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> | |
| 0c908945 | 6 | ;; Maintainer: Jay Belanger <belanger@truman.edu> |
| 136211a9 EZ |
7 | |
| 8 | ;; This file is part of GNU Emacs. | |
| 9 | ||
| 10 | ;; GNU Emacs is distributed in the hope that it will be useful, | |
| 11 | ;; but WITHOUT ANY WARRANTY. No author or distributor | |
| 12 | ;; accepts responsibility to anyone for the consequences of using it | |
| 13 | ;; or for whether it serves any particular purpose or works at all, | |
| 14 | ;; unless he says so in writing. Refer to the GNU Emacs General Public | |
| 15 | ;; License for full details. | |
| 16 | ||
| 17 | ;; Everyone is granted permission to copy, modify and redistribute | |
| 18 | ;; GNU Emacs, but only under the conditions described in the | |
| 19 | ;; GNU Emacs General Public License. A copy of this license is | |
| 20 | ;; supposed to have been given to you along with GNU Emacs so you | |
| 21 | ;; can know your rights and responsibilities. It should be in a | |
| 22 | ;; file named COPYING. Among other things, the copyright notice | |
| 23 | ;; and this notice must be preserved on all copies. | |
| 24 | ||
| 3132f345 | 25 | ;;; Commentary: |
| 136211a9 | 26 | |
| 3132f345 | 27 | ;;; Code: |
| 136211a9 EZ |
28 | |
| 29 | ;; This file is autoloaded from calc-ext.el. | |
| 30 | (require 'calc-ext) | |
| 31 | ||
| 32 | (require 'calc-macs) | |
| 33 | ||
| 34 | (defun calc-Need-calc-alg () nil) | |
| 35 | ||
| 136211a9 EZ |
36 | ;;; Algebra commands. |
| 37 | ||
| 38 | (defun calc-alg-evaluate (arg) | |
| 39 | (interactive "p") | |
| 40 | (calc-slow-wrapper | |
| 41 | (calc-with-default-simplification | |
| 42 | (let ((math-simplify-only nil)) | |
| 43 | (calc-modify-simplify-mode arg) | |
| d3896480 | 44 | (calc-enter-result 1 "dsmp" (calc-top 1)))))) |
| 136211a9 EZ |
45 | |
| 46 | (defun calc-modify-simplify-mode (arg) | |
| 47 | (if (= (math-abs arg) 2) | |
| 48 | (setq calc-simplify-mode 'alg) | |
| 49 | (if (>= (math-abs arg) 3) | |
| 50 | (setq calc-simplify-mode 'ext))) | |
| 51 | (if (< arg 0) | |
| d3896480 | 52 | (setq calc-simplify-mode (list calc-simplify-mode)))) |
| 136211a9 EZ |
53 | |
| 54 | (defun calc-simplify () | |
| 55 | (interactive) | |
| 56 | (calc-slow-wrapper | |
| 57 | (calc-with-default-simplification | |
| d3896480 | 58 | (calc-enter-result 1 "simp" (math-simplify (calc-top-n 1)))))) |
| 136211a9 EZ |
59 | |
| 60 | (defun calc-simplify-extended () | |
| 61 | (interactive) | |
| 62 | (calc-slow-wrapper | |
| 63 | (calc-with-default-simplification | |
| d3896480 | 64 | (calc-enter-result 1 "esmp" (math-simplify-extended (calc-top-n 1)))))) |
| 136211a9 EZ |
65 | |
| 66 | (defun calc-expand-formula (arg) | |
| 67 | (interactive "p") | |
| 68 | (calc-slow-wrapper | |
| 69 | (calc-with-default-simplification | |
| 70 | (let ((math-simplify-only nil)) | |
| 71 | (calc-modify-simplify-mode arg) | |
| a1506d29 | 72 | (calc-enter-result 1 "expf" |
| 136211a9 EZ |
73 | (if (> arg 0) |
| 74 | (let ((math-expand-formulas t)) | |
| 75 | (calc-top-n 1)) | |
| 76 | (let ((top (calc-top-n 1))) | |
| 77 | (or (math-expand-formula top) | |
| d3896480 | 78 | top)))))))) |
| 136211a9 EZ |
79 | |
| 80 | (defun calc-factor (arg) | |
| 81 | (interactive "P") | |
| 82 | (calc-slow-wrapper | |
| 83 | (calc-unary-op "fctr" (if (calc-is-hyperbolic) | |
| 84 | 'calcFunc-factors 'calcFunc-factor) | |
| d3896480 | 85 | arg))) |
| 136211a9 EZ |
86 | |
| 87 | (defun calc-expand (n) | |
| 88 | (interactive "P") | |
| 89 | (calc-slow-wrapper | |
| 90 | (calc-enter-result 1 "expa" | |
| 91 | (append (list 'calcFunc-expand | |
| 92 | (calc-top-n 1)) | |
| d3896480 | 93 | (and n (list (prefix-numeric-value n))))))) |
| 136211a9 EZ |
94 | |
| 95 | (defun calc-collect (&optional var) | |
| 96 | (interactive "sCollect terms involving: ") | |
| 97 | (calc-slow-wrapper | |
| 98 | (if (or (equal var "") (equal var "$") (null var)) | |
| 99 | (calc-enter-result 2 "clct" (cons 'calcFunc-collect | |
| 100 | (calc-top-list-n 2))) | |
| 101 | (let ((var (math-read-expr var))) | |
| 102 | (if (eq (car-safe var) 'error) | |
| 103 | (error "Bad format in expression: %s" (nth 1 var))) | |
| 104 | (calc-enter-result 1 "clct" (list 'calcFunc-collect | |
| 105 | (calc-top-n 1) | |
| d3896480 | 106 | var)))))) |
| 136211a9 EZ |
107 | |
| 108 | (defun calc-apart (arg) | |
| 109 | (interactive "P") | |
| 110 | (calc-slow-wrapper | |
| d3896480 | 111 | (calc-unary-op "aprt" 'calcFunc-apart arg))) |
| 136211a9 EZ |
112 | |
| 113 | (defun calc-normalize-rat (arg) | |
| 114 | (interactive "P") | |
| 115 | (calc-slow-wrapper | |
| d3896480 | 116 | (calc-unary-op "nrat" 'calcFunc-nrat arg))) |
| 136211a9 EZ |
117 | |
| 118 | (defun calc-poly-gcd (arg) | |
| 119 | (interactive "P") | |
| 120 | (calc-slow-wrapper | |
| d3896480 | 121 | (calc-binary-op "pgcd" 'calcFunc-pgcd arg))) |
| 136211a9 | 122 | |
| 0c908945 | 123 | |
| 136211a9 EZ |
124 | (defun calc-poly-div (arg) |
| 125 | (interactive "P") | |
| 126 | (calc-slow-wrapper | |
| 0c908945 JB |
127 | (let ((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)) | |
| 136 | (message "(No remainder)"))))))) | |
| 136211a9 EZ |
137 | |
| 138 | (defun calc-poly-rem (arg) | |
| 139 | (interactive "P") | |
| 140 | (calc-slow-wrapper | |
| d3896480 | 141 | (calc-binary-op "prem" 'calcFunc-prem arg))) |
| 136211a9 EZ |
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)))) |
| 136211a9 EZ |
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))))) |
| 136211a9 EZ |
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)) |
| 136211a9 | 186 | |
| 0c908945 JB |
187 | ;; math-eval-rules-cache and math-eval-rules-cache-other are |
| 188 | ;; declared in calc.el, but are used here by math-recompile-eval-rules. | |
| 189 | (defvar math-eval-rules-cache) | |
| 190 | (defvar math-eval-rules-cache-other) | |
| 191 | ||
| 136211a9 EZ |
192 | (defun math-recompile-eval-rules () |
| 193 | (setq math-eval-rules-cache (and (calc-has-rules 'var-EvalRules) | |
| 194 | (math-compile-rewrites | |
| 195 | '(var EvalRules var-EvalRules))) | |
| 196 | math-eval-rules-cache-other (assq nil math-eval-rules-cache) | |
| d3896480 | 197 | math-eval-rules-cache-tag (calc-var-value 'var-EvalRules))) |
| 136211a9 EZ |
198 | |
| 199 | ||
| 200 | ;;; Try to expand a formula according to its definition. | |
| 201 | (defun math-expand-formula (expr) | |
| 202 | (and (consp expr) | |
| 203 | (symbolp (car expr)) | |
| 204 | (or (get (car expr) 'calc-user-defn) | |
| 205 | (get (car expr) 'math-expandable)) | |
| 206 | (let ((res (let ((math-expand-formulas t)) | |
| 207 | (apply (car expr) (cdr expr))))) | |
| 208 | (and (not (eq (car-safe res) (car expr))) | |
| d3896480 | 209 | res)))) |
| 136211a9 EZ |
210 | |
| 211 | ||
| 212 | ||
| 213 | ||
| 214 | ;;; True if A comes before B in a canonical ordering of expressions. [P X X] | |
| 215 | (defun math-beforep (a b) ; [Public] | |
| 216 | (cond ((and (Math-realp a) (Math-realp b)) | |
| 217 | (let ((comp (math-compare a b))) | |
| 218 | (or (eq comp -1) | |
| 219 | (and (eq comp 0) | |
| 220 | (not (equal a b)) | |
| 221 | (> (length (memq (car-safe a) | |
| 222 | '(bigneg nil bigpos frac float))) | |
| 223 | (length (memq (car-safe b) | |
| 224 | '(bigneg nil bigpos frac float)))))))) | |
| 225 | ((equal b '(neg (var inf var-inf))) nil) | |
| 226 | ((equal a '(neg (var inf var-inf))) t) | |
| 227 | ((equal a '(var inf var-inf)) nil) | |
| 228 | ((equal b '(var inf var-inf)) t) | |
| 229 | ((Math-realp a) | |
| 230 | (if (and (eq (car-safe b) 'intv) (math-intv-constp b)) | |
| 231 | (if (or (math-beforep a (nth 2 b)) (Math-equal a (nth 2 b))) | |
| 232 | t | |
| 233 | nil) | |
| 234 | t)) | |
| 235 | ((Math-realp b) | |
| 236 | (if (and (eq (car-safe a) 'intv) (math-intv-constp a)) | |
| 237 | (if (math-beforep (nth 2 a) b) | |
| 238 | t | |
| 239 | nil) | |
| 240 | nil)) | |
| 241 | ((and (eq (car a) 'intv) (eq (car b) 'intv) | |
| 242 | (math-intv-constp a) (math-intv-constp b)) | |
| 243 | (let ((comp (math-compare (nth 2 a) (nth 2 b)))) | |
| 244 | (cond ((eq comp -1) t) | |
| 245 | ((eq comp 1) nil) | |
| 246 | ((and (memq (nth 1 a) '(2 3)) (memq (nth 1 b) '(0 1))) t) | |
| 247 | ((and (memq (nth 1 a) '(0 1)) (memq (nth 1 b) '(2 3))) nil) | |
| 248 | ((eq (setq comp (math-compare (nth 3 a) (nth 3 b))) -1) t) | |
| 249 | ((eq comp 1) nil) | |
| 250 | ((and (memq (nth 1 a) '(0 2)) (memq (nth 1 b) '(1 3))) t) | |
| 251 | (t nil)))) | |
| 252 | ((not (eq (not (Math-objectp a)) (not (Math-objectp b)))) | |
| 253 | (Math-objectp a)) | |
| 254 | ((eq (car a) 'var) | |
| 255 | (if (eq (car b) 'var) | |
| 256 | (string-lessp (symbol-name (nth 1 a)) (symbol-name (nth 1 b))) | |
| 257 | (not (Math-numberp b)))) | |
| 258 | ((eq (car b) 'var) (Math-numberp a)) | |
| 259 | ((eq (car a) (car b)) | |
| 260 | (while (and (setq a (cdr a) b (cdr b)) a | |
| 261 | (equal (car a) (car b)))) | |
| 262 | (and b | |
| 263 | (or (null a) | |
| 264 | (math-beforep (car a) (car b))))) | |
| d3896480 | 265 | (t (string-lessp (symbol-name (car a)) (symbol-name (car b)))))) |
| 136211a9 EZ |
266 | |
| 267 | ||
| d3896480 | 268 | (defsubst math-simplify-extended (a) |
| 136211a9 | 269 | (let ((math-living-dangerously t)) |
| d3896480 CW |
270 | (math-simplify a))) |
| 271 | ||
| 272 | (defalias 'calcFunc-esimplify 'math-simplify-extended) | |
| 136211a9 | 273 | |
| 0c908945 JB |
274 | ;; math-top-only is local to math-simplify, but is used by |
| 275 | ;; math-simplify-step, which is called by math-simplify. | |
| 276 | (defvar math-top-only) | |
| 277 | ||
| 136211a9 EZ |
278 | (defun math-simplify (top-expr) |
| 279 | (let ((math-simplifying t) | |
| 0c908945 | 280 | (math-top-only (consp calc-simplify-mode)) |
