nth 2 |
| 1186 | (nth 1 math-simplify-expr)))))))) | |
| 1187 | (and (eq (car-safe (nth 1 math-simplify-expr)) '-) | |
| 1188 | (math-equal-int (nth 2 (nth 1 math-simplify-expr)) 1) | |
| 1189 | (eq (car-safe (nth 1 (nth 1 math-simplify-expr))) '^) | |
| 1190 | (math-equal-int (nth 2 (nth 1 (nth 1 math-simplify-expr))) 2) | |
| 1191 | (and (eq (car-safe (nth 1 (nth 1 (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
1192 | 'calcFunc-cosh) |
| 1193 | (list 'calcFunc-sinh | |
| 0c908945 JB |
1194 | (nth 1 (nth 1 (nth 1 (nth 1 math-simplify-expr))))))) |
| 1195 | (and (eq (car-safe (nth 1 math-simplify-expr)) '+) | |
| 1196 | (let ((a (nth 1 (nth 1 math-simplify-expr))) | |
| 1197 | (b (nth 2 (nth 1 math-simplify-expr)))) | |
| 136211a9 | 1198 | (and (or (and (math-equal-int a 1) |
| 0c908945 | 1199 | (setq a b b (nth 1 (nth 1 math-simplify-expr)))) |
| 136211a9 EZ |
1200 | (math-equal-int b 1)) |
| 1201 | (eq (car-safe a) '^) | |
| 1202 | (math-equal-int (nth 2 a) 2) | |
| 1203 | (or (and (eq (car-safe (nth 1 a)) 'calcFunc-sinh) | |
| 1204 | (list 'calcFunc-cosh (nth 1 (nth 1 a)))) | |
| 6a5412e4 JB |
1205 | (and (eq (car-safe (nth 1 a)) 'calcFunc-csch) |
| 1206 | (list 'calcFunc-coth (nth 1 (nth 1 a)))) | |
| 136211a9 EZ |
1207 | (and (eq (car-safe (nth 1 a)) 'calcFunc-tan) |
| 1208 | (list '/ 1 (list 'calcFunc-cos | |
| 6a5412e4 JB |
1209 | (nth 1 (nth 1 a))))) |
| 1210 | (and (eq (car-safe (nth 1 a)) 'calcFunc-cot) | |
| 1211 | (list '/ 1 (list 'calcFunc-sin | |
| 136211a9 | 1212 | (nth 1 (nth 1 a))))))))) |
| 0c908945 | 1213 | (and (eq (car-safe (nth 1 math-simplify-expr)) '^) |
| 136211a9 | 1214 | (list '^ |
| 0c908945 JB |
1215 | (nth 1 (nth 1 math-simplify-expr)) |
| 1216 | (math-div (nth 2 (nth 1 math-simplify-expr)) 2))) | |
| 1217 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sqrt) | |
| 1218 | (list '^ (nth 1 (nth 1 math-simplify-expr)) (math-div 1 4))) | |
| 1219 | (and (memq (car-safe (nth 1 math-simplify-expr)) '(* /)) | |
| 1220 | (list (car (nth 1 math-simplify-expr)) | |
| 1221 | (list 'calcFunc-sqrt (nth 1 (nth 1 math-simplify-expr))) | |
| 1222 | (list 'calcFunc-sqrt (nth 2 (nth 1 math-simplify-expr))))) | |
| 1223 | (and (memq (car-safe (nth 1 math-simplify-expr)) '(+ -)) | |
| 1224 | (not (math-any-floats (nth 1 math-simplify-expr))) | |
| 136211a9 | 1225 | (let ((f (calcFunc-factors (calcFunc-expand |
| 0c908945 | 1226 | (nth 1 math-simplify-expr))))) |
| 136211a9 EZ |
1227 | (and (math-vectorp f) |
| 1228 | (or (> (length f) 2) | |
| 1229 | (> (nth 2 (nth 1 f)) 1)) | |
| 1230 | (let ((out 1) (rest 1) (sums 1) fac pow) | |
| 1231 | (while (setq f (cdr f)) | |
| 1232 | (setq fac (nth 1 (car f)) | |
| 1233 | pow (nth 2 (car f))) | |
| 1234 | (if (> pow 1) | |
| 1235 | (setq out (math-mul out (math-pow | |
| 1236 | fac (/ pow 2))) | |
| 1237 | pow (% pow 2))) | |
| 1238 | (if (> pow 0) | |
| 1239 | (if (memq (car-safe fac) '(+ -)) | |
| 1240 | (setq sums (math-mul-thru sums fac)) | |
| 1241 | (setq rest (math-mul rest fac))))) | |
| 1242 | (and (not (and (eq out 1) (memq rest '(1 -1)))) | |
| 1243 | (math-mul | |
| 1244 | out | |
| 1245 | (list 'calcFunc-sqrt | |
| d3896480 | 1246 | (math-mul sums rest)))))))))))) |
| 136211a9 EZ |
1247 | |
| 1248 | ;;; Rather than factoring x into primes, just check for the first ten primes. | |
| 1249 | (defun math-squared-factor (x) | |
| 1250 | (if (Math-integerp x) | |
| 1251 | (let ((prsqr '(4 9 25 49 121 169 289 361 529 841)) | |
| 1252 | (fac 1) | |
| 1253 | res) | |
| 1254 | (while prsqr | |
| 1255 | (if (eq (cdr (setq res (math-idivmod x (car prsqr)))) 0) | |
| 1256 | (setq x (car res) | |
| 1257 | fac (math-mul fac (car prsqr))) | |
| 1258 | (setq prsqr (cdr prsqr)))) | |
| d3896480 | 1259 | fac))) |
| 136211a9 EZ |
1260 | |
| 1261 | (math-defsimplify calcFunc-exp | |
| 0c908945 | 1262 | (math-simplify-exp (nth 1 math-simplify-expr))) |
| 136211a9 EZ |
1263 | |
| 1264 | (defun math-simplify-exp (x) | |
