| | 1 | ;;; calc-alg.el --- algebraic functions for Calc |
| | 2 | |
| | 3 | ;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc. |
| | 4 | |
| | 5 | ;; Author: David Gillespie <daveg@synaptics.com> |
| | 6 | ;; Maintainer: Jay Belanger <belanger@truman.edu> |
| | 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 | |
| | 25 | ;;; Commentary: |
| | 26 | |
| | 27 | ;;; Code: |
| | 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 | |
| | 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) |
| | 44 | (calc-enter-result 1 "dsmp" (calc-top 1)))))) |
| | 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) |
| | 52 | (setq calc-simplify-mode (list calc-simplify-mode)))) |
| | 53 | |
| | 54 | (defun calc-simplify () |
| | 55 | (interactive) |
| | 56 | (calc-slow-wrapper |
| | 57 | (calc-with-default-simplification |
| | 58 | (calc-enter-result 1 "simp" (math-simplify (calc-top-n 1)))))) |
| | 59 | |
| | 60 | (defun calc-simplify-extended () |
| | 61 | (interactive) |
| | 62 | (calc-slow-wrapper |
| | 63 | (calc-with-default-simplification |
| | 64 | (calc-enter-result 1 "esmp" (math-simplify-extended (calc-top-n 1)))))) |
| | 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) |
| | 72 | (calc-enter-result 1 "expf" |
| | 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) |
| | 78 | top)))))))) |
| | 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) |
| | 85 | arg))) |
| | 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)) |
| | 93 | (and n (list (prefix-numeric-value n))))))) |
| | 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) |
| | 106 | var)))))) |
| | 107 | |
| | 108 | (defun calc-apart (arg) |
| | 109 | (interactive "P") |
| | 110 | (calc-slow-wrapper |
| | 111 | (calc-unary-op "aprt" 'calcFunc-apart arg))) |
| | 112 | |
| | 113 | (defun calc-normalize-rat (arg) |
| | 114 | (interactive "P") |
| | 115 | (calc-slow-wrapper |
| | 116 | (calc-unary-op "nrat" 'calcFunc-nrat arg))) |
| | 117 | |
| | 118 | (defun calc-poly-gcd (arg) |
| | 119 | (interactive "P") |
| | 120 | (calc-slow-wrapper |
| | 121 | (calc-binary-op "pgcd" 'calcFunc-pgcd arg))) |
| | 122 | |
| | 123 | |
| | 124 | (defun calc-poly-div (arg) |
| | 125 | (interactive "P") |
| | 126 | (calc-slow-wrapper |
| | 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)"))))))) |
| | 137 | |
| | 138 | (defun calc-poly-rem (arg) |
| | 139 | (interactive "P") |
| | 140 | (calc-slow-wrapper |
| | 141 | (calc-binary-op "prem" 'calcFunc-prem arg))) |
| | 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) |
| | 148 | (calc-binary-op "pdvr" 'calcFunc-pdivrem arg)))) |
| | 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) |
| | 177 | (error "No occurrences found"))) |
| | 178 | (calc-enter-result num "sbst" (math-expr-subst expr old new))))) |
| | 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)) |
| | 185 | name)) |
| | 186 | |
| | 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 | |
| | 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) |
| | 197 | math-eval-rules-cache-tag (calc-var-value 'var-EvalRules))) |
| | 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))) |
| | 209 | res)))) |
| | 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))))) |
| | 265 | (t (string-lessp (symbol-name (car a)) (symbol-name (car b)))))) |
| | 266 | |
| | 267 | |
| | 268 | (defsubst math-simplify-extended (a) |
| | 269 | (let ((math-living-dangerously t)) |
| | 270 | (math-simplify a))) |
| | 271 | |
| | 272 | (defalias 'calcFunc-esimplify 'math-simplify-extended) |
| | 273 | |
| | 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 | |
| | 278 | (defun math-simplify (top-expr) |
| | 279 | (let ((math-simplifying t) |
| | 280 | (math-top-only (consp calc-simplify-mode)) |
| | 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) |
| | 293 | (if math-top-only |
| | 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))))) |
| | 310 | top-expr) |
| | 311 | |
| | 312 | (defalias 'calcFunc-simplify 'math-simplify) |
| | 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 |
| | 320 | (let ((aa (if (or math-top-only |
| | 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)))))) |
| | 333 | aa))) |
| | 334 | |
| | 335 | |
| | 336 | ;; Placeholder, to synchronize autoloading. |
| | 337 | (defun math-need-std-simps () |
| | 338 | nil) |
| | 339 | |
| | 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 | |
| | 344 | (math-defsimplify (+ -) |
| | 345 | (math-simplify-plus)) |