| 136211a9 EZ |
281 | (simp-rules (append (and (calc-has-rules 'var-AlgSimpRules) |
| 282 | '((var AlgSimpRules var-AlgSimpRules))) | |
| 283 | (and math-living-dangerously | |
| 284 | (calc-has-rules 'var-ExtSimpRules) | |
| 285 | '((var ExtSimpRules var-ExtSimpRules))) | |
| 286 | (and math-simplifying-units | |
| 287 | (calc-has-rules 'var-UnitSimpRules) | |
| 288 | '((var UnitSimpRules var-UnitSimpRules))) | |
| 289 | (and math-integrating | |
| 290 | (calc-has-rules 'var-IntegSimpRules) | |
| 291 | '((var IntegSimpRules var-IntegSimpRules))))) | |
| 292 | res) | |
| 0c908945 | 293 | (if math-top-only |
| 136211a9 EZ |
294 | (let ((r simp-rules)) |
| 295 | (setq res (math-simplify-step (math-normalize top-expr)) | |
| 296 | calc-simplify-mode '(nil) | |
| 297 | top-expr (math-normalize res)) | |
| 298 | (while r | |
| 299 | (setq top-expr (math-rewrite top-expr (car r) | |
| 300 | '(neg (var inf var-inf))) | |
| 301 | r (cdr r)))) | |
| 302 | (calc-with-default-simplification | |
| 303 | (while (let ((r simp-rules)) | |
| 304 | (setq res (math-normalize top-expr)) | |
| 305 | (while r | |
| 306 | (setq res (math-rewrite res (car r)) | |
| 307 | r (cdr r))) | |
| 308 | (not (equal top-expr (setq res (math-simplify-step res))))) | |
| 309 | (setq top-expr res))))) | |
| d3896480 CW |
310 | top-expr) |
| 311 | ||
| 312 | (defalias 'calcFunc-simplify 'math-simplify) | |
| 136211a9 EZ |
313 | |
| 314 | ;;; The following has a "bug" in that if any recursive simplifications | |
| 315 | ;;; occur only the first handler will be tried; this doesn't really | |
| 316 | ;;; matter, since math-simplify-step is iterated to a fixed point anyway. | |
| 317 | (defun math-simplify-step (a) | |
| 318 | (if (Math-primp a) | |
| 319 | a | |
| 0c908945 | 320 | (let ((aa (if (or math-top-only |
| 136211a9 EZ |
321 | (memq (car a) '(calcFunc-quote calcFunc-condition |
| 322 | calcFunc-evalto))) | |
| 323 | a | |
| 324 | (cons (car a) (mapcar 'math-simplify-step (cdr a)))))) | |
| 325 | (and (symbolp (car aa)) | |
| 326 | (let ((handler (get (car aa) 'math-simplify))) | |
| 327 | (and handler | |
| 328 | (while (and handler | |
| 329 | (equal (setq aa (or (funcall (car handler) aa) | |
| 330 | aa)) | |
| 331 | a)) | |
| 332 | (setq handler (cdr handler)))))) | |
| d3896480 | 333 | aa))) |
| 136211a9 EZ |
334 | |
| 335 | ||
| d3896480 | 336 | ;; Placeholder, to synchronize autoloading. |
| 136211a9 | 337 | (defun math-need-std-simps () |
| d3896480 | 338 | nil) |
| 136211a9 | 339 | |
| 0c908945 JB |
340 | ;; The function created by math-defsimplify uses the variable |
| 341 | ;; math-simplify-expr, and so is used by functions in math-defsimplify | |
| 342 | (defvar math-simplify-expr) | |
| 343 | ||
| 136211a9 EZ |
344 | (math-defsimplify (+ -) |
| 345 | (math-simplify-plus)) | |
| 346 | ||
| 347 | (defun math-simplify-plus () | |
| 0c908945 JB |
348 | (cond ((and (memq (car-safe (nth 1 math-simplify-expr)) '(+ -)) |
| 349 | (Math-numberp (nth 2 (nth 1 math-simplify-expr))) | |
| 350 | (not (Math-numberp (nth 2 math-simplify-expr)))) | |
| 351 | (let ((x (nth 2 math-simplify-expr)) | |
| 352 | (op (car math-simplify-expr))) | |
| 353 | (setcar (cdr (cdr math-simplify-expr)) (nth 2 (nth 1 math-simplify-expr))) | |
| 354 | (setcar math-simplify-expr (car (nth 1 math-simplify-expr))) | |
| 355 | (setcar (cdr (cdr (nth 1 math-simplify-expr))) x) | |
| 356 | (setcar (nth 1 math-simplify-expr) op))) | |
| 357 | ((and (eq (car math-simplify-expr) '+) | |
| 358 | (Math-numberp (nth 1 math-simplify-expr)) | |
| 359 | (not (Math-numberp (nth 2 math-simplify-expr)))) | |
| 360 | (let ((x (nth 2 math-simplify-expr))) | |
| 361 | (setcar (cdr (cdr math-simplify-expr)) (nth 1 math-simplify-expr)) | |
| 362 | (setcar (cdr math-simplify-expr) x)))) | |
| 363 | (let ((aa math-simplify-expr) | |
| 136211a9 EZ |
364 | aaa temp) |
| 365 | (while (memq (car-safe (setq aaa (nth 1 aa))) '(+ -)) | |
| 0c908945 JB |
366 | (if (setq temp (math-combine-sum (nth 2 aaa) (nth 2 math-simplify-expr) |
| 367 | (eq (car aaa) '-) | |
| 368 | (eq (car math-simplify-expr) '-) t)) | |
| 136211a9 | 369 | (progn |
| 0c908945 JB |
370 | (setcar (cdr (cdr math-simplify-expr)) temp) |
| 371 | (setcar math-simplify-expr '+) | |
| 136211a9 EZ |
372 | (setcar (cdr (cdr aaa)) 0))) |
| 373 | (setq aa (nth 1 aa))) | |
| 0c908945 JB |
374 | (if (setq temp (math-combine-sum aaa (nth 2 math-simplify-expr) |
| 375 | nil (eq (car math-simplify-expr) '-) t)) | |
| 136211a9 | 376 | (progn |
| 0c908945 JB |
377 | (setcar (cdr (cdr math-simplify-expr)) temp) |
| 378 | (setcar math-simplify-expr '+) | |
| 136211a9 | 379 | (setcar (cdr aa) 0))) |
| 0c908945 | 380 | math-simplify-expr)) |
| 136211a9 EZ |
381 | |
| 382 | (math-defsimplify * | |
| 383 | (math-simplify-times)) | |
| 384 | ||
| 385 | (defun math-simplify-times () | |
| 0c908945 JB |
386 | (if (eq (car-safe (nth 2 math-simplify-expr)) '*) |
| 387 | (and (math-beforep (nth 1 (nth 2 math-simplify-expr)) (nth 1 math-simplify-expr)) | |
| 388 | (or (math-known-scalarp (nth 1 math-simplify-expr) t) | |
| 389 | (math-known-scalarp (nth 1 (nth 2 math-simplify-expr)) t)) | |
| 390 | (let ((x (nth 1 math-simplify-expr))) | |
| 391 | (setcar (cdr math-simplify-expr) (nth 1 (nth 2 math-simplify-expr))) | |
| 392 | (setcar (cdr (nth 2 math-simplify-expr)) x))) | |
| 393 | (and (math-beforep (nth 2 math-simplify-expr) (nth 1 math-simplify-expr)) | |
| 394 | (or (math-known-scalarp (nth 1 math-simplify-expr) t) | |
| 395 | (math-known-scalarp (nth 2 math-simplify-expr) t)) | |
| 396 | (let ((x (nth 2 math-simplify-expr))) | |
| 397 | (setcar (cdr (cdr math-simplify-expr)) (nth 1 math-simplify-expr)) | |
| 398 | (setcar (cdr math-simplify-expr) x)))) | |
| 399 | (let ((aa math-simplify-expr) | |
| 136211a9 | 400 | aaa temp |
| 0c908945 JB |
401 | (safe t) (scalar (math-known-scalarp (nth 1 math-simplify-expr)))) |
| 402 | (if (and (Math-ratp (nth 1 math-simplify-expr)) | |
| 403 | (setq temp (math-common-constant-factor (nth 2 math-simplify-expr)))) | |
| 136211a9 | 404 | (progn |
| 0c908945 JB |
405 | (setcar (cdr (cdr math-simplify-expr)) |
| 406 | (math-cancel-common-factor (nth 2 math-simplify-expr) temp)) | |
| 407 | (setcar (cdr math-simplify-expr) (math-mul (nth 1 math-simplify-expr) temp)))) | |
| 136211a9 EZ |
408 | (while (and (eq (car-safe (setq aaa (nth 2 aa))) '*) |
| 409 | safe) | |
| 0c908945 JB |
410 | (if (setq temp (math-combine-prod (nth 1 math-simplify-expr) |
| 411 | (nth 1 aaa) nil nil t)) | |
| 136211a9 | 412 | (progn |
| 0c908945 | 413 | (setcar (cdr math-simplify-expr) temp) |
| 136211a9 EZ |
414 | (setcar (cdr aaa) 1))) |
| 415 | (setq safe (or scalar (math-known-scalarp (nth 1 aaa) t)) | |
| 416 | aa (nth 2 aa))) | |
| 0c908945 | 417 | (if (and (setq temp (math-combine-prod aaa (nth 1 math-simplify-expr) nil nil t)) |
| 136211a9 EZ |
418 | safe) |
| 419 | (progn | |
| 0c908945 | 420 | (setcar (cdr math-simplify-expr) temp) |
| 136211a9 | 421 | (setcar (cdr (cdr aa)) 1))) |
| 0c908945 JB |
422 | (if (and (eq (car-safe (nth 1 math-simplify-expr)) 'frac) |
| 423 | (memq (nth 1 (nth 1 math-simplify-expr)) '(1 -1))) | |
| 424 | (math-div (math-mul (nth 2 math-simplify-expr) | |
| 425 | (nth 1 (nth 1 math-simplify-expr))) | |
| 426 | (nth 2 (nth 1 math-simplify-expr))) | |
| 427 | math-simplify-expr))) | |
| 136211a9 EZ |
428 | |
| 429 | (math-defsimplify / | |
| 430 | (math-simplify-divide)) | |
| 431 | ||
| 432 | (defun math-simplify-divide () | |
| 0c908945 | 433 | (let ((np (cdr math-simplify-expr)) |
| 136211a9 | 434 | (nover nil) |
| 0c908945 JB |
435 | (nn (and (or (eq (car math-simplify-expr) '/) |
| 436 | (not (Math-realp (nth 2 math-simplify-expr)))) | |
| 437 | (math-common-constant-factor (nth 2 math-simplify-expr)))) | |
| 136211a9 EZ |
438 | n op) |
| 439 | (if nn | |
| 440 | (progn | |
| 0c908945 JB |
441 | (setq n (and (or (eq (car math-simplify-expr) '/) |
| 442 | (not (Math-realp (nth 1 math-simplify-expr)))) | |
| 443 | (math-common-constant-factor (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
444 | (if (and (eq (car-safe nn) 'frac) (eq (nth 1 nn) 1) (not n)) |
| 445 | (progn | |
| 0c908945 JB |
446 | (setcar (cdr math-simplify-expr) |
| 447 | (math-mul (nth 2 nn) (nth 1 math-simplify-expr))) | |
| 448 | (setcar (cdr (cdr math-simplify-expr)) | |
| 449 | (math-cancel-common-factor (nth 2 math-simplify-expr) nn)) | |
| 136211a9 | 450 | (if (and (math-negp nn) |
| 0c908945 JB |
451 | (setq op (assq (car math-simplify-expr) calc-tweak-eqn-table))) |
| 452 | (setcar math-simplify-expr (nth 1 op)))) | |
| 136211a9 EZ |
453 | (if (and n (not (eq (setq n (math-frac-gcd n nn)) 1))) |
| 454 | (progn | |
| 0c908945 JB |
455 | (setcar (cdr math-simplify-expr) |
| 456 | (math-cancel-common-factor (nth 1 math-simplify-expr) n)) | |
| 457 | (setcar (cdr (cdr math-simplify-expr)) | |
| 458 | (math-cancel-common-factor (nth 2 math-simplify-expr) n)) | |
| 136211a9 | 459 | (if (and (math-negp n) |
| 0c908945 JB |
460 | (setq op (assq (car math-simplify-expr) |
| 461 | calc-tweak-eqn-table))) | |
| 462 | (setcar math-simplify-expr (nth 1 op)))))))) | |
| 136211a9 | 463 | (if (and (eq (car-safe (car np)) '/) |
| 0c908945 | 464 | (math-known-scalarp (nth 2 math-simplify-expr) t)) |
| 136211a9 | 465 | (progn |
| 0c908945 | 466 | (setq np (cdr (nth 1 math-simplify-expr))) |
| 136211a9 EZ |
467 | (while (eq (car-safe (setq n (car np))) '*) |
| 468 | (and (math-known-scalarp (nth 2 n) t) | |
| 0c908945 | 469 | (math-simplify-divisor (cdr n) (cdr (cdr math-simplify-expr)) nil t)) |
| 136211a9 | 470 | (setq np (cdr (cdr n)))) |
| 0c908945 | 471 | (math-simplify-divisor np (cdr (cdr math-simplify-expr)) nil t) |
| 136211a9 | 472 | (setq nover t |