| 1265 | (or (and (eq (car-safe x) 'calcFunc-ln) | |
| 1266 | (nth 1 x)) | |
| 1267 | (and math-living-dangerously | |
| 1268 | (or (and (eq (car-safe x) 'calcFunc-arcsinh) | |
| 1269 | (math-add (nth 1 x) | |
| 1270 | (list 'calcFunc-sqrt | |
| 1271 | (math-add (math-sqr (nth 1 x)) 1)))) | |
| 1272 | (and (eq (car-safe x) 'calcFunc-arccosh) | |
| 1273 | (math-add (nth 1 x) | |
| 1274 | (list 'calcFunc-sqrt | |
| 1275 | (math-sub (math-sqr (nth 1 x)) 1)))) | |
| 1276 | (and (eq (car-safe x) 'calcFunc-arctanh) | |
| 1277 | (math-div (list 'calcFunc-sqrt (math-add 1 (nth 1 x))) | |
| 1278 | (list 'calcFunc-sqrt (math-sub 1 (nth 1 x))))) | |
| 1279 | (let ((m (math-should-expand-trig x 'exp))) | |
| 1280 | (and m (integerp (car m)) | |
| 1281 | (list '^ (list 'calcFunc-exp (nth 1 m)) (car m)))))) | |
| 1282 | (and calc-symbolic-mode | |
| 1283 | (math-known-imagp x) | |
| 1284 | (let* ((ip (calcFunc-im x)) | |
| 1285 | (n (math-linear-in ip '(var pi var-pi))) | |
| 1286 | s c) | |
| 1287 | (and n | |
| 1288 | (setq s (math-known-sin (car n) (nth 1 n) 120 0)) | |
| 1289 | (setq c (math-known-sin (car n) (nth 1 n) 120 300)) | |
| d3896480 | 1290 | (list '+ c (list '* s '(var i var-i)))))))) |
| 136211a9 EZ |
1291 | |
| 1292 | (math-defsimplify calcFunc-ln | |
| 0c908945 | 1293 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-exp) |
| 136211a9 | 1294 | (or math-living-dangerously |
| 0c908945 JB |
1295 | (math-known-realp (nth 1 (nth 1 math-simplify-expr)))) |
| 1296 | (nth 1 (nth 1 math-simplify-expr))) | |
| 1297 | (and (eq (car-safe (nth 1 math-simplify-expr)) '^) | |
| 1298 | (equal (nth 1 (nth 1 math-simplify-expr)) '(var e var-e)) | |
| 136211a9 | 1299 | (or math-living-dangerously |
| 0c908945 JB |
1300 | (math-known-realp (nth 2 (nth 1 math-simplify-expr)))) |
| 1301 | (nth 2 (nth 1 math-simplify-expr))) | |
| 136211a9 | 1302 | (and calc-symbolic-mode |
| 0c908945 JB |
1303 | (math-known-negp (nth 1 math-simplify-expr)) |
| 1304 | (math-add (list 'calcFunc-ln (math-neg (nth 1 math-simplify-expr))) | |
| 2c6dfebb | 1305 | '(* (var pi var-pi) (var i var-i)))) |
| 136211a9 | 1306 | (and calc-symbolic-mode |
| 0c908945 JB |
1307 | (math-known-imagp (nth 1 math-simplify-expr)) |
| 1308 | (let* ((ip (calcFunc-im (nth 1 math-simplify-expr))) | |
| 136211a9 EZ |
1309 | (ips (math-possible-signs ip))) |
| 1310 | (or (and (memq ips '(4 6)) | |
| 1311 | (math-add (list 'calcFunc-ln ip) | |
| 1312 | '(/ (* (var pi var-pi) (var i var-i)) 2))) | |
| 1313 | (and (memq ips '(1 3)) | |
| 1314 | (math-sub (list 'calcFunc-ln (math-neg ip)) | |
| d3896480 | 1315 | '(/ (* (var pi var-pi) (var i var-i)) 2)))))))) |
| 136211a9 EZ |
1316 | |
| 1317 | (math-defsimplify ^ | |
| 1318 | (math-simplify-pow)) | |
| 1319 | ||
| 1320 | (defun math-simplify-pow () | |
| 1321 | (or (and math-living-dangerously | |
| 0c908945 | 1322 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) '^) |
| 136211a9 | 1323 | (list '^ |
| 0c908945 JB |
1324 | (nth 1 (nth 1 math-simplify-expr)) |
| 1325 | (math-mul (nth 2 math-simplify-expr) | |
| 1326 | (nth 2 (nth 1 math-simplify-expr))))) | |
| 1327 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sqrt) | |
| 136211a9 | 1328 | (list '^ |
| 0c908945 JB |
1329 | (nth 1 (nth 1 math-simplify-expr)) |
| 1330 | (math-div (nth 2 math-simplify-expr) 2))) | |
| 1331 | (and (memq (car-safe (nth 1 math-simplify-expr)) '(* /)) | |
| 1332 | (list (car (nth 1 math-simplify-expr)) | |
| 1333 | (list '^ (nth 1 (nth 1 math-simplify-expr)) | |
| 1334 | (nth 2 math-simplify-expr)) | |
| 1335 | (list '^ (nth 2 (nth 1 math-simplify-expr)) | |
| 1336 | (nth 2 math-simplify-expr)))))) | |
| 1337 | (and (math-equal-int (nth 1 math-simplify-expr) 10) | |
| 1338 | (eq (car-safe (nth 2 math-simplify-expr)) 'calcFunc-log10) | |
| 1339 | (nth 1 (nth 2 math-simplify-expr))) | |
| 1340 | (and (equal (nth 1 math-simplify-expr) '(var e var-e)) | |