| | 346 | |
| | 347 | (defun math-simplify-plus () |
| | 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) |
| | 364 | aaa temp) |
| | 365 | (while (memq (car-safe (setq aaa (nth 1 aa))) '(+ -)) |
| | 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)) |
| | 369 | (progn |
| | 370 | (setcar (cdr (cdr math-simplify-expr)) temp) |
| | 371 | (setcar math-simplify-expr '+) |
| | 372 | (setcar (cdr (cdr aaa)) 0))) |
| | 373 | (setq aa (nth 1 aa))) |
| | 374 | (if (setq temp (math-combine-sum aaa (nth 2 math-simplify-expr) |
| | 375 | nil (eq (car math-simplify-expr) '-) t)) |
| | 376 | (progn |
| | 377 | (setcar (cdr (cdr math-simplify-expr)) temp) |
| | 378 | (setcar math-simplify-expr '+) |
| | 379 | (setcar (cdr aa) 0))) |
| | 380 | math-simplify-expr)) |
| | 381 | |
| | 382 | (math-defsimplify * |
| | 383 | (math-simplify-times)) |
| | 384 | |
| | 385 | (defun math-simplify-times () |
| | 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) |
| | 400 | aaa temp |
| | 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)))) |
| | 404 | (progn |
| | 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)))) |
| | 408 | (while (and (eq (car-safe (setq aaa (nth 2 aa))) '*) |
| | 409 | safe) |
| | 410 | (if (setq temp (math-combine-prod (nth 1 math-simplify-expr) |
| | 411 | (nth 1 aaa) nil nil t)) |
| | 412 | (progn |
| | 413 | (setcar (cdr math-simplify-expr) temp) |
| | 414 | (setcar (cdr aaa) 1))) |
| | 415 | (setq safe (or scalar (math-known-scalarp (nth 1 aaa) t)) |
| | 416 | aa (nth 2 aa))) |
| | 417 | (if (and (setq temp (math-combine-prod aaa (nth 1 math-simplify-expr) nil nil t)) |
| | 418 | safe) |
| | 419 | (progn |
| | 420 | (setcar (cdr math-simplify-expr) temp) |
| | 421 | (setcar (cdr (cdr aa)) 1))) |
| | 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))) |
| | 428 | |
| | 429 | (math-defsimplify / |
| | 430 | (math-simplify-divide)) |
| | 431 | |
| | 432 | (defun math-simplify-divide () |
| | 433 | (let ((np (cdr math-simplify-expr)) |
| | 434 | (nover nil) |
| | 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)))) |
| | 438 | n op) |
| | 439 | (if nn |
| | 440 | (progn |
| | 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)))) |
| | 444 | (if (and (eq (car-safe nn) 'frac) (eq (nth 1 nn) 1) (not n)) |
| | 445 | (progn |
| | 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)) |
| | 450 | (if (and (math-negp nn) |
| | 451 | (setq op (assq (car math-simplify-expr) calc-tweak-eqn-table))) |
| | 452 | (setcar math-simplify-expr (nth 1 op)))) |
| | 453 | (if (and n (not (eq (setq n (math-frac-gcd n nn)) 1))) |
| | 454 | (progn |
| | 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)) |
| | 459 | (if (and (math-negp n) |
| | 460 | (setq op (assq (car math-simplify-expr) |
| | 461 | calc-tweak-eqn-table))) |
| | 462 | (setcar math-simplify-expr (nth 1 op)))))))) |
| | 463 | (if (and (eq (car-safe (car np)) '/) |
| | 464 | (math-known-scalarp (nth 2 math-simplify-expr) t)) |
| | 465 | (progn |
| | 466 | (setq np (cdr (nth 1 math-simplify-expr))) |
| | 467 | (while (eq (car-safe (setq n (car np))) '*) |
| | 468 | (and (math-known-scalarp (nth 2 n) t) |
| | 469 | (math-simplify-divisor (cdr n) (cdr (cdr math-simplify-expr)) nil t)) |
| | 470 | (setq np (cdr (cdr n)))) |
| | 471 | (math-simplify-divisor np (cdr (cdr math-simplify-expr)) nil t) |
| | 472 | (setq nover t |
| | 473 | np (cdr (cdr (nth 1 math-simplify-expr)))))) |
| | 474 | (while (eq (car-safe (setq n (car np))) '*) |
| | 475 | (and (math-known-scalarp (nth 2 n) t) |
| | 476 | (math-simplify-divisor (cdr n) (cdr (cdr math-simplify-expr)) nover t)) |
| | 477 | (setq np (cdr (cdr n)))) |
| | 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) |
| | 486 | |
| | 487 | (defun math-simplify-divisor (np dp math-simplify-divisor-nover |
| | 488 | math-simplify-divisor-dover) |
| | 489 | (cond ((eq (car-safe (car dp)) '/) |
| | 490 | (math-simplify-divisor np (cdr (car dp)) |
| | 491 | math-simplify-divisor-nover |
| | 492 | math-simplify-divisor-dover) |
| | 493 | (and (math-known-scalarp (nth 1 (car dp)) t) |
| | 494 | (math-simplify-divisor np (cdr (cdr (car dp))) |
| | 495 | math-simplify-divisor-nover |
| | 496 | (not math-simplify-divisor-dover)))) |
| | 497 | ((or (or (eq (car math-simplify-expr) '/) |
| | 498 | (let ((signs (math-possible-signs (car np)))) |
| | 499 | (or (memq signs '(1 4)) |
| | 500 | (and (memq (car math-simplify-expr) '(calcFunc-eq calcFunc-neq)) |
| | 501