| 0c908945 | 473 | np (cdr (cdr (nth 1 math-simplify-expr)))))) |
| 136211a9 EZ |
474 | (while (eq (car-safe (setq n (car np))) '*) |
| 475 | (and (math-known-scalarp (nth 2 n) t) | |
| 0c908945 | 476 | (math-simplify-divisor (cdr n) (cdr (cdr math-simplify-expr)) nover t)) |
| 136211a9 | 477 | (setq np (cdr (cdr n)))) |
| 0c908945 JB |
478 | (math-simplify-divisor np (cdr (cdr math-simplify-expr)) nover t) |
| 479 | math-simplify-expr)) | |
| 480 | ||
| 481 | ;; The variables math-simplify-divisor-nover and math-simplify-divisor-dover | |
| 482 | ;; are local variables for math-simplify-divisor, but are used by | |
| 483 | ;; math-simplify-one-divisor. | |
| 484 | (defvar math-simplify-divisor-nover) | |
| 485 | (defvar math-simplify-divisor-dover) | |
| 136211a9 | 486 | |
| 0c908945 JB |
487 | (defun math-simplify-divisor (np dp math-simplify-divisor-nover |
| 488 | math-simplify-divisor-dover) | |
| 136211a9 | 489 | (cond ((eq (car-safe (car dp)) '/) |
| 0c908945 JB |
490 | (math-simplify-divisor np (cdr (car dp)) |
| 491 | math-simplify-divisor-nover | |
| 492 | math-simplify-divisor-dover) | |
| 136211a9 EZ |
493 | (and (math-known-scalarp (nth 1 (car dp)) t) |
| 494 | (math-simplify-divisor np (cdr (cdr (car dp))) | |
| 0c908945 JB |
495 | math-simplify-divisor-nover |
| 496 | (not math-simplify-divisor-dover)))) | |
| 497 | ((or (or (eq (car math-simplify-expr) '/) | |
| 136211a9 EZ |
498 | (let ((signs (math-possible-signs (car np)))) |
| 499 | (or (memq signs '(1 4)) | |
| 0c908945 | 500 | (and (memq (car math-simplify-expr) '(calcFunc-eq calcFunc-neq)) |
| 136211a9 EZ |
501 | (eq signs 5)) |
| 502 | math-living-dangerously))) | |
| 503 | (math-numberp (car np))) | |
| 358c90f4 JB |
504 | (let (d |
| 505 | (safe t) | |
| 506 | (scalar (math-known-scalarp (car np)))) | |
| 136211a9 EZ |
507 | (while (and (eq (car-safe (setq d (car dp))) '*) |
| 508 | safe) | |
| 509 | (math-simplify-one-divisor np (cdr d)) | |
| 510 | (setq safe (or scalar (math-known-scalarp (nth 1 d) t)) | |
| 511 | dp (cdr (cdr d)))) | |
| 512 | (if safe | |
| d3896480 | 513 | (math-simplify-one-divisor np dp)))))) |
| 136211a9 EZ |
514 | |
| 515 | (defun math-simplify-one-divisor (np dp) | |
| 0c908945 JB |
516 | (let ((temp (math-combine-prod (car np) (car dp) math-simplify-divisor-nover |
| 517 | math-simplify-divisor-dover t)) | |
| 518 | op) | |
| 519 | (if temp | |
| 520 | (progn | |
| 521 | (and (not (memq (car math-simplify-expr) '(/ calcFunc-eq calcFunc-neq))) | |
| 522 | (math-known-negp (car dp)) | |
| 523 | (setq op (assq (car math-simplify-expr) calc-tweak-eqn-table)) | |
| 524 | (setcar math-simplify-expr (nth 1 op))) | |
| 525 | (setcar np (if math-simplify-divisor-nover (math-div 1 temp) temp)) | |
| 526 | (setcar dp 1)) | |
| 527 | (and math-simplify-divisor-dover (not math-simplify-divisor-nover) | |
| 528 | (eq (car math-simplify-expr) '/) | |
| 529 | (eq (car-safe (car dp)) 'calcFunc-sqrt) | |
| 530 | (Math-integerp (nth 1 (car dp))) | |
| 531 | (progn | |
| 532 | (setcar np (math-mul (car np) | |
| 533 | (list 'calcFunc-sqrt (nth 1 (car dp))))) | |
| 534 | (setcar dp (nth 1 (car dp)))))))) | |
| 136211a9 EZ |
535 | |
| 536 | (defun math-common-constant-factor (expr) | |
| 537 | (if (Math-realp expr) | |
| 538 | (if (Math-ratp expr) | |
| 539 | (and (not (memq expr '(0 1 -1))) | |
| 540 | (math-abs expr)) | |
| 541 | (if (math-ratp (setq expr (math-to-simple-fraction expr))) | |
| 542 | (math-common-constant-factor expr))) | |
| 543 | (if (memq (car expr) '(+ - cplx sdev)) | |
| 544 | (let ((f1 (math-common-constant-factor (nth 1 expr))) | |
| 545 | (f2 (math-common-constant-factor (nth 2 expr)))) | |
| 546 | (and f1 f2 | |
| 547 | (not (eq (setq f1 (math-frac-gcd f1 f2)) 1)) | |
| 548 | f1)) | |
| 549 | (if (memq (car expr) '(* polar)) | |
| 550 | (math-common-constant-factor (nth 1 expr)) | |
| 551 | (if (eq (car expr) '/) | |
| 552 | (or (math-common-constant-factor (nth 1 expr)) | |
| 553 | (and (Math-integerp (nth 2 expr)) | |
| d3896480 | 554 | (list 'frac 1 (math-abs (nth 2 expr)))))))))) |
| 136211a9 EZ |
555 | |
| 556 | (defun math-cancel-common-factor (expr val) | |
| 557 | (if (memq (car-safe expr) '(+ - cplx sdev)) | |
| 558 | (progn | |
| 559 | (setcar (cdr expr) (math-cancel-common-factor (nth 1 expr) val)) | |
| 560 | (setcar (cdr (cdr expr)) (math-cancel-common-factor (nth 2 expr) val)) | |
| 561 | expr) | |
| 562 | (if (eq (car-safe expr) '*) | |
| 563 | (math-mul (math-cancel-common-factor (nth 1 expr) val) (nth 2 expr)) | |
| d3896480 | 564 | (math-div expr val)))) |
| 136211a9 EZ |
565 | |
| 566 | (defun math-frac-gcd (a b) | |
| 567 | (if (Math-zerop a) | |
| 568 | b | |
| 569 | (if (Math-zerop b) | |
| 570 | a | |
| 571 | (if (and (Math-integerp a) | |
| 572 | (Math-integerp b)) | |
| 573 | (math-gcd a b) | |
| 574 | (and (Math-integerp a) (setq a (list 'frac a 1))) | |
| 575 | (and (Math-integerp b) (setq b (list 'frac b 1))) | |
| 576 | (math-make-frac (math-gcd (nth 1 a) (nth 1 b)) | |
| d3896480 | 577 | (math-gcd (nth 2 a) (nth 2 b))))))) |
| 136211a9 EZ |
578 | |
| 579 | (math-defsimplify % | |
| 580 | (math-simplify-mod)) | |
| 581 | ||
| 582 | (defun math-simplify-mod () | |
| 0c908945 JB |
583 | (and (Math-realp (nth 2 math-simplify-expr)) |
| 584 | (Math-posp (nth 2 math-simplify-expr)) | |
| 585 | (let ((lin (math-is-linear (nth 1 math-simplify-expr))) | |
| 136211a9 EZ |
586 | t1 t2 t3) |
| 587 | (or (and lin | |
| 588 | (or (math-negp (car lin)) | |
| 0c908945 | 589 | (not (Math-lessp (car lin) (nth 2 math-simplify-expr)))) |
| 136211a9 EZ |
590 | (list '% |
| 591 | (list '+ | |
| 592 | (math-mul (nth 1 lin) (nth 2 lin)) | |
| 0c908945 JB |
593 | (math-mod (car lin) (nth 2 math-simplify-expr))) |
| 594 | (nth 2 math-simplify-expr))) | |
| 136211a9 EZ |
595 | (and lin |
| 596 | (not (math-equal-int (nth 1 lin) 1)) | |
| 597 | (math-num-integerp (nth 1 lin)) | |
| 0c908945 JB |
598 | (math-num-integerp (nth 2 math-simplify-expr)) |
| 599 | (setq t1 (calcFunc-gcd (nth 1 lin) (nth 2 math-simplify-expr))) | |
| 136211a9 EZ |
600 | (not (math-equal-int t1 1)) |
| 601 | (list '* | |
| 602 | t1 | |
| 603 | (list '% | |
| 604 | (list '+ | |
| 605 | (math-mul (math-div (nth 1 lin) t1) | |
| 606 | (nth 2 lin)) | |
| 607 | (let ((calc-prefer-frac t)) | |
| 608 | (math-div (car lin) t1))) | |
| 0c908945 JB |
609 | (math-div (nth 2 math-simplify-expr) t1)))) |
| 610 | (and (math-equal-int (nth 2 math-simplify-expr) 1) | |
| 136211a9 EZ |
611 | (math-known-integerp (if lin |
| 612 | (math-mul (nth 1 lin) (nth 2 lin)) | |
| 0c908945 | 613 | (nth 1 math-simplify-expr))) |
| d3896480 | 614 | (if lin (math-mod (car lin) 1) 0)))))) |
| 136211a9 EZ |
615 | |
| 616 | (math-defsimplify (calcFunc-eq calcFunc-neq calcFunc-lt | |
| 617 | calcFunc-gt calcFunc-leq calcFunc-geq) | |
| 0c908945 | 618 | (if (= (length math-simplify-expr) 3) |
| 136211a9 EZ |
619 | (math-simplify-ineq))) |
| 620 | ||
| 621 | (defun math-simplify-ineq () | |
| 0c908945 | 622 | (let ((np (cdr math-simplify-expr)) |
| 136211a9 EZ |
623 | n) |
| 624 | (while (memq (car-safe (setq n (car np))) '(+ -)) | |
| 0c908945 | 625 | (math-simplify-add-term (cdr (cdr n)) (cdr (cdr math-simplify-expr)) |
| 136211a9 EZ |
626 | (eq (car n) '-) nil) |
| 627 | (setq np (cdr n))) | |
| 0c908945 JB |
628 | (math-simplify-add-term np (cdr (cdr math-simplify-expr)) nil |
| 629 | (eq np (cdr math-simplify-expr))) | |
| 136211a9 | 630 | (math-simplify-divide) |
| 0c908945 JB |
631 | (let ((signs (math-possible-signs (cons '- (cdr math-simplify-expr))))) |
| 632 | (or (cond ((eq (car math-simplify-expr) 'calcFunc-eq) | |
| 136211a9 EZ |
633 | (or (and (eq signs 2) 1) |
| 634 | (and (memq signs '(1 4 5)) 0))) | |
| 0c908945 | 635 | ((eq (car math-simplify-expr) 'calcFunc-neq) |
| 136211a9 EZ |
636 | (or (and (eq signs 2) 0) |
| 637 | (and (memq signs '(1 4 5)) 1))) | |
| 0c908945 | 638 | ((eq (car math-simplify-expr) 'calcFunc-lt) |
| 136211a9 EZ |
639 | (or (and (eq signs 1) 1) |
| 640 | (and (memq signs '(2 4 6)) 0))) | |
| 0c908945 | 641 | ((eq (car math-simplify-expr) 'calcFunc-gt) |
| 136211a9 EZ |
642 | (or (and (eq signs 4) 1) |
| 643 | (and (memq signs '(1 2 3)) 0))) | |
| 0c908945 | 644 | ((eq (car math-simplify-expr) 'calcFunc-leq) |
| 136211a9 EZ |
645 | (or (and (eq signs 4) 0) |
| 646 | (and (memq signs '(1 2 3)) 1))) | |
| 0c908945 | 647 | ((eq (car math-simplify-expr) 'calcFunc-geq) |
| 136211a9 EZ |
648 | (or (and (eq signs 1) 0) |
| 649 | (and (memq signs '(2 4 6)) 1)))) | |
| 0c908945 | 650 | math-simplify-expr)))) |
| 136211a9 EZ |
651 | |
| 652 | (defun math-simplify-add-term (np dp minus lplain) | |
| 653 | (or (math-vectorp (car np)) | |
| 654 | (let ((rplain t) | |
| 655 | n d dd temp) | |
| 656 | (while (memq (car-safe (setq n (car np) d (car dp))) '(+ -)) | |
| 657 | (setq rplain nil) | |
| 658 | (if (setq temp (math-combine-sum n (nth 2 d) | |
| 659 | minus (eq (car d) '+) t)) | |
| 660 | (if (or lplain (eq (math-looks-negp temp) minus)) | |
| 661 | (progn | |
| 662 | (setcar np (setq n (if minus (math-neg temp) temp))) | |
| 663 | (setcar (cdr (cdr d)) 0)) | |
| 664 | (progn | |
| 665 | (setcar np 0) | |
| 666 | (setcar (cdr (cdr d)) (setq n (if (eq (car d) '+) | |
| 667 | (math-neg temp) | |
| 668 | temp)))))) | |
| 669 | (setq dp (cdr d))) | |
| 670 | (if (setq temp (math-combine-sum n d minus t t)) | |
| 671 | (if (or lplain | |
| 672 | (and (not rplain) | |
| 673 | (eq (math-looks-negp temp) minus))) | |
| 674 | (progn | |
| 675 | (setcar np (setq n (if minus (math-neg temp) temp))) | |
| 676 | (setcar dp 0)) | |
| 677 | (progn | |
| 678 | (setcar np 0) | |
| d3896480 | 679 | (setcar dp (setq n (math-neg temp))))))))) |
| 136211a9 EZ |
680 | |
| 681 | (math-defsimplify calcFunc-sin | |
| 0c908945 JB |