| 1341 | (math-simplify-exp (nth 2 math-simplify-expr))) | |
| 1342 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-exp) | |
| 136211a9 | 1343 | (not math-integrating) |
| 0c908945 JB |
1344 | (list 'calcFunc-exp (math-mul (nth 1 (nth 1 math-simplify-expr)) |
| 1345 | (nth 2 math-simplify-expr)))) | |
| 1346 | (and (equal (nth 1 math-simplify-expr) '(var i var-i)) | |
| 136211a9 | 1347 | (math-imaginary-i) |
| 0c908945 JB |
1348 | (math-num-integerp (nth 2 math-simplify-expr)) |
| 1349 | (let ((x (math-mod (math-trunc (nth 2 math-simplify-expr)) 4))) | |
| 136211a9 | 1350 | (cond ((eq x 0) 1) |
| 0c908945 | 1351 | ((eq x 1) (nth 1 math-simplify-expr)) |
| 136211a9 | 1352 | ((eq x 2) -1) |
| 0c908945 | 1353 | ((eq x 3) (math-neg (nth 1 math-simplify-expr)))))) |
| 136211a9 | 1354 | (and math-integrating |
| 0c908945 JB |
1355 | (integerp (nth 2 math-simplify-expr)) |
| 1356 | (>= (nth 2 math-simplify-expr) 2) | |
| 1357 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cos) | |
| 1358 | (math-mul (math-pow (nth 1 math-simplify-expr) | |
| 1359 | (- (nth 2 math-simplify-expr) 2)) | |
| 136211a9 EZ |
1360 | (math-sub 1 |
| 1361 | (math-sqr | |
| 1362 | (list 'calcFunc-sin | |
| 0c908945 JB |
1363 | (nth 1 (nth 1 math-simplify-expr))))))) |
| 1364 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cosh) | |
| 1365 | (math-mul (math-pow (nth 1 math-simplify-expr) | |
| 1366 | (- (nth 2 math-simplify-expr) 2)) | |
| 136211a9 EZ |
1367 | (math-add 1 |
| 1368 | (math-sqr | |
| 1369 | (list 'calcFunc-sinh | |
| 0c908945 JB |
1370 | (nth 1 (nth 1 math-simplify-expr))))))))) |
| 1371 | (and (eq (car-safe (nth 2 math-simplify-expr)) 'frac) | |
| 1372 | (Math-ratp (nth 1 math-simplify-expr)) | |
| 1373 | (Math-posp (nth 1 math-simplify-expr)) | |
| 1374 | (if (equal (nth 2 math-simplify-expr) '(frac 1 2)) | |
| 1375 | (list 'calcFunc-sqrt (nth 1 math-simplify-expr)) | |
| 1376 | (let ((flr (math-floor (nth 2 math-simplify-expr)))) | |
| 136211a9 | 1377 | (and (not (Math-zerop flr)) |
| 0c908945 JB |
1378 | (list '* (list '^ (nth 1 math-simplify-expr) flr) |
| 1379 | (list '^ (nth 1 math-simplify-expr) | |
| 1380 | (math-sub (nth 2 math-simplify-expr) flr))))))) | |
| 1381 | (and (eq (math-quarter-integer (nth 2 math-simplify-expr)) 2) | |
| 136211a9 EZ |
1382 | (let ((temp (math-simplify-sqrt))) |
| 1383 | (and temp | |
| 0c908945 | 1384 | (list '^ temp (math-mul (nth 2 math-simplify-expr) 2))))))) |
| 136211a9 EZ |
1385 | |
| 1386 | (math-defsimplify calcFunc-log10 | |
| 0c908945 JB |
1387 | (and (eq (car-safe (nth 1 math-simplify-expr)) '^) |
| 1388 | (math-equal-int (nth 1 (nth 1 math-simplify-expr)) 10) | |
| 136211a9 | 1389 | (or math-living-dangerously |
| 0c908945 JB |
1390 | (math-known-realp (nth 2 (nth 1 math-simplify-expr)))) |
| 1391 | (nth 2 (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
1392 | |
| 1393 | ||
| 1394 | (math-defsimplify calcFunc-erf | |
| 0c908945 JB |
1395 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) |
| 1396 | (math-neg (list 'calcFunc-erf (math-neg (nth 1 math-simplify-expr))))) | |
| 1397 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-conj) | |
| 1398 | (list 'calcFunc-conj | |
| 1399 | (list 'calcFunc-erf (nth 1 (nth 1 math-simplify-expr))))))) | |
| 136211a9 EZ |
1400 | |
| 1401 | (math-defsimplify calcFunc-erfc | |
| 0c908945 JB |
1402 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) |
| 1403 | (math-sub 2 (list 'calcFunc-erfc (math-neg (nth 1 math-simplify-expr))))) | |
| 1404 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-conj) | |
| 1405 | (list 'calcFunc-conj | |
| 1406 | (list 'calcFunc-erfc (nth 1 (nth 1 math-simplify-expr))))))) | |
| 136211a9 EZ |
1407 | |
| 1408 | ||
| 1409 | (defun math-linear-in (expr term &optional always) | |
| 1410 | (if (math-expr-contains expr term) | |
| 1411 | (let* ((calc-prefer-frac t) | |
| 1412 | (p (math-is-polynomial expr term 1))) | |
| 1413 | (and (cdr p) | |
| 1414 | p)) | |