682 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin) |
| 683 | (nth 1 (nth 1 math-simplify-expr))) | |
| 684 | (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 685 | (math-neg (list 'calcFunc-sin (math-neg (nth 1 math-simplify-expr))))) | |
| 136211a9 | 686 | (and (eq calc-angle-mode 'rad) |
| 0c908945 | 687 | (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi)))) |
| 136211a9 EZ |
688 | (and n |
| 689 | (math-known-sin (car n) (nth 1 n) 120 0)))) | |
| 690 | (and (eq calc-angle-mode 'deg) | |
| 0c908945 | 691 | (let ((n (math-integer-plus (nth 1 math-simplify-expr)))) |
| 136211a9 EZ |
692 | (and n |
| 693 | (math-known-sin (car n) (nth 1 n) '(frac 2 3) 0)))) | |
| 0c908945 JB |
694 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos) |
| 695 | (list 'calcFunc-sqrt (math-sub 1 (math-sqr | |
| 696 | (nth 1 (nth 1 math-simplify-expr)))))) | |
| 697 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctan) | |
| 698 | (math-div (nth 1 (nth 1 math-simplify-expr)) | |
| 136211a9 | 699 | (list 'calcFunc-sqrt |
| 0c908945 JB |
700 | (math-add 1 (math-sqr |
| 701 | (nth 1 (nth 1 math-simplify-expr))))))) | |
| 702 | (let ((m (math-should-expand-trig (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
703 | (and m (integerp (car m)) |
| 704 | (let ((n (car m)) (a (nth 1 m))) | |
| 705 | (list '+ | |
| 706 | (list '* (list 'calcFunc-sin (list '* (1- n) a)) | |
| 707 | (list 'calcFunc-cos a)) | |
| 708 | (list '* (list 'calcFunc-cos (list '* (1- n) a)) | |
| d3896480 | 709 | (list 'calcFunc-sin a)))))))) |
| 136211a9 EZ |
710 | |
| 711 | (math-defsimplify calcFunc-cos | |
| 0c908945 JB |
712 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos) |
| 713 | (nth 1 (nth 1 math-simplify-expr))) | |
| 714 | (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 715 | (list 'calcFunc-cos (math-neg (nth 1 math-simplify-expr)))) | |
| 136211a9 | 716 | (and (eq calc-angle-mode 'rad) |
| 0c908945 | 717 | (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi)))) |
| 136211a9 EZ |
718 | (and n |
| 719 | (math-known-sin (car n) (nth 1 n) 120 300)))) | |
| 720 | (and (eq calc-angle-mode 'deg) | |
| 0c908945 | 721 | (let ((n (math-integer-plus (nth 1 math-simplify-expr)))) |
| 136211a9 EZ |
722 | (and n |
| 723 | (math-known-sin (car n) (nth 1 n) '(frac 2 3) 300)))) | |
| 0c908945 JB |
724 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin) |
| 725 | (list 'calcFunc-sqrt | |
| 726 | (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr)))))) | |
| 727 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctan) | |
| 136211a9 EZ |
728 | (math-div 1 |
| 729 | (list 'calcFunc-sqrt | |
| 0c908945 JB |
730 | (math-add 1 |
| 731 | (math-sqr (nth 1 (nth 1 math-simplify-expr))))))) | |
| 732 | (let ((m (math-should-expand-trig (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
733 | (and m (integerp (car m)) |
| 734 | (let ((n (car m)) (a (nth 1 m))) | |
| 735 | (list '- | |
| 736 | (list '* (list 'calcFunc-cos (list '* (1- n) a)) | |
| 737 | (list 'calcFunc-cos a)) | |
| 738 | (list '* (list 'calcFunc-sin (list '* (1- n) a)) | |
| d3896480 | 739 | (list 'calcFunc-sin a)))))))) |
| 136211a9 EZ |
740 | |
| 741 | (defun math-should-expand-trig (x &optional hyperbolic) | |
| 742 | (let ((m (math-is-multiple x))) | |
| 743 | (and math-living-dangerously | |
| 744 | m (or (and (integerp (car m)) (> (car m) 1)) | |
| 745 | (equal (car m) '(frac 1 2))) | |
| 746 | (or math-integrating | |
| 747 | (memq (car-safe (nth 1 m)) | |
| 748 | (if hyperbolic | |
| 749 | '(calcFunc-arcsinh calcFunc-arccosh calcFunc-arctanh) | |
| 750 | '(calcFunc-arcsin calcFunc-arccos calcFunc-arctan))) | |
| 751 | (and (eq (car-safe (nth 1 m)) 'calcFunc-ln) | |
| 752 | (eq hyperbolic 'exp))) | |
| d3896480 | 753 | m))) |
| 136211a9 EZ |
754 | |
| 755 | (defun math-known-sin (plus n mul off) | |
| 756 | (setq n (math-mul n mul)) | |
| 757 | (and (math-num-integerp n) | |
| 758 | (setq n (math-mod (math-add (math-trunc n) off) 240)) | |
| 759 | (if (>= n 120) | |
| 760 | (and (setq n (math-known-sin plus (- n 120) 1 0)) | |
| 761 | (math-neg n)) | |
| 762 | (if (> n 60) | |
| 763 | (setq n (- 120 n))) | |
| 764 | (if (math-zerop plus) | |
| 765 | (and (or calc-symbolic-mode | |
| 766 | (memq n '(0 20 60))) | |
| 767 | (cdr (assq n | |
| 768 | '( (0 . 0) | |
| 769 | (10 . (/ (calcFunc-sqrt | |
| 770 | (- 2 (calcFunc-sqrt 3))) 2)) | |
| 771 | (12 . (/ (- (calcFunc-sqrt 5) 1) 4)) | |
| 772 | (15 . (/ (calcFunc-sqrt | |
| 773 | (- 2 (calcFunc-sqrt 2))) 2)) | |
| 774 | (20 . (/ 1 2)) | |
| 775 | (24 . (* (^ (/ 1 2) (/ 3 2)) | |
| 776 | (calcFunc-sqrt | |
| 777 | (- 5 (calcFunc-sqrt 5))))) | |
| 778 | (30 . (/ (calcFunc-sqrt 2) 2)) | |
| 779 | (36 . (/ (+ (calcFunc-sqrt 5) 1) 4)) | |
| 780 | (40 . (/ (calcFunc-sqrt 3) 2)) | |
| 781 | (45 . (/ (calcFunc-sqrt | |
| 782 | (+ 2 (calcFunc-sqrt 2))) 2)) | |
| 783 | (48 . (* (^ (/ 1 2) (/ 3 2)) | |
| 784 | (calcFunc-sqrt | |
| 785 | (+ 5 (calcFunc-sqrt 5))))) | |
| 786 | (50 . (/ (calcFunc-sqrt | |
| 787 | (+ 2 (calcFunc-sqrt 3))) 2)) | |
| 788 | (60 . 1))))) | |
| 789 | (cond ((eq n 0) (math-normalize (list 'calcFunc-sin plus))) | |
| 790 | ((eq n 60) (math-normalize (list 'calcFunc-cos plus))) | |
| d3896480 | 791 | (t nil)))))) |
| 136211a9 EZ |
792 | |
| 793 | (math-defsimplify calcFunc-tan | |
| 0c908945 JB |
794 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctan) |
| 795 | (nth 1 (nth 1 math-simplify-expr))) | |
| 796 | (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 797 | (math-neg (list 'calcFunc-tan (math-neg (nth 1 math-simplify-expr))))) | |
| 136211a9 | 798 | (and (eq calc-angle-mode 'rad) |
| 0c908945 | 799 | (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi)))) |
| 136211a9 EZ |
800 | (and n |
| 801 | (math-known-tan (car n) (nth 1 n) 120)))) | |
| 802 | (and (eq calc-angle-mode 'deg) | |
| 0c908945 | 803 | (let ((n (math-integer-plus (nth 1 math-simplify-expr)))) |
| 136211a9 EZ |
804 | (and n |
| 805 | (math-known-tan (car n) (nth 1 n) '(frac 2 3))))) | |
| 0c908945 JB |
806 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin) |
| 807 | (math-div (nth 1 (nth 1 math-simplify-expr)) | |
| 136211a9 | 808 | (list 'calcFunc-sqrt |
| 0c908945 JB |
809 | (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr))))))) |
| 810 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos) | |
| 136211a9 | 811 | (math-div (list 'calcFunc-sqrt |
| 0c908945 JB |
812 | (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr))))) |
| 813 | (nth 1 (nth 1 math-simplify-expr)))) | |
| 814 | (let ((m (math-should-expand-trig (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
815 | (and m |
| 816 | (if (equal (car m) '(frac 1 2)) | |
| 817 | (math-div (math-sub 1 (list 'calcFunc-cos (nth 1 m))) | |
| 818 | (list 'calcFunc-sin (nth 1 m))) | |
| 0c908945 JB |
819 | (math-div (list 'calcFunc-sin (nth 1 math-simplify-expr)) |
| 820 | (list 'calcFunc-cos (nth 1 math-simplify-expr)))))))) | |
| 136211a9 EZ |
821 | |
| 822 | (defun math-known-tan (plus n mul) | |
| 823 | (setq n (math-mul n mul)) | |
| 824 | (and (math-num-integerp n) | |
| 825 | (setq n (math-mod (math-trunc n) 120)) | |
| 826 | (if (> n 60) | |
| 827 | (and (setq n (math-known-tan plus (- 120 n) 1)) | |
| 828 | (math-neg n)) | |
| 829 | (if (math-zerop plus) | |
| 830 | (and (or calc-symbolic-mode | |
| 831 | (memq n '(0 30 60))) | |
| 832 | (cdr (assq n '( (0 . 0) | |
| 833 | (10 . (- 2 (calcFunc-sqrt 3))) | |
| 834 | (12 . (calcFunc-sqrt | |
| 835 | (- 1 (* (/ 2 5) (calcFunc-sqrt 5))))) | |
| 836 | (15 . (- (calcFunc-sqrt 2) 1)) | |
| 837 | (20 . (/ (calcFunc-sqrt 3) 3)) | |
| 838 | (24 . (calcFunc-sqrt | |
| 839 | (- 5 (* 2 (calcFunc-sqrt 5))))) | |
| 840 | (30 . 1) | |
| 841 | (36 . (calcFunc-sqrt | |
| 842 | (+ 1 (* (/ 2 5) (calcFunc-sqrt 5))))) | |
| 843 | (40 . (calcFunc-sqrt 3)) | |
| 844 | (45 . (+ (calcFunc-sqrt 2) 1)) | |
| 845 | (48 . (calcFunc-sqrt | |
| 846 | (+ 5 (* 2 (calcFunc-sqrt 5))))) | |
| 847 | (50 . (+ 2 (calcFunc-sqrt 3))) | |
| 848 | (60 . (var uinf var-uinf)))))) | |
| 849 | (cond ((eq n 0) (math-normalize (list 'calcFunc-tan plus))) | |
| 850 | ((eq n 60) (math-normalize (list '/ -1 | |
| 851 | (list 'calcFunc-tan plus)))) | |
| d3896480 | 852 | (t nil)))))) |
| 136211a9 EZ |
853 | |
| 854 | (math-defsimplify calcFunc-sinh | |
| 0c908945 JB |
855 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh) |
| 856 | (nth 1 (nth 1 math-simplify-expr))) | |
| 857 | (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 858 | (math-neg (list 'calcFunc-sinh (math-neg (nth 1 math-simplify-expr))))) | |
| 859 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccosh) | |
| 136211a9 | 860 | math-living-dangerously |
| 0c908945 JB |
861 | (list 'calcFunc-sqrt |
| 862 | (math-sub (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1))) | |
| 863 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh) | |
| 136211a9 | 864 | math-living-dangerously |
| 0c908945 | 865 | (math-div (nth 1 (nth 1 math-simplify-expr)) |
| 136211a9 | 866 | (list 'calcFunc-sqrt |
| 0c908945 JB |
867 | (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr))))))) |
| 868 | (let ((m (math-should-expand-trig (nth 1 math-simplify-expr) t))) | |
| 136211a9 EZ |
869 | (and m (integerp (car m)) |
| 870 | (let ((n (car m)) (a (nth 1 m))) | |
| 871 | (if (> n 1) | |
| 872 | (list '+ | |
| 873 | (list '* (list 'calcFunc-sinh (list '* (1- n) a)) | |
| 874 | (list 'calcFunc-cosh a)) | |
| 875 | (list '* (list 'calcFunc-cosh (list '* (1- n) a)) | |
| d3896480 | 876 | (list 'calcFunc-sinh a))))))))) |
| 136211a9 EZ |
877 | |
| 878 | (math-defsimplify calcFunc-cosh | |
| 0c908945 JB |
879 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccosh) |
| 880 | (nth 1 (nth 1 math-simplify-expr))) | |