| d3896480 | 1415 | (and always (list expr 0)))) |
| 136211a9 EZ |
1416 | |
| 1417 | (defun math-multiple-of (expr term) | |
| 1418 | (let ((p (math-linear-in expr term))) | |
| 1419 | (and p | |
| 1420 | (math-zerop (car p)) | |
| d3896480 | 1421 | (nth 1 p)))) |
| 136211a9 | 1422 | |
| d3896480 | 1423 | ; not perfect, but it'll do |
| 136211a9 EZ |
1424 | (defun math-integer-plus (expr) |
| 1425 | (cond ((Math-integerp expr) | |
| 1426 | (list 0 expr)) | |
| 1427 | ((and (memq (car expr) '(+ -)) | |
| 1428 | (Math-integerp (nth 1 expr))) | |
| 1429 | (list (if (eq (car expr) '+) (nth 2 expr) (math-neg (nth 2 expr))) | |
| 1430 | (nth 1 expr))) | |
| 1431 | ((and (memq (car expr) '(+ -)) | |
| 1432 | (Math-integerp (nth 2 expr))) | |
| 1433 | (list (nth 1 expr) | |
| 1434 | (if (eq (car expr) '+) (nth 2 expr) (math-neg (nth 2 expr))))) | |
| d3896480 | 1435 | (t nil))) |
| 136211a9 EZ |
1436 | |
| 1437 | (defun math-is-linear (expr &optional always) | |
| 1438 | (let ((offset nil) | |
| 1439 | (coef nil)) | |
| 1440 | (if (eq (car-safe expr) '+) | |
| 1441 | (if (Math-objectp (nth 1 expr)) | |
| 1442 | (setq offset (nth 1 expr) | |
| 1443 | expr (nth 2 expr)) | |
| 1444 | (if (Math-objectp (nth 2 expr)) | |
| 1445 | (setq offset (nth 2 expr) | |
| 1446 | expr (nth 1 expr)))) | |
| 1447 | (if (eq (car-safe expr) '-) | |
| 1448 | (if (Math-objectp (nth 1 expr)) | |
| 1449 | (setq offset (nth 1 expr) | |
| 1450 | expr (math-neg (nth 2 expr))) | |
| 1451 | (if (Math-objectp (nth 2 expr)) | |
| 1452 | (setq offset (math-neg (nth 2 expr)) | |
| 1453 | expr (nth 1 expr)))))) | |
| 1454 | (setq coef (math-is-multiple expr always)) | |
| 1455 | (if offset | |
| 1456 | (list offset (or (car coef) 1) (or (nth 1 coef) expr)) | |
| 1457 | (if coef | |
| d3896480 | 1458 | (cons 0 coef))))) |
| 136211a9 EZ |
1459 | |
| 1460 | (defun math-is-multiple (expr &optional always) | |
| 1461 | (or (if (eq (car-safe expr) '*) | |
| 1462 | (if (Math-objectp (nth 1 expr)) | |
| 1463 | (list (nth 1 expr) (nth 2 expr))) | |
| 1464 | (if (eq (car-safe expr) '/) | |
| 1465 | (if (and (Math-objectp (nth 1 expr)) | |
| 1466 | (not (math-equal-int (nth 1 expr) 1))) | |
| 1467 | (list (nth 1 expr) (math-div 1 (nth 2 expr))) | |
| 1468 | (if (Math-objectp (nth 2 expr)) | |
| 1469 | (list (math-div 1 (nth 2 expr)) (nth 1 expr)) | |
| 1470 | (let ((res (math-is-multiple (nth 1 expr)))) | |
| 1471 | (if res | |
| 1472 | (list (car res) | |
| 1473 | (math-div (nth 2 (nth 1 expr)) (nth 2 expr))) | |
| 1474 | (setq res (math-is-multiple (nth 2 expr))) | |
| 1475 | (if res | |
| 1476 | (list (math-div 1 (car res)) | |
| 1477 | (math-div (nth 1 expr) | |
| 1478 | (nth 2 (nth 2 expr))))))))) | |
| 1479 | (if (eq (car-safe expr) 'neg) | |
| 1480 | (list -1 (nth 1 expr))))) | |
| 1481 | (if (Math-objvecp expr) | |
| 1482 | (and (eq always 1) | |
| 1483 | (list expr 1)) | |
| a1506d29 | 1484 | (and always |
| d3896480 | 1485 | (list 1 expr))))) |
| 136211a9 EZ |
1486 | |
| 1487 | (defun calcFunc-lin (expr &optional var) | |
| 1488 | (if var | |
| 1489 | (let ((res (math-linear-in expr var t))) | |
| 1490 | (or res (math-reject-arg expr "Linear term expected")) | |
| 1491 | (list 'vec (car res) (nth 1 res) var)) | |
| 1492 | (let ((res (math-is-linear expr t))) | |
| 1493 | (or res (math-reject-arg expr "Linear term expected")) | |
| d3896480 | 1494 | (cons 'vec res)))) |
| 136211a9 EZ |
1495 | |
| 1496 | (defun calcFunc-linnt (expr &optional var) | |
| 1497 | (if var | |
| 1498 | (let ((res (math-linear-in expr var))) | |
| 1499 | (or res (math-reject-arg expr "Linear term expected")) | |
| 1500 | (list 'vec (car res) (nth 1 res) var)) | |
| 1501 | (let ((res (math-is-linear expr))) | |
| 1502 | (or res (math-reject-arg expr "Linear term expected")) | |
| d3896480 | 1503 | (cons 'vec res)))) |
| 136211a9 EZ |
1504 | |
| 1505 | (defun calcFunc-islin (expr &optional var) | |
| 1506 | (if (and (Math-objvecp expr) (not var)) | |