| 881 | (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 882 | (list 'calcFunc-cosh (math-neg (nth 1 math-simplify-expr)))) | |
| 883 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh) | |
| 136211a9 | 884 | math-living-dangerously |
| 0c908945 JB |
885 | (list 'calcFunc-sqrt |
| 886 | (math-add (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1))) | |
| 887 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh) | |
| 136211a9 EZ |
888 | math-living-dangerously |
| 889 | (math-div 1 | |
| 890 | (list 'calcFunc-sqrt | |
| 0c908945 JB |
891 | (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr))))))) |
| 892 | (let ((m (math-should-expand-trig (nth 1 math-simplify-expr) t))) | |
| 136211a9 EZ |
893 | (and m (integerp (car m)) |
| 894 | (let ((n (car m)) (a (nth 1 m))) | |
| 895 | (if (> n 1) | |
| 896 | (list '+ | |
| 897 | (list '* (list 'calcFunc-cosh (list '* (1- n) a)) | |
| 898 | (list 'calcFunc-cosh a)) | |
| 899 | (list '* (list 'calcFunc-sinh (list '* (1- n) a)) | |
| d3896480 | 900 | (list 'calcFunc-sinh a))))))))) |
| 136211a9 EZ |
901 | |
| 902 | (math-defsimplify calcFunc-tanh | |
| 0c908945 JB |
903 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh) |
| 904 | (nth 1 (nth 1 math-simplify-expr))) | |
| 905 | (and (math-looks-negp (nth 1 math-simplify-expr)) | |
| 906 | (math-neg (list 'calcFunc-tanh (math-neg (nth 1 math-simplify-expr))))) | |
| 907 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh) | |
| 136211a9 | 908 | math-living-dangerously |
| 0c908945 | 909 | (math-div (nth 1 (nth 1 math-simplify-expr)) |
| 136211a9 | 910 | (list 'calcFunc-sqrt |
| 0c908945 JB |
911 | (math-add (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1)))) |
| 912 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccosh) | |
| 136211a9 EZ |
913 | math-living-dangerously |
| 914 | (math-div (list 'calcFunc-sqrt | |
| 0c908945 JB |
915 | (math-sub (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1)) |
| 916 | (nth 1 (nth 1 math-simplify-expr)))) | |
| 917 | (let ((m (math-should-expand-trig (nth 1 math-simplify-expr) t))) | |
| 136211a9 EZ |
918 | (and m |
| 919 | (if (equal (car m) '(frac 1 2)) | |
| 920 | (math-div (math-sub (list 'calcFunc-cosh (nth 1 m)) 1) | |
| 921 | (list 'calcFunc-sinh (nth 1 m))) | |
| 0c908945 JB |
922 | (math-div (list 'calcFunc-sinh (nth 1 math-simplify-expr)) |
| 923 | (list 'calcFunc-cosh (nth 1 math-simplify-expr)))))))) | |
| 136211a9 EZ |
924 | |
| 925 | (math-defsimplify calcFunc-arcsin | |
| 0c908945 JB |
926 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) |
| 927 | (math-neg (list 'calcFunc-arcsin (math-neg (nth 1 math-simplify-expr))))) | |
| 928 | (and (eq (nth 1 math-simplify-expr) 1) | |
| 136211a9 | 929 | (math-quarter-circle t)) |
| 0c908945 | 930 | (and (equal (nth 1 math-simplify-expr) '(frac 1 2)) |
| 136211a9 EZ |
931 | (math-div (math-half-circle t) 6)) |
| 932 | (and math-living-dangerously | |
| 0c908945 JB |
933 | (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sin) |
| 934 | (nth 1 (nth 1 math-simplify-expr))) | |
| 136211a9 | 935 | (and math-living-dangerously |
| 0c908945 | 936 | (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cos) |
| 136211a9 | 937 | (math-sub (math-quarter-circle t) |
| 0c908945 | 938 | (nth 1 (nth 1 math-simplify-expr)))))) |
| 136211a9 EZ |
939 | |
| 940 | (math-defsimplify calcFunc-arccos | |
| 0c908945 | 941 | (or (and (eq (nth 1 math-simplify-expr) 0) |
| 136211a9 | 942 | (math-quarter-circle t)) |
| 0c908945 | 943 | (and (eq (nth 1 math-simplify-expr) -1) |
| 136211a9 | 944 | (math-half-circle t)) |
| 0c908945 | 945 | (and (equal (nth 1 math-simplify-expr) '(frac 1 2)) |
| 136211a9 | 946 | (math-div (math-half-circle t) 3)) |
| 0c908945 | 947 | (and (equal (nth 1 math-simplify-expr) '(frac -1 2)) |
| 136211a9 EZ |
948 | (math-div (math-mul (math-half-circle t) 2) 3)) |
| 949 | (and math-living-dangerously | |
| 0c908945 JB |
950 | (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cos) |
| 951 | (nth 1 (nth 1 math-simplify-expr))) | |
| 136211a9 | 952 | (and math-living-dangerously |
| 0c908945 | 953 | (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sin) |
| 136211a9 | 954 | (math-sub (math-quarter-circle t) |
| 0c908945 | 955 | (nth 1 (nth 1 math-simplify-expr)))))) |
| 136211a9 EZ |
956 | |
| 957 | (math-defsimplify calcFunc-arctan | |
| 0c908945 JB |
958 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) |
| 959 | (math-neg (list 'calcFunc-arctan (math-neg (nth 1 math-simplify-expr))))) | |
| 960 | (and (eq (nth 1 math-simplify-expr) 1) | |
| 136211a9 EZ |
961 | (math-div (math-half-circle t) 4)) |
| 962 | (and math-living-dangerously | |
| 0c908945 JB |
963 | (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-tan) |
| 964 | (nth 1 (nth 1 math-simplify-expr))))) | |
| 136211a9 EZ |
965 | |
| 966 | (math-defsimplify calcFunc-arcsinh | |
| 0c908945 JB |
967 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) |
| 968 | (math-neg (list 'calcFunc-arcsinh (math-neg (nth 1 math-simplify-expr))))) | |
| 969 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sinh) | |
| 136211a9 | 970 | (or math-living-dangerously |
| 0c908945 JB |
971 | (math-known-realp (nth 1 (nth 1 math-simplify-expr)))) |
| 972 | (nth 1 (nth 1 math-simplify-expr))))) | |
| 136211a9 EZ |
973 | |
| 974 | (math-defsimplify calcFunc-arccosh | |
| 0c908945 | 975 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cosh) |
| 136211a9 | 976 | (or math-living-dangerously |
| 0c908945 JB |
977 | (math-known-realp (nth 1 (nth 1 math-simplify-expr)))) |
| 978 | (nth 1 (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
979 | |
| 980 | (math-defsimplify calcFunc-arctanh | |
| 0c908945 JB |
981 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) |
| 982 | (math-neg (list 'calcFunc-arctanh (math-neg (nth 1 math-simplify-expr))))) | |
| 983 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-tanh) | |
| 136211a9 | 984 | (or math-living-dangerously |
| 0c908945 JB |
985 | (math-known-realp (nth 1 (nth 1 math-simplify-expr)))) |
| 986 | (nth 1 (nth 1 math-simplify-expr))))) | |
| 136211a9 EZ |
987 | |
| 988 | (math-defsimplify calcFunc-sqrt | |
| d3896480 | 989 | (math-simplify-sqrt)) |
| 136211a9 EZ |
990 | |
| 991 | (defun math-simplify-sqrt () | |
| 0c908945 JB |
992 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'frac) |
| 993 | (math-div (list 'calcFunc-sqrt | |
| 994 | (math-mul (nth 1 (nth 1 math-simplify-expr)) | |
| 995 | (nth 2 (nth 1 math-simplify-expr)))) | |
| 996 | (nth 2 (nth 1 math-simplify-expr)))) | |
| 997 | (let ((fac (if (math-objectp (nth 1 math-simplify-expr)) | |
| 998 | (math-squared-factor (nth 1 math-simplify-expr)) | |
| 999 | (math-common-constant-factor (nth 1 math-simplify-expr))))) | |
| 136211a9 EZ |
1000 | (and fac (not (eq fac 1)) |
| 1001 | (math-mul (math-normalize (list 'calcFunc-sqrt fac)) | |
| 1002 | (math-normalize | |
| 1003 | (list 'calcFunc-sqrt | |
| 0c908945 JB |
1004 | (math-cancel-common-factor |
| 1005 | (nth 1 math-simplify-expr) fac)))))) | |
| 136211a9 | 1006 | (and math-living-dangerously |
| 0c908945 JB |
1007 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) '-) |
| 1008 | (math-equal-int (nth 1 (nth 1 math-simplify-expr)) 1) | |
| 1009 | (eq (car-safe (nth 2 (nth 1 math-simplify-expr))) '^) | |
| 1010 | (math-equal-int (nth 2 (nth 2 (nth 1 math-simplify-expr))) 2) | |
| 1011 | (or (and (eq (car-safe (nth 1 (nth 2 (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
1012 | 'calcFunc-sin) |
| 1013 | (list 'calcFunc-cos | |
| 0c908945 JB |
1014 | (nth 1 (nth 1 (nth 2 (nth 1 math-simplify-expr)))))) |
| 1015 | (and (eq (car-safe (nth 1 (nth 2 (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
1016 | 'calcFunc-cos) |
| 1017 | (list 'calcFunc-sin | |
| 0c908945 JB |
1018 | (nth 1 (nth 1 (nth 2 |
| 1019 | (nth 1 math-simplify-expr)))))))) | |
| 1020 | (and (eq (car-safe (nth 1 math-simplify-expr)) '-) | |
| 1021 | (math-equal-int (nth 2 (nth 1 math-simplify-expr)) 1) | |
| 1022 | (eq (car-safe (nth 1 (nth 1 math-simplify-expr))) '^) | |
| 1023 | (math-equal-int (nth 2 (nth 1 (nth 1 math-simplify-expr))) 2) | |
| 1024 | (and (eq (car-safe (nth 1 (nth 1 (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
1025 | 'calcFunc-cosh) |
| 1026 | (list 'calcFunc-sinh | |
| 0c908945 JB |
1027 | (nth 1 (nth 1 (nth 1 (nth 1 math-simplify-expr))))))) |
| 1028 | (and (eq (car-safe (nth 1 math-simplify-expr)) '+) | |
| 1029 | (let ((a (nth 1 (nth 1 math-simplify-expr))) | |
| 1030 | (b (nth 2 (nth 1 math-simplify-expr)))) | |
| 136211a9 | 1031 | (and (or (and (math-equal-int a 1) |
| 0c908945 | 1032 | (setq a b b (nth 1 (nth 1 math-simplify-expr)))) |
| 136211a9 EZ |
1033 | (math-equal-int b 1)) |
| 1034 | (eq (car-safe a) '^) | |
| 1035 | (math-equal-int (nth 2 a) 2) | |
| 1036 | (or (and (eq (car-safe (nth 1 a)) 'calcFunc-sinh) | |
| 1037 | (list 'calcFunc-cosh (nth 1 (nth 1 a)))) | |
| 1038 | (and (eq (car-safe (nth 1 a)) 'calcFunc-tan) | |
| 1039 | (list '/ 1 (list 'calcFunc-cos | |
| 1040 | (nth 1 (nth 1 a))))))))) | |
| 0c908945 | 1041 | (and (eq (car-safe (nth 1 math-simplify-expr)) '^) |
| 136211a9 | 1042 | (list '^ |
| 0c908945 JB |
1043 | (nth 1 (nth 1 math-simplify-expr)) |
| 1044 | (math-div (nth 2 (nth 1 math-simplify-expr)) 2))) | |
| 1045 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sqrt) | |
| 1046 | (list '^ (nth 1 (nth 1 math-simplify-expr)) (math-div 1 4))) | |
| 1047 | (and (memq (car-safe (nth 1 math-simplify-expr)) '(* /)) | |
| 1048 | (list (car (nth 1 math-simplify-expr)) | |
| 1049 | (list 'calcFunc-sqrt (nth 1 (nth 1 math-simplify-expr))) | |
| 1050 | (list 'calcFunc-sqrt (nth 2 (nth 1 math-simplify-expr))))) | |
| 1051 | (and (memq (car-safe (nth 1 math-simplify-expr)) '(+ -)) | |