| 1507 | 0 | |
| 1508 | (calcFunc-lin expr var) | |
| d3896480 | 1509 | 1)) |
| 136211a9 EZ |
1510 | |
| 1511 | (defun calcFunc-islinnt (expr &optional var) | |
| 1512 | (if (Math-objvecp expr) | |
| 1513 | 0 | |
| 1514 | (calcFunc-linnt expr var) | |
| d3896480 | 1515 | 1)) |
| 136211a9 EZ |
1516 | |
| 1517 | ||
| 1518 | ||
| 1519 | ||
| 1520 | ;;; Simple operations on expressions. | |
| 1521 | ||
| 6f826971 | 1522 | ;;; Return number of occurrences of thing in expr, or nil if none. |
| 136211a9 EZ |
1523 | (defun math-expr-contains-count (expr thing) |
| 1524 | (cond ((equal expr thing) 1) | |
| 1525 | ((Math-primp expr) nil) | |
| 1526 | (t | |
| 1527 | (let ((num 0)) | |
| 1528 | (while (setq expr (cdr expr)) | |
| 1529 | (setq num (+ num (or (math-expr-contains-count | |
| 1530 | (car expr) thing) 0)))) | |
| 1531 | (and (> num 0) | |
| d3896480 | 1532 | num))))) |
| 136211a9 EZ |
1533 | |
| 1534 | (defun math-expr-contains (expr thing) | |
| 1535 | (cond ((equal expr thing) 1) | |
| 1536 | ((Math-primp expr) nil) | |
| 1537 | (t | |
| 1538 | (while (and (setq expr (cdr expr)) | |
| 1539 | (not (math-expr-contains (car expr) thing)))) | |
| d3896480 | 1540 | expr))) |
| 136211a9 EZ |
1541 | |
| 1542 | ;;; Return non-nil if any variable of thing occurs in expr. | |
| 1543 | (defun math-expr-depends (expr thing) | |
| 1544 | (if (Math-primp thing) | |
| 1545 | (and (eq (car-safe thing) 'var) | |
| 1546 | (math-expr-contains expr thing)) | |
| 1547 | (while (and (setq thing (cdr thing)) | |
| 1548 | (not (math-expr-depends expr (car thing))))) | |
| d3896480 | 1549 | thing)) |
| 136211a9 EZ |
1550 | |
| 1551 | ;;; Substitute all occurrences of old for new in expr (non-destructive). | |
| 0c908945 JB |
1552 | |
| 1553 | ;; The variables math-expr-subst-old and math-expr-subst-new are local | |
| 1554 | ;; for math-expr-subst, but used by math-expr-subst-rec. | |
| 1555 | (defvar math-expr-subst-old) | |
| 1556 | (defvar math-expr-subst-new) | |
| 1557 | ||
| 1558 | (defun math-expr-subst (expr math-expr-subst-old math-expr-subst-new) | |
| d3896480 CW |
1559 | (math-expr-subst-rec expr)) |
| 1560 | ||
| 1561 | (defalias 'calcFunc-subst 'math-expr-subst) | |
| 136211a9 EZ |
1562 | |
| 1563 | (defun math-expr-subst-rec (expr) | |
| 0c908945 | 1564 | (cond ((equal expr math-expr-subst-old) math-expr-subst-new) |
| 136211a9 EZ |
1565 | ((Math-primp expr) expr) |
| 1566 | ((memq (car expr) '(calcFunc-deriv | |
| 1567 | calcFunc-tderiv)) | |
| 1568 | (if (= (length expr) 2) | |
| 0c908945 JB |
1569 | (if (equal (nth 1 expr) math-expr-subst-old) |
| 1570 | (append expr (list math-expr-subst-new)) | |
| 136211a9 EZ |
1571 | expr) |
| 1572 | (list (car expr) (nth 1 expr) | |
| 1573 | (math-expr-subst-rec (nth 2 expr))))) | |
| 1574 | (t | |
| 1575 | (cons (car expr) | |
| d3896480 | 1576 | (mapcar 'math-expr-subst-rec (cdr expr)))))) |
| 136211a9 EZ |
1577 | |
| 1578 | ;;; Various measures of the size of an expression. | |
| 1579 | (defun math-expr-weight (expr) | |
| 1580 | (if (Math-primp expr) | |
| 1581 | 1 | |
| 1582 | (let ((w 1)) | |
| 1583 | (while (setq expr (cdr expr)) | |
| 1584 | (setq w (+ w (math-expr-weight (car expr))))) | |
| d3896480 | 1585 | w))) |
| 136211a9 EZ |
1586 | |
| 1587 | (defun math-expr-height (expr) | |
| 1588 | (if (Math-primp expr) | |
| 1589 | 0 | |
| 1590 | (let ((h 0)) | |
| 1591 | (while (setq expr (cdr expr)) | |
| 1592 | (setq h (max h (math-expr-height (car expr))))) | |
| d3896480 | 1593 | (1+ h)))) |
| 136211a9 EZ |
1594 | |
| 1595 | ||
| 1596 | ||
| 1597 | ||
| 1598 | ;;; Polynomial operations (to support the integrator and solve-for). | |
| 1599 | ||
| 1600 | (defun calcFunc-collect (expr base) | |
| 1601 | (let ((p (math-is-polynomial expr base 50 t))) | |
| 1602 | (if (cdr p) | |
| 1603 | (math-normalize ; fix selection bug | |
| 1604 | (math-build-polynomial-expr p base)) | |
| d3896480 | 1605 | expr))) |
| 136211a9 EZ |
1606 | |
| 1607 | ;;; If expr is of the form "a + bx + cx^2 + ...", return the list (a b c ...), | |
| 0c908945 JB |
1608 | ;;; else return nil if not in polynomial form. If "loose" (math-is-poly-loose), |
| 1609 | ;;; coefficients may contain x, e.g., sin(x) + cos(x) x^2 is a loose polynomial in x. | |
| 1610 | ||
| 1611 | ;; The variables math-is-poly-degree and math-is-poly-loose are local to | |
| 1612 | ;; math-is-polynomial, but are used by math-is-poly-rec | |
| 1613 | (defvar math-is-poly-degree) | |
| 1614 | (defvar math-is-poly-loose) | |
| 1615 | ||
| 1616 | (defun math-is-polynomial (expr var &optional math-is-poly-degree math-is-poly-loose) | |
| 1617 | (let* ((math-poly-base-variable (if math-is-poly-loose | |
| 1618 | (if (eq math-is-poly-loose 'gen) var '(var XXX XXX)) | |
| 136211a9 EZ |
1619 | math-poly-base-variable)) |
| 1620 | (poly (math-is-poly-rec expr math-poly-neg-powers))) | |
| 0c908945 JB |
1621 | (and (or (null math-is-poly-degree) |
| 1622 | (<= (length poly) (1+ math-is-poly-degree))) | |
| d3896480 | 1623 | poly))) |
| 136211a9 EZ |
1624 | |
| 1625 | (defun math-is-poly-rec (expr negpow) | |
| 1626 | (math-poly-simplify | |
| 1627 | (or (cond ((or (equal expr var) | |
| 1628 | (eq (car-safe expr) '^)) | |
| 1629 | (let ((pow 1) | |
| 1630 | (expr expr)) | |
| 1631 | (or (equal expr var) | |
| 1632 | (setq pow (nth 2 expr) | |
| 1633 | expr (nth 1 expr))) | |
| 1634 | (or (eq math-poly-mult-powers 1) | |
| 1635 | (setq pow (let ((m (math-is-multiple pow 1))) | |
| 1636 | (and (eq (car-safe (car m)) 'cplx) | |
| 1637 | (Math-zerop (nth 1 (car m))) | |
| 1638 | (setq m (list (nth 2 (car m)) | |
| 1639 | (math-mul (nth 1 m) | |
| 1640 | '(var i var-i))))) | |
| 1641 | (and (if math-poly-mult-powers | |
| 1642 | (equal math-poly-mult-powers | |
| 1643 | (nth 1 m)) | |
| 1644 | (setq math-poly-mult-powers (nth 1 m))) | |
| 1645 | (or (equal expr var) | |
| 1646 | (eq math-poly-mult-powers 1)) | |
| 1647 | (car m))))) | |
| 1648 | (if (consp pow) | |
| 1649 | (progn | |
| 1650 | (setq pow (math-to-simple-fraction pow)) | |
| 1651 | (and (eq (car-safe pow) 'frac) | |
| 1652 | math-poly-frac-powers | |
| 1653 | (equal expr var) | |
| 1654 | (setq math-poly-frac-powers | |
| 1655 | (calcFunc-lcm math-poly-frac-powers | |
| 1656 | (nth 2 pow)))))) | |
| 1657 | (or (memq math-poly-frac-powers '(1 nil)) | |
| 1658 | (setq pow (math-mul pow math-poly-frac-powers))) | |
| 1659 | (if (integerp pow) | |
| 1660 | (if (and (= pow 1) | |
| 1661 | (equal expr var)) | |
| 1662 | (list 0 1) | |
| 1663 | (if (natnump pow) | |
| 1664 | (let ((p1 (if (equal expr var) | |
| 1665 | (list 0 1) | |
| 1666 | (math-is-poly-rec expr nil))) | |
| 1667 | (n pow) | |
| 1668 | (accum (list 1))) | |
| 1669 | (and p1 | |
| 0c908945 JB |
1670 | (or (null math-is-poly-degree) |
| 1671 | (<= (* (1- (length p1)) n) math-is-poly-degree)) | |
| 136211a9 EZ |
1672 | (progn |
| 1673 | (while (>= n 1) | |
| 1674 | (setq accum (math-poly-mul accum p1) | |
| 1675 | n (1- n))) | |
| 1676 | accum))) | |
| 1677 | (and negpow | |
| 1678 | (math-is-poly-rec expr nil) | |
| 1679 | (setq math-poly-neg-powers | |
| 1680 | (cons (math-pow expr (- pow)) | |
| 1681 | math-poly-neg-powers)) | |
| 1682 | (list (list '^ expr pow)))))))) | |
| 1683 | ((Math-objectp expr) | |
| 1684 | (list expr)) | |
| 1685 | ((memq (car expr) '(+ -)) | |
| 1686 | (let ((p1 (math-is-poly-rec (nth 1 expr) negpow))) | |
| 1687 | (and p1 | |
| 1688 | (let ((p2 (math-is-poly-rec (nth 2 expr) negpow))) | |
| 1689 | (and p2 | |
| 1690 | (math-poly-mix p1 1 p2 | |
| 1691 | (if (eq (car expr) '+) 1 -1))))))) | |
| 1692 | ((eq (car expr) 'neg) | |
| 1693 | (mapcar 'math-neg (math-is-poly-rec (nth 1 expr) negpow))) | |
| 1694 | ((eq (car expr) '*) | |
| 1695 | (let ((p1 (math-is-poly-rec (nth 1 expr) negpow))) | |
| 1696 | (and p1 | |
| 1697 | (let ((p2 (math-is-poly-rec (nth 2 expr) negpow))) | |
| 1698 | (and p2 | |