| 1052 | (not (math-any-floats (nth 1 math-simplify-expr))) | |
| 136211a9 | 1053 | (let ((f (calcFunc-factors (calcFunc-expand |
| 0c908945 | 1054 | (nth 1 math-simplify-expr))))) |
| 136211a9 EZ |
1055 | (and (math-vectorp f) |
| 1056 | (or (> (length f) 2) | |
| 1057 | (> (nth 2 (nth 1 f)) 1)) | |
| 1058 | (let ((out 1) (rest 1) (sums 1) fac pow) | |
| 1059 | (while (setq f (cdr f)) | |
| 1060 | (setq fac (nth 1 (car f)) | |
| 1061 | pow (nth 2 (car f))) | |
| 1062 | (if (> pow 1) | |
| 1063 | (setq out (math-mul out (math-pow | |
| 1064 | fac (/ pow 2))) | |
| 1065 | pow (% pow 2))) | |
| 1066 | (if (> pow 0) | |
| 1067 | (if (memq (car-safe fac) '(+ -)) | |
| 1068 | (setq sums (math-mul-thru sums fac)) | |
| 1069 | (setq rest (math-mul rest fac))))) | |
| 1070 | (and (not (and (eq out 1) (memq rest '(1 -1)))) | |
| 1071 | (math-mul | |
| 1072 | out | |
| 1073 | (list 'calcFunc-sqrt | |
| d3896480 | 1074 | (math-mul sums rest)))))))))))) |
| 136211a9 EZ |
1075 | |
| 1076 | ;;; Rather than factoring x into primes, just check for the first ten primes. | |
| 1077 | (defun math-squared-factor (x) | |
| 1078 | (if (Math-integerp x) | |
| 1079 | (let ((prsqr '(4 9 25 49 121 169 289 361 529 841)) | |
| 1080 | (fac 1) | |
| 1081 | res) | |
| 1082 | (while prsqr | |
| 1083 | (if (eq (cdr (setq res (math-idivmod x (car prsqr)))) 0) | |
| 1084 | (setq x (car res) | |
| 1085 | fac (math-mul fac (car prsqr))) | |
| 1086 | (setq prsqr (cdr prsqr)))) | |
| d3896480 | 1087 | fac))) |
| 136211a9 EZ |
1088 | |
| 1089 | (math-defsimplify calcFunc-exp | |
| 0c908945 | 1090 | (math-simplify-exp (nth 1 math-simplify-expr))) |
| 136211a9 EZ |
1091 | |
| 1092 | (defun math-simplify-exp (x) | |
| 1093 | (or (and (eq (car-safe x) 'calcFunc-ln) | |
| 1094 | (nth 1 x)) | |
| 1095 | (and math-living-dangerously | |
| 1096 | (or (and (eq (car-safe x) 'calcFunc-arcsinh) | |
| 1097 | (math-add (nth 1 x) | |
| 1098 | (list 'calcFunc-sqrt | |
| 1099 | (math-add (math-sqr (nth 1 x)) 1)))) | |
| 1100 | (and (eq (car-safe x) 'calcFunc-arccosh) | |
| 1101 | (math-add (nth 1 x) | |
| 1102 | (list 'calcFunc-sqrt | |
| 1103 | (math-sub (math-sqr (nth 1 x)) 1)))) | |
| 1104 | (and (eq (car-safe x) 'calcFunc-arctanh) | |
| 1105 | (math-div (list 'calcFunc-sqrt (math-add 1 (nth 1 x))) | |
| 1106 | (list 'calcFunc-sqrt (math-sub 1 (nth 1 x))))) | |
| 1107 | (let ((m (math-should-expand-trig x 'exp))) | |
| 1108 | (and m (integerp (car m)) | |
| 1109 | (list '^ (list 'calcFunc-exp (nth 1 m)) (car m)))))) | |
| 1110 | (and calc-symbolic-mode | |
| 1111 | (math-known-imagp x) | |
| 1112 | (let* ((ip (calcFunc-im x)) | |
| 1113 | (n (math-linear-in ip '(var pi var-pi))) | |
| 1114 | s c) | |
| 1115 | (and n | |
| 1116 | (setq s (math-known-sin (car n) (nth 1 n) 120 0)) | |
| 1117 | (setq c (math-known-sin (car n) (nth 1 n) 120 300)) | |
| d3896480 | 1118 | (list '+ c (list '* s '(var i var-i)))))))) |
| 136211a9 EZ |
1119 | |
| 1120 | (math-defsimplify calcFunc-ln | |
| 0c908945 | 1121 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-exp) |
| 136211a9 | 1122 | (or math-living-dangerously |
| 0c908945 JB |
1123 | (math-known-realp (nth 1 (nth 1 math-simplify-expr)))) |
| 1124 | (nth 1 (nth 1 math-simplify-expr))) | |
| 1125 | (and (eq (car-safe (nth 1 math-simplify-expr)) '^) | |
| 1126 | (equal (nth 1 (nth 1 math-simplify-expr)) '(var e var-e)) | |
| 136211a9 | 1127 | (or math-living-dangerously |
| 0c908945 JB |
1128 | (math-known-realp (nth 2 (nth 1 math-simplify-expr)))) |
| 1129 | (nth 2 (nth 1 math-simplify-expr))) | |
| 136211a9 | 1130 | (and calc-symbolic-mode |
| 0c908945 JB |
1131 | (math-known-negp (nth 1 math-simplify-expr)) |
| 1132 | (math-add (list 'calcFunc-ln (math-neg (nth 1 math-simplify-expr))) | |
| 2c6dfebb | 1133 | '(* (var pi var-pi) (var i var-i)))) |
| 136211a9 | 1134 | (and calc-symbolic-mode |
| 0c908945 JB |
1135 | (math-known-imagp (nth 1 math-simplify-expr)) |
| 1136 | (let* ((ip (calcFunc-im (nth 1 math-simplify-expr))) | |
| 136211a9 EZ |
1137 | (ips (math-possible-signs ip))) |
| 1138 | (or (and (memq ips '(4 6)) | |
| 1139 | (math-add (list 'calcFunc-ln ip) | |
| 1140 | '(/ (* (var pi var-pi) (var i var-i)) 2))) | |
| 1141 | (and (memq ips '(1 3)) | |
| 1142 | (math-sub (list 'calcFunc-ln (math-neg ip)) | |
| d3896480 | 1143 | '(/ (* (var pi var-pi) (var i var-i)) 2)))))))) |
| 136211a9 EZ |
1144 | |
| 1145 | (math-defsimplify ^ | |
| 1146 | (math-simplify-pow)) | |
| 1147 | ||
| 1148 | (defun math-simplify-pow () | |
| 1149 | (or (and math-living-dangerously | |
| 0c908945 | 1150 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) '^) |
| 136211a9 | 1151 | (list '^ |
| 0c908945 JB |
1152 | (nth 1 (nth 1 math-simplify-expr)) |
| 1153 | (math-mul (nth 2 math-simplify-expr) | |
| 1154 | (nth 2 (nth 1 math-simplify-expr))))) | |
| 1155 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sqrt) | |
| 136211a9 | 1156 | (list '^ |
| 0c908945 JB |
1157 | (nth 1 (nth 1 math-simplify-expr)) |
| 1158 | (math-div (nth 2 math-simplify-expr) 2))) | |
| 1159 | (and (memq (car-safe (nth 1 math-simplify-expr)) '(* /)) | |
| 1160 | (list (car (nth 1 math-simplify-expr)) | |
| 1161 | (list '^ (nth 1 (nth 1 math-simplify-expr)) | |
| 1162 | (nth 2 math-simplify-expr)) | |
| 1163 | (list '^ (nth 2 (nth 1 math-simplify-expr)) | |
| 1164 | (nth 2 math-simplify-expr)))))) | |
| 1165 | (and (math-equal-int (nth 1 math-simplify-expr) 10) | |
| 1166 | (eq (car-safe (nth 2 math-simplify-expr)) 'calcFunc-log10) | |
| 1167 | (nth 1 (nth 2 math-simplify-expr))) | |
| 1168 | (and (equal (nth 1 math-simplify-expr) '(var e var-e)) | |
| 1169 | (math-simplify-exp (nth 2 math-simplify-expr))) | |
| 1170 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-exp) | |
| 136211a9 | 1171 | (not math-integrating) |
| 0c908945 JB |
1172 | (list 'calcFunc-exp (math-mul (nth 1 (nth 1 math-simplify-expr)) |
| 1173 | (nth 2 math-simplify-expr)))) | |
| 1174 | (and (equal (nth 1 math-simplify-expr) '(var i var-i)) | |
| 136211a9 | 1175 | (math-imaginary-i) |
| 0c908945 JB |
1176 | (math-num-integerp (nth 2 math-simplify-expr)) |
| 1177 | (let ((x (math-mod (math-trunc (nth 2 math-simplify-expr)) 4))) | |
| 136211a9 | 1178 | (cond ((eq x 0) 1) |
| 0c908945 | 1179 | ((eq x 1) (nth 1 math-simplify-expr)) |
| 136211a9 | 1180 | ((eq x 2) -1) |
| 0c908945 | 1181 | ((eq x 3) (math-neg (nth 1 math-simplify-expr)))))) |
| 136211a9 | 1182 | (and math-integrating |
| 0c908945 JB |
1183 | (integerp (nth 2 math-simplify-expr)) |
| 1184 | (>= (nth 2 math-simplify-expr) 2) | |
| 1185 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cos) | |
| 1186 | (math-mul (math-pow (nth 1 math-simplify-expr) | |
| 1187 | (- (nth 2 math-simplify-expr) 2)) | |
| 136211a9 EZ |
1188 | (math-sub 1 |
| 1189 | (math-sqr | |
| 1190 | (list 'calcFunc-sin | |
| 0c908945 JB |
1191 | (nth 1 (nth 1 math-simplify-expr))))))) |
| 1192 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cosh) | |
| 1193 | (math-mul (math-pow (nth 1 math-simplify-expr) | |
| 1194 | (- (nth 2 math-simplify-expr) 2)) | |
| 136211a9 EZ |
1195 | (math-add 1 |
| 1196 | (math-sqr | |
| 1197 | (list 'calcFunc-sinh | |
| 0c908945 JB |
1198 | (nth 1 (nth 1 math-simplify-expr))))))))) |
| 1199 | (and (eq (car-safe (nth 2 math-simplify-expr)) 'frac) | |
| 1200 | (Math-ratp (nth 1 math-simplify-expr)) | |
| 1201 | (Math-posp (nth 1 math-simplify-expr)) | |
| 1202 | (if (equal (nth 2 math-simplify-expr) '(frac 1 2)) | |
| 1203 | (list 'calcFunc-sqrt (nth 1 math-simplify-expr)) | |
| 1204 | (let ((flr (math-floor (nth 2 math-simplify-expr)))) | |
| 136211a9 | 1205 | (and (not (Math-zerop flr)) |
| 0c908945 JB |
1206 | (list '* (list '^ (nth 1 math-simplify-expr) flr) |
| 1207 | (list '^ (nth 1 math-simplify-expr) | |
| 1208 | (math-sub (nth 2 math-simplify-expr) flr))))))) | |
| 1209 | (and (eq (math-quarter-integer (nth 2 math-simplify-expr)) 2) | |
| 136211a9 EZ |
1210 | (let ((temp (math-simplify-sqrt))) |
| 1211 | (and temp | |
| 0c908945 | 1212 | (list '^ temp (math-mul (nth 2 math-simplify-expr) 2))))))) |
| 136211a9 EZ |
1213 | |
| 1214 | (math-defsimplify calcFunc-log10 | |
| 0c908945 JB |
1215 | (and (eq (car-safe (nth 1 math-simplify-expr)) '^) |
| 1216 | (math-equal-int (nth 1 (nth 1 math-simplify-expr)) 10) | |
| 136211a9 | 1217 | (or math-living-dangerously |
| 0c908945 JB |
1218 | (math-known-realp (nth 2 (nth 1 math-simplify-expr)))) |
| 1219 | (nth 2 (nth 1 math-simplify-expr)))) | |
| 136211a9 EZ |
1220 | |
| 1221 | ||
| 1222 | (math-defsimplify calcFunc-erf | |
| 0c908945 JB |
1223 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) |
| 1224 | (math-neg (list 'calcFunc-erf (math-neg (nth 1 math-simplify-expr))))) | |
| 1225 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-conj) | |
| 1226 | (list 'calcFunc-conj | |
| 1227 | (list 'calcFunc-erf (nth 1 (nth 1 math-simplify-expr))))))) | |
| 136211a9 EZ |
1228 | |
| 1229 | (math-defsimplify calcFunc-erfc | |
| 0c908945 JB |
1230 | (or (and (math-looks-negp (nth 1 math-simplify-expr)) |
| 1231 | (math-sub 2 (list 'calcFunc-erfc (math-neg (nth 1 math-simplify-expr))))) | |
| 1232 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-conj) | |
| 1233 | (list 'calcFunc-conj | |
| 1234 | (list 'calcFunc-erfc (nth 1 (nth 1 math-simplify-expr))))))) | |
| 136211a9 EZ |
1235 | |
| 1236 | ||
| 1237 | (defun math-linear-in (expr term &optional always) | |
| 1238 | (if (math-expr-contains expr term) | |
| 1239 | (let* ((calc-prefer-frac t) | |
| 1240 | (p (math-is-polynomial expr term 1))) | |
| 1241 | (and (cdr p) | |
| 1242 | p)) | |
| d3896480 | 1243 | (and always (list expr 0)))) |
| 136211a9 EZ |
1244 | |
| 1245 | (defun math-multiple-of (expr term) | |
| 1246 | (let ((p (math-linear-in expr term))) | |