| 0c908945 JB |
1699 | (or (null math-is-poly-degree) |
| 1700 | (<= (- (+ (length p1) (length p2)) 2) | |
| 1701 | math-is-poly-degree)) | |
| 136211a9 EZ |
1702 | (math-poly-mul p1 p2)))))) |
| 1703 | ((eq (car expr) '/) | |
| 1704 | (and (or (not (math-poly-depends (nth 2 expr) var)) | |
| 1705 | (and negpow | |
| 1706 | (math-is-poly-rec (nth 2 expr) nil) | |
| 1707 | (setq math-poly-neg-powers | |
| 1708 | (cons (nth 2 expr) math-poly-neg-powers)))) | |
| 1709 | (not (Math-zerop (nth 2 expr))) | |
| 1710 | (let ((p1 (math-is-poly-rec (nth 1 expr) negpow))) | |
| 1711 | (mapcar (function (lambda (x) (math-div x (nth 2 expr)))) | |
| 1712 | p1)))) | |
| 1713 | ((and (eq (car expr) 'calcFunc-exp) | |
| 1714 | (equal var '(var e var-e))) | |
| 1715 | (math-is-poly-rec (list '^ var (nth 1 expr)) negpow)) | |
| 1716 | ((and (eq (car expr) 'calcFunc-sqrt) | |
| 1717 | math-poly-frac-powers) | |
| 1718 | (math-is-poly-rec (list '^ (nth 1 expr) '(frac 1 2)) negpow)) | |
| 1719 | (t nil)) | |
| 1720 | (and (or (not (math-poly-depends expr var)) | |
| 0c908945 | 1721 | math-is-poly-loose) |
| 136211a9 | 1722 | (not (eq (car expr) 'vec)) |
| d3896480 | 1723 | (list expr))))) |
| 136211a9 EZ |
1724 | |
| 1725 | ;;; Check if expr is a polynomial in var; if so, return its degree. | |
| 1726 | (defun math-polynomial-p (expr var) | |
| 1727 | (cond ((equal expr var) 1) | |
| 1728 | ((Math-primp expr) 0) | |
| 1729 | ((memq (car expr) '(+ -)) | |
| 1730 | (let ((p1 (math-polynomial-p (nth 1 expr) var)) | |
| 1731 | p2) | |
| 1732 | (and p1 (setq p2 (math-polynomial-p (nth 2 expr) var)) | |
| 1733 | (max p1 p2)))) | |
| 1734 | ((eq (car expr) '*) | |
| 1735 | (let ((p1 (math-polynomial-p (nth 1 expr) var)) | |
| 1736 | p2) | |
| 1737 | (and p1 (setq p2 (math-polynomial-p (nth 2 expr) var)) | |
| 1738 | (+ p1 p2)))) | |
| 1739 | ((eq (car expr) 'neg) | |
| 1740 | (math-polynomial-p (nth 1 expr) var)) | |
| 1741 | ((and (eq (car expr) '/) | |
| 1742 | (not (math-poly-depends (nth 2 expr) var))) | |
| 1743 | (math-polynomial-p (nth 1 expr) var)) | |
| 1744 | ((and (eq (car expr) '^) | |
| 1745 | (natnump (nth 2 expr))) | |
| 1746 | (let ((p1 (math-polynomial-p (nth 1 expr) var))) | |
| 1747 | (and p1 (* p1 (nth 2 expr))))) | |
| 1748 | ((math-poly-depends expr var) nil) | |
| d3896480 | 1749 | (t 0))) |
| 136211a9 EZ |
1750 | |
| 1751 | (defun math-poly-depends (expr var) | |
| 1752 | (if math-poly-base-variable | |
| 1753 | (math-expr-contains expr math-poly-base-variable) | |
| d3896480 | 1754 | (math-expr-depends expr var))) |
| 136211a9 EZ |
1755 | |
| 1756 | ;;; Find the variable (or sub-expression) which is the base of polynomial expr. | |
| 0c908945 JB |
1757 | ;; The variables math-poly-base-const-ok and math-poly-base-pred are |
| 1758 | ;; local to math-polynomial-base, but are used by math-polynomial-base-rec. | |
| 1759 | (defvar math-poly-base-const-ok) | |
| 1760 | (defvar math-poly-base-pred) | |
| 1761 | ||
| 885e6671 JB |
1762 | ;; The variable math-poly-base-top-expr is local to math-polynomial-base, |
| 1763 | ;; but is used by math-polynomial-p1 in calc-poly.el, which is called | |
| 1764 | ;; by math-polynomial-base. | |
| 1765 | ||
| 1766 | (defun math-polynomial-base (math-poly-base-top-expr &optional math-poly-base-pred) | |
| 0c908945 JB |
1767 | (or math-poly-base-pred |
| 1768 | (setq math-poly-base-pred (function (lambda (base) (math-polynomial-p | |
| 885e6671 | 1769 | math-poly-base-top-expr base))))) |
| 0c908945 | 1770 | (or (let ((math-poly-base-const-ok nil)) |
| 885e6671 | 1771 | (math-polynomial-base-rec math-poly-base-top-expr)) |
| 0c908945 | 1772 | (let ((math-poly-base-const-ok t)) |
| 885e6671 | 1773 | (math-polynomial-base-rec math-poly-base-top-expr)))) |
| 136211a9 EZ |
1774 | |
| 1775 | (defun math-polynomial-base-rec (mpb-expr) | |
| 1776 | (and (not (Math-objvecp mpb-expr)) | |
| 1777 | (or (and (memq (car mpb-expr) '(+ - *)) | |