| 1247 | (and p | |
| 1248 | (math-zerop (car p)) | |
| d3896480 | 1249 | (nth 1 p)))) |
| 136211a9 | 1250 | |
| d3896480 | 1251 | ; not perfect, but it'll do |
| 136211a9 EZ |
1252 | (defun math-integer-plus (expr) |
| 1253 | (cond ((Math-integerp expr) | |
| 1254 | (list 0 expr)) | |
| 1255 | ((and (memq (car expr) '(+ -)) | |
| 1256 | (Math-integerp (nth 1 expr))) | |
| 1257 | (list (if (eq (car expr) '+) (nth 2 expr) (math-neg (nth 2 expr))) | |
| 1258 | (nth 1 expr))) | |
| 1259 | ((and (memq (car expr) '(+ -)) | |
| 1260 | (Math-integerp (nth 2 expr))) | |
| 1261 | (list (nth 1 expr) | |
| 1262 | (if (eq (car expr) '+) (nth 2 expr) (math-neg (nth 2 expr))))) | |
| d3896480 | 1263 | (t nil))) |
| 136211a9 EZ |
1264 | |
| 1265 | (defun math-is-linear (expr &optional always) | |
| 1266 | (let ((offset nil) | |
| 1267 | (coef nil)) | |
| 1268 | (if (eq (car-safe expr) '+) | |
| 1269 | (if (Math-objectp (nth 1 expr)) | |
| 1270 | (setq offset (nth 1 expr) | |
| 1271 | expr (nth 2 expr)) | |
| 1272 | (if (Math-objectp (nth 2 expr)) | |
| 1273 | (setq offset (nth 2 expr) | |
| 1274 | expr (nth 1 expr)))) | |
| 1275 | (if (eq (car-safe expr) '-) | |
| 1276 | (if (Math-objectp (nth 1 expr)) | |
| 1277 | (setq offset (nth 1 expr) | |
| 1278 | expr (math-neg (nth 2 expr))) | |
| 1279 | (if (Math-objectp (nth 2 expr)) | |
| 1280 | (setq offset (math-neg (nth 2 expr)) | |
| 1281 | expr (nth 1 expr)))))) | |
| 1282 | (setq coef (math-is-multiple expr always)) | |
| 1283 | (if offset | |
| 1284 | (list offset (or (car coef) 1) (or (nth 1 coef) expr)) | |
| 1285 | (if coef | |
| d3896480 | 1286 | (cons 0 coef))))) |
| 136211a9 EZ |
1287 | |
| 1288 | (defun math-is-multiple (expr &optional always) | |
| 1289 | (or (if (eq (car-safe expr) '*) | |
| 1290 | (if (Math-objectp (nth 1 expr)) | |
| 1291 | (list (nth 1 expr) (nth 2 expr))) | |
| 1292 | (if (eq (car-safe expr) '/) | |
| 1293 | (if (and (Math-objectp (nth 1 expr)) | |
| 1294 | (not (math-equal-int (nth 1 expr) 1))) | |
| 1295 | (list (nth 1 expr) (math-div 1 (nth 2 expr))) | |
| 1296 | (if (Math-objectp (nth 2 expr)) | |
| 1297 | (list (math-div 1 (nth 2 expr)) (nth 1 expr)) | |
| 1298 | (let ((res (math-is-multiple (nth 1 expr)))) | |
| 1299 | (if res | |
| 1300 | (list (car res) | |
| 1301 | (math-div (nth 2 (nth 1 expr)) (nth 2 expr))) | |
| 1302 | (setq res (math-is-multiple (nth 2 expr))) | |
| 1303 | (if res | |
| 1304 | (list (math-div 1 (car res)) | |
| 1305 | (math-div (nth 1 expr) | |
| 1306 | (nth 2 (nth 2 expr))))))))) | |
| 1307 | (if (eq (car-safe expr) 'neg) | |
| 1308 | (list -1 (nth 1 expr))))) | |
| 1309 | (if (Math-objvecp expr) | |
| 1310 | (and (eq always 1) | |
| 1311 | (list expr 1)) | |
| a1506d29 | 1312 | (and always |
| d3896480 | 1313 | (list 1 expr))))) |
| 136211a9 EZ |
1314 | |
| 1315 | (defun calcFunc-lin (expr &optional var) | |
| 1316 | (if var | |
| 1317 | (let ((res (math-linear-in expr var t))) | |
| 1318 | (or res (math-reject-arg expr "Linear term expected")) | |
| 1319 | (list 'vec (car res) (nth 1 res) var)) | |
| 1320 | (let ((res (math-is-linear expr t))) | |
| 1321 | (or res (math-reject-arg expr "Linear term expected")) | |
| d3896480 | 1322 | (cons 'vec res)))) |
| 136211a9 EZ |
1323 | |
| 1324 | (defun calcFunc-linnt (expr &optional var) | |
| 1325 | (if var | |
| 1326 | (let ((res (math-linear-in expr var))) | |
| 1327 | (or res (math-reject-arg expr "Linear term expected")) | |
| 1328 | (list 'vec (car res) (nth 1 res) var)) | |
| 1329 | (let ((res (math-is-linear expr))) | |
| 1330 | (or res (math-reject-arg expr "Linear term expected")) | |
| d3896480 | 1331 | (cons 'vec res)))) |
| 136211a9 EZ |
1332 | |
| 1333 | (defun calcFunc-islin (expr &optional var) | |
| 1334 | (if (and (Math-objvecp expr) (not var)) | |
| 1335 | 0 | |
| 1336 | (calcFunc-lin expr var) | |
| d3896480 | 1337 | 1)) |
| 136211a9 EZ |
1338 | |
| 1339 | (defun calcFunc-islinnt (expr &optional var) | |
| 1340 | (if (Math-objvecp expr) | |
| 1341 | 0 | |
| 1342 | (calcFunc-linnt expr var) | |
| d3896480 | 1343 | 1)) |
| 136211a9 EZ |
1344 | |
| 1345 | ||
| 1346 | ||
| 1347 | ||
| 1348 | ;;; Simple operations on expressions. | |
| 1349 | ||
| 6f826971 | 1350 | ;;; Return number of occurrences of thing in expr, or nil if none. |
| 136211a9 EZ |
1351 | (defun math-expr-contains-count (expr thing) |
| 1352 | (cond ((equal expr thing) 1) | |
| 1353 | ((Math-primp expr) nil) | |
| 1354 | (t | |
| 1355 | (let ((num 0)) | |
| 1356 | (while (setq expr (cdr expr)) | |
| 1357 | (setq num (+ num (or (math-expr-contains-count | |
| 1358 | (car expr) thing) 0)))) | |
| 1359 | (and (> num 0) | |
| d3896480 | 1360 | num))))) |
| 136211a9 EZ |
1361 | |
| 1362 | (defun math-expr-contains (expr thing) | |
| 1363 | (cond ((equal expr thing) 1) | |
| 1364 | ((Math-primp expr) nil) | |
| 1365 | (t | |
| 1366 | (while (and (setq expr (cdr expr)) | |
| 1367 | (not (math-expr-contains (car expr) thing)))) | |
| d3896480 | 1368 | expr))) |
| 136211a9 EZ |
1369 | |
| 1370 | ;;; Return non-nil if any variable of thing occurs in expr. | |
| 1371 | (defun math-expr-depends (expr thing) | |
| 1372 | (if (Math-primp thing) | |
| 1373 | (and (eq (car-safe thing) 'var) | |
| 1374 | (math-expr-contains expr thing)) | |
| 1375 | (while (and (setq thing (cdr thing)) | |
| 1376 | (not (math-expr-depends expr (car thing))))) | |
| d3896480 | 1377 | thing)) |
| 136211a9 EZ |
1378 | |
| 1379 | ;;; Substitute all occurrences of old for new in expr (non-destructive). | |
| 0c908945 JB |
1380 | |
| 1381 | ;; The variables math-expr-subst-old and math-expr-subst-new are local | |
| 1382 | ;; for math-expr-subst, but used by math-expr-subst-rec. | |
| 1383 | (defvar math-expr-subst-old) | |
| 1384 | (defvar math-expr-subst-new) | |
| 1385 | ||
| 1386 | (defun math-expr-subst (expr math-expr-subst-old math-expr-subst-new) | |
| d3896480 CW |
1387 | (math-expr-subst-rec expr)) |
| 1388 | ||
| 1389 | (defalias 'calcFunc-subst 'math-expr-subst) | |
| 136211a9 EZ |
1390 | |
| 1391 | (defun math-expr-subst-rec (expr) | |
| 0c908945 | 1392 | (cond ((equal expr math-expr-subst-old) math-expr-subst-new) |
| 136211a9 EZ |
1393 | ((Math-primp expr) expr) |
| 1394 | ((memq (car expr) '(calcFunc-deriv | |
| 1395 | calcFunc-tderiv)) | |
| 1396 | (if (= (length expr) 2) | |
| 0c908945 JB |
1397 | (if (equal (nth 1 expr) math-expr-subst-old) |
| 1398 | (append expr (list math-expr-subst-new)) | |
| 136211a9 EZ |
1399 | expr) |
| 1400 | (list (car expr) (nth 1 expr) | |
| 1401 | (math-expr-subst-rec (nth 2 expr))))) | |
| 1402 | (t | |
| 1403 | (cons (car expr) | |
| d3896480 | 1404 | (mapcar 'math-expr-subst-rec (cdr expr)))))) |
| 136211a9 EZ |
1405 | |
| 1406 | ;;; Various measures of the size of an expression. | |
| 1407 | (defun math-expr-weight (expr) | |
| 1408 | (if (Math-primp expr) | |
| 1409 | 1 | |
| 1410 | (let ((w 1)) | |
| 1411 | (while (setq expr (cdr expr)) | |
| 1412 | (setq w (+ w (math-expr-weight (car expr))))) | |
| d3896480 | 1413 | w))) |
| 136211a9 EZ |
1414 | |
| 1415 | (defun math-expr-height (expr) | |
| 1416 | (if (Math-primp expr) | |
| 1417 | 0 | |
| 1418 | (let ((h 0)) | |
| 1419 | (while (setq expr (cdr expr)) | |
| 1420 | (setq h (max h (math-expr-height (car expr))))) | |
| d3896480 | 1421 | (1+ h)))) |
| 136211a9 EZ |
1422 | |
| 1423 | ||
| 1424 | ||
| 1425 | ||
| 1426 | ;;; Polynomial operations (to support the integrator and solve-for). | |
| 1427 | ||
| 1428 | (defun calcFunc-collect (expr base) | |
| 1429 | (let ((p (math-is-polynomial expr base 50 t))) | |
| 1430 | (if (cdr p) | |
| 1431 | (math-normalize ; fix selection bug | |
| 1432 | (math-build-polynomial-expr p base)) | |
| d3896480 | 1433 | expr))) |
| 136211a9 EZ |
1434 | |
| 1435 | ;;; If expr is of the form "a + bx + cx^2 + ...", return the list (a b c ...), | |
| 0c908945 JB |
1436 | ;;; else return nil if not in polynomial form. If "loose" (math-is-poly-loose), |
| 1437 | ;;; coefficients may contain x, e.g., sin(x) + cos(x) x^2 is a loose polynomial in x. | |
| 1438 | ||
| 1439 | ;; The variables math-is-poly-degree and math-is-poly-loose are local to | |
| 1440 | ;; math-is-polynomial, but are used by math-is-poly-rec | |
| 1441 | (defvar math-is-poly-degree) | |
| 1442 | (defvar math-is-poly-loose) | |
| 1443 | ||
| 1444 | (defun math-is-polynomial (expr var &optional math-is-poly-degree math-is-poly-loose) | |
| 1445 | (let* ((math-poly-base-variable (if math-is-poly-loose | |
| 1446 | (if (eq math-is-poly-loose 'gen) var '(var XXX XXX)) | |
| 136211a9 EZ |
1447 | math-poly-base-variable)) |
| 1448 | (poly (math-is-poly-rec expr math-poly-neg-powers))) | |
| 0c908945 JB |
1449 | (and (or (null math-is-poly-degree) |
| 1450 | (<= (length poly) (1+ math-is-poly-degree))) | |
| d3896480 | 1451 | poly))) |
| 136211a9 EZ |
1452 | |
| 1453 | (defun math-is-poly-rec (expr negpow) | |
| 1454 | (math-poly-simplify | |
| 1455 | (or (cond ((or (equal expr var) | |
| 1456 | (eq (car-safe expr) '^)) | |
| 1457 | (let ((pow 1) | |
| 1458 | (expr expr)) | |
| 1459 | (or (equal expr var) | |
| 1460 | (setq pow (nth 2 expr) | |
| 1461 | expr (nth 1 expr))) | |
| 1462 | (or (eq math-poly-mult-powers 1) | |
| 1463 | (setq pow (let ((m (math-is-multiple pow 1))) | |
| 1464 | (and (eq (car-safe (car m)) 'cplx) | |
| 1465 | (Math-zerop (nth 1 (car m))) | |
| 1466 | (setq m (list (nth 2 (car m)) | |
| 1467 | (math-mul (nth 1 m) | |
| 1468 | '(var i var-i))))) | |
| 1469 | (and (if math-poly-mult-powers | |
| 1470 | (equal math-poly-mult-powers | |
| 1471 | (nth 1 m)) | |
| 1472 | (setq math-poly-mult-powers (nth 1 m))) | |
| 1473 | (or (equal expr var) | |
| 1474 | (eq math-poly-mult-powers 1)) | |
| 1475 | (car m))))) | |
| 1476 | (if (consp pow) | |
| 1477 | (progn | |
| 1478 | (setq pow (math-to-simple-fraction pow)) | |
| 1479 | (and (eq (car-safe pow) 'frac) | |
| 1480 | math-poly-frac-powers | |
| 1481 | (equal expr var) | |
| 1482 | (setq math-poly-frac-powers | |
| 1483 | (calcFunc-lcm math-poly-frac-powers | |
| 1484 | (nth 2 pow)))))) | |
| 1485 | (or (memq math-poly-frac-powers '(1 nil)) | |
| 1486 | (setq pow (math-mul pow math-poly-frac-powers))) | |
| 1487 | (if (integerp pow) | |
| 1488 | (if (and (= pow 1) | |
| 1489 | (equal expr var)) | |
| 1490 | (list 0 1) | |
| 1491 | (if (natnump pow) | |
| 1492 | (let ((p1 (if (equal expr var) | |
| 1493 | (list 0 1) | |
| 1494 | (math-is-poly-rec expr nil))) | |
| 1495 | (n pow) | |
| 1496 | (accum (list 1))) | |
| 1497 | (and p1 | |
| 0c908945 JB |
1498 | (or (null math-is-poly-degree) |
| 1499 | (<= (* (1- (length p1)) n) math-is-poly-degree)) | |
| 136211a9 EZ |
1500 | (progn |
| 1501 | (while (>= n 1) | |
| 1502 | (setq accum (math-poly-mul accum p1) | |
| 1503 | n (1- n))) | |
| 1504 | accum))) | |
| 1505 | (and negpow | |
| 1506 | (math-is-poly-rec expr nil) | |
| 1507 | (setq math-poly-neg-powers | |
| 1508 | (cons (math-pow expr (- pow)) | |
| 1509 | math-poly-neg-powers)) | |
| 1510 | (list (list '^ expr pow)))))))) | |
| 1511 | ((Math-objectp expr) | |
| 1512 | (list expr)) | |
| 1513 | ((memq (car expr) '(+ -)) | |
| 1514 | (let ((p1 (math-is-poly-rec (nth 1 expr) negpow))) | |
| 1515 | (and p1 | |
| 1516 | (let ((p2 (math-is-poly-rec (nth 2 expr) negpow))) | |
| 1517 | (and p2 | |
| 1518 | (math-poly-mix p1 1 p2 | |
| 1519 | (if (eq (car expr) '+) 1 -1))))))) | |
| 1520 | ((eq (car expr) 'neg) | |
| 1521 | (mapcar 'math-neg (math-is-poly-rec (nth 1 expr) negpow))) | |
| 1522 | ((eq (car expr) '*) | |
| 1523 | (let ((p1 (math-is-poly-rec (nth 1 expr) negpow))) | |
| 1524 | (and p1 | |
| 1525 | (let ((p2 (math-is-poly-rec (nth 2 expr) negpow))) | |
| 1526 | (and p2 | |
| 0c908945 JB |
1527 | (or (null math-is-poly-degree) |
| 1528 | (<= (- (+ (length p1) (length p2)) 2) | |
| 1529 | math-is-poly-degree)) | |
| 136211a9 EZ |
1530 | (math-poly-mul p1 p2)))))) |
| 1531 | ((eq (car expr) '/) | |
| 1532 | (and (or (not (math-poly-depends (nth 2 expr) var)) | |
| 1533 | (and negpow | |
| 1534 | (math-is-poly-rec (nth 2 expr) nil) | |
| 1535 | (setq math-poly-neg-powers | |
| 1536 | (cons (nth 2 expr) math-poly-neg-powers)))) | |
| 1537 | (not (Math-zerop (nth 2 expr))) | |
| 1538 | (let ((p1 (math-is-poly-rec (nth 1 expr) negpow))) | |
| 1539 | (mapcar (function (lambda (x) (math-div x (nth 2 expr)))) | |
| 1540 | p1)))) | |
| 1541 | ((and (eq (car expr) 'calcFunc-exp) | |
| 1542 | (equal var '(var e var-e))) | |
| 1543 | (math-is-poly-rec (list '^ var (nth 1 expr)) negpow)) | |
| 1544 | ((and (eq (car expr) 'calcFunc-sqrt) | |
| 1545 | math-poly-frac-powers) | |
| 1546 | (math-is-poly-rec (list '^ (nth 1 expr) '(frac 1 2)) negpow)) | |
| 1547 | (t nil)) | |
| 1548 | (and (or (not (math-poly-depends expr var)) | |
| 0c908945 | 1549 | math-is-poly-loose) |
| 136211a9 | 1550 | (not (eq (car expr) 'vec)) |
| d3896480 | 1551 | (list expr))))) |
| 136211a9 EZ |
1552 | |
| 1553 | ;;; Check if expr is a polynomial in var; if so, return its degree. | |
| 1554 | (defun math-polynomial-p (expr var) | |
| 1555 | (cond ((equal expr var) 1) | |
| 1556 | ((Math-primp expr) 0) | |
| 1557 | ((memq (car expr) '(+ -)) | |
| 1558 | (let ((p1 (math-polynomial-p (nth 1 expr) var)) | |
| 1559 | p2) | |
| 1560 | (and p1 (setq p2 (math-polynomial-p (nth 2 expr) var)) | |
| 1561 | (max p1 p2)))) | |
| 1562 | ((eq (car expr) '*) | |
| 1563 | (let ((p1 (math-polynomial-p (nth 1 expr) var)) | |
| 1564 | p2) | |
| 1565 | (and p1 (setq p2 (math-polynomial-p (nth 2 expr) var)) | |
| 1566 | (+ p1 p2)))) | |
| 1567 | ((eq (car expr) 'neg) | |
| 1568 | (math-polynomial-p (nth 1 expr) var)) | |
| 1569 | ((and (eq (car expr) '/) | |
| 1570 | (not (math-poly-depends (nth 2 expr) var))) | |
| 1571 | (math-polynomial-p (nth 1 expr) var)) | |
| 1572 | ((and (eq (car expr) '^) | |
| 1573 | (natnump (nth 2 expr))) | |
| 1574 | (let ((p1 (math-polynomial-p (nth 1 expr) var))) | |
| 1575 | (and p1 (* p1 (nth 2 expr))))) | |
| 1576 | ((math-poly-depends expr var) nil) | |
| d3896480 | 1577 | (t 0))) |
| 136211a9 EZ |
1578 | |
| 1579 | (defun math-poly-depends (expr var) | |
| 1580 | (if math-poly-base-variable | |
| 1581 | (math-expr-contains expr math-poly-base-variable) | |
| d3896480 | 1582 | (math-expr-depends expr var))) |
| 136211a9 EZ |
1583 | |
| 1584 | ;;; Find the variable (or sub-expression) which is the base of polynomial expr. | |
| 0c908945 JB |
1585 | ;; The variables math-poly-base-const-ok and math-poly-base-pred are |
| 1586 | ;; local to math-polynomial-base, but are used by math-polynomial-base-rec. | |
| 1587 | (defvar math-poly-base-const-ok) | |
| 1588 | (defvar math-poly-base-pred) | |
| 1589 | ||
| 885e6671 JB |
1590 | ;; The variable math-poly-base-top-expr is local to math-polynomial-base, |
| 1591 | ;; but is used by math-polynomial-p1 in calc-poly.el, which is called | |
| 1592 | ;; by math-polynomial-base. | |
| 1593 | ||
| 1594 | (defun math-polynomial-base (math-poly-base-top-expr &optional math-poly-base-pred) | |
| 0c908945 JB |
1595 | (or math-poly-base-pred |
| 1596 | (setq math-poly-base-pred (function (lambda (base) (math-polynomial-p | |
| 885e6671 | 1597 | math-poly-base-top-expr base))))) |
| 0c908945 | 1598 | (or (let ((math-poly-base-const-ok nil)) |
| 885e6671 | 1599 | (math-polynomial-base-rec math-poly-base-top-expr)) |
| 0c908945 | 1600 | (let ((math-poly-base-const-ok t)) |
| 885e6671 | 1601 | (math-polynomial-base-rec math-poly-base-top-expr)))) |
| 136211a9 EZ |
1602 | |
| 1603 | (defun math-polynomial-base-rec (mpb-expr) | |
| 1604 | (and (not (Math-objvecp mpb-expr)) | |
| 1605 | (or (and (memq (car mpb-expr) '(+ - *)) | |
| 1606 | (or (math-polynomial-base-rec (nth 1 mpb-expr)) | |
| 1607 | (math-polynomial-base-rec (nth 2 mpb-expr)))) | |
| 1608 | (and (memq (car mpb-expr) '(/ neg)) | |
| 1609 | (math-polynomial-base-rec (nth 1 mpb-expr))) | |
| 1610 | (and (eq (car mpb-expr) '^) | |
| 1611 | (math-polynomial-base-rec (nth 1 mpb-expr))) | |
| 1612 | (and (eq (car mpb-expr) 'calcFunc-exp) | |
| 1613 | (math-polynomial-base-rec '(var e var-e))) | |
| 0c908945 JB |
1614 | (and (or math-poly-base-const-ok (math-expr-contains-vars mpb-expr)) |
| 1615 | (funcall math-poly-base-pred mpb-expr) | |
| d3896480 | 1616 | mpb-expr)))) |
| 136211a9 EZ |
1617 | |
| 1618 | ;;; Return non-nil if expr refers to any variables. | |
| 1619 | (defun math-expr-contains-vars (expr) | |
| 1620 | (or (eq (car-safe expr) 'var) | |
| 1621 | (and (not (Math-primp expr)) | |
| 1622 | (progn | |
| 1623 | (while (and (setq expr (cdr expr)) | |
| 1624 | (not (math-expr-contains-vars (car expr))))) | |
| d3896480 | 1625 | expr)))) |
| 136211a9 EZ |
1626 | |
| 1627 | ;;; Simplify a polynomial in list form by stripping off high-end zeros. | |
| 1628 | ;;; This always leaves the constant part, i.e., nil->nil and nonnil->nonnil. | |
| 1629 | (defun math-poly-simplify (p) | |
| 1630 | (and p | |
| 1631 | (if (Math-zerop (nth (1- (length p)) p)) | |
| 1632 | (let ((pp (copy-sequence p))) | |
| 1633 | (while (and (cdr pp) | |
| 1634 | (Math-zerop (nth (1- (length pp)) pp))) | |
| 1635 | (setcdr (nthcdr (- (length pp) 2) pp) nil)) | |
| 1636 | pp) | |
| d3896480 | 1637 | p))) |
| 136211a9 EZ |
1638 | |
| 1639 | ;;; Compute ac*a + bc*b for polynomials in list form a, b and | |
| 1640 | ;;; coefficients ac, bc. Result may be unsimplified. | |
| 1641 | (defun math-poly-mix (a ac b bc) | |
| 1642 | (and (or a b) | |
| 1643 | (cons (math-add (math-mul (or (car a) 0) ac) | |
| 1644 | (math-mul (or (car b) 0) bc)) | |
| d3896480 | 1645 | (math-poly-mix (cdr a) ac (cdr b) bc)))) |
| 136211a9 EZ |
1646 | |
| 1647 | (defun math-poly-zerop (a) | |
| 1648 | (or (null a) | |
| d3896480 | 1649 | (and (null (cdr a)) (Math-zerop (car a))))) |
| 136211a9 EZ |
1650 | |
| 1651 | ;;; Multiply two polynomials in list form. | |
| 1652 | (defun math-poly-mul (a b) | |
| 1653 | (and a b | |
| 1654 | (math-poly-mix b (car a) | |
| d3896480 | 1655 | (math-poly-mul (cdr a) (cons 0 b)) 1))) |
| 136211a9 EZ |
1656 | |
| 1657 | ;;; Build an expression from a polynomial list. | |
| 1658 | (defun math-build-polynomial-expr (p var) | |
| 1659 | (if p | |
| 1660 | (if (Math-numberp var) | |
| 1661 | (math-with-extra-prec 1 | |
| 1662 | (let* ((rp (reverse p)) | |
| 1663 | (accum (car rp))) | |
| 1664 | (while (setq rp (cdr rp)) | |
| 1665 | (setq accum (math-add (car rp) (math-mul accum var)))) | |
| 1666 | accum)) | |
| 1667 | (let* ((rp (reverse p)) | |
| 1668 | (n (1- (length rp))) | |
| 1669 | (accum (math-mul (car rp) (math-pow var n))) | |
| 1670 | term) | |
| 1671 | (while (setq rp (cdr rp)) | |
| 1672 | (setq n (1- n)) | |
| 1673 | (or (math-zerop (car rp)) | |
| 1674 | (setq accum (list (if (math-looks-negp (car rp)) '- '+) | |
| 1675 | accum | |
| 1676 | (math-mul (if (math-looks-negp (car rp)) | |
| 1677 | (math-neg (car rp)) | |
| 1678 | (car rp)) | |
| 1679 | (math-pow var n)))))) | |
| 1680 | accum)) | |
| d3896480 | 1681 | 0)) |
| 136211a9 EZ |
1682 | |
| 1683 | ||
| 1684 | (defun math-to-simple-fraction (f) | |
| 1685 | (or (and (eq (car-safe f) 'float) | |
| 1686 | (or (and (>= (nth 2 f) 0) | |
| 1687 | (math-scale-int (nth 1 f) (nth 2 f))) | |
| 1688 | (and (integerp (nth 1 f)) | |
| 1689 | (> (nth 1 f) -1000) | |
| 1690 | (< (nth 1 f) 1000) | |
| 1691 | (math-make-frac (nth 1 f) | |
| 1692 | (math-scale-int 1 (- (nth 2 f))))))) | |
| d3896480 | 1693 | f)) |
| 136211a9 | 1694 | |
| ab5796a9 | 1695 | ;;; arch-tag: 52e7dcdf-9688-464d-a02b-4bbe789348d0 |
| d3896480 | 1696 | ;;; calc-alg.el ends here |