| 1778 | (or (math-polynomial-base-rec (nth 1 mpb-expr)) | |
| 1779 | (math-polynomial-base-rec (nth 2 mpb-expr)))) | |
| 1780 | (and (memq (car mpb-expr) '(/ neg)) | |
| 1781 | (math-polynomial-base-rec (nth 1 mpb-expr))) | |
| 1782 | (and (eq (car mpb-expr) '^) | |
| 1783 | (math-polynomial-base-rec (nth 1 mpb-expr))) | |
| 1784 | (and (eq (car mpb-expr) 'calcFunc-exp) | |
| 1785 | (math-polynomial-base-rec '(var e var-e))) | |
| 0c908945 JB |
1786 | (and (or math-poly-base-const-ok (math-expr-contains-vars mpb-expr)) |
| 1787 | (funcall math-poly-base-pred mpb-expr) | |
| d3896480 | 1788 | mpb-expr)))) |
| 136211a9 EZ |
1789 | |
| 1790 | ;;; Return non-nil if expr refers to any variables. | |
| 1791 | (defun math-expr-contains-vars (expr) | |
| 1792 | (or (eq (car-safe expr) 'var) | |
| 1793 | (and (not (Math-primp expr)) | |
| 1794 | (progn | |
| 1795 | (while (and (setq expr (cdr expr)) | |
| 1796 | (not (math-expr-contains-vars (car expr))))) | |
| d3896480 | 1797 | expr)))) |
| 136211a9 EZ |
1798 | |
| 1799 | ;;; Simplify a polynomial in list form by stripping off high-end zeros. | |
| 1800 | ;;; This always leaves the constant part, i.e., nil->nil and nonnil->nonnil. | |
| 1801 | (defun math-poly-simplify (p) | |
| 1802 | (and p | |
| 1803 | (if (Math-zerop (nth (1- (length p)) p)) | |
| 1804 | (let ((pp (copy-sequence p))) | |
| 1805 | (while (and (cdr pp) | |
| 1806 | (Math-zerop (nth (1- (length pp)) pp))) | |
| 1807 | (setcdr (nthcdr (- (length pp) 2) pp) nil)) | |
| 1808 | pp) | |
| d3896480 | 1809 | p))) |
| 136211a9 EZ |
1810 | |
| 1811 | ;;; Compute ac*a + bc*b for polynomials in list form a, b and | |
| 1812 | ;;; coefficients ac, bc. Result may be unsimplified. | |
| 1813 | (defun math-poly-mix (a ac b bc) | |
| 1814 | (and (or a b) | |
| 1815 | (cons (math-add (math-mul (or (car a) 0) ac) | |
| 1816 | (math-mul (or (car b) 0) bc)) | |
| d3896480 | 1817 | (math-poly-mix (cdr a) ac (cdr b) bc)))) |
| 136211a9 EZ |
1818 | |
| 1819 | (defun math-poly-zerop (a) | |
| 1820 | (or (null a) | |
| d3896480 | 1821 | (and (null (cdr a)) (Math-zerop (car a))))) |
| 136211a9 EZ |
1822 | |
| 1823 | ;;; Multiply two polynomials in list form. | |
| 1824 | (defun math-poly-mul (a b) | |
| 1825 | (and a b | |
| 1826 | (math-poly-mix b (car a) | |
| d3896480 | 1827 | (math-poly-mul (cdr a) (cons 0 b)) 1))) |
| 136211a9 EZ |
1828 | |
| 1829 | ;;; Build an expression from a polynomial list. | |
| 1830 | (defun math-build-polynomial-expr (p var) | |
| 1831 | (if p | |
| 1832 | (if (Math-numberp var) | |
| 1833 | (math-with-extra-prec 1 | |
| 1834 | (let* ((rp (reverse p)) | |
| 1835 | (accum (car rp))) | |
| 1836 | (while (setq rp (cdr rp)) | |
| 1837 | (setq accum (math-add (car rp) (math-mul accum var)))) | |
| 1838 | accum)) | |
| 1839 | (let* ((rp (reverse p)) | |
| 1840 | (n (1- (length rp))) | |
| 1841 | (accum (math-mul (car rp) (math-pow var n))) | |
| 1842 | term) | |
| 1843 | (while (setq rp (cdr rp)) | |
| 1844 | (setq n (1- n)) | |
| 1845 | (or (math-zerop (car rp)) | |
| 1846 | (setq accum (list (if (math-looks-negp (car rp)) '- '+) | |
| 1847 | accum | |
| 1848 | (math-mul (if (math-looks-negp (car rp)) | |
| 1849 | (math-neg (car rp)) | |
| 1850 | (car rp)) | |
| 1851 | (math-pow var n)))))) | |
| 1852 | accum)) | |
| d3896480 | 1853 | 0)) |
| 136211a9 EZ |
1854 | |
| 1855 | ||
| 1856 | (defun math-to-simple-fraction (f) | |
| 1857 | (or (and (eq (car-safe f) 'float) | |
| 1858 | (or (and (>= (nth 2 f) 0) | |
| 1859 | (math-scale-int (nth 1 f) (nth 2 f))) | |
| 1860 | (and (integerp (nth 1 f)) | |
| 1861 | (> (nth 1 f) -1000) | |
| 1862 | (< (nth 1 f) 1000) | |
| 1863 | (math-make-frac (nth 1 f) | |
| 1864 | (math-scale-int 1 (- (nth 2 f))))))) | |
| d3896480 | 1865 | f)) |
| 136211a9 | 1866 | |
| 41cf648d JB |
1867 | (provide 'calc-alg) |
| 1868 | ||
| ab5796a9 | 1869 | ;;; arch-tag: 52e7dcdf-9688-464d-a02b-4bbe789348d0 |
| d3896480 | 1870 | ;;; calc-alg.el ends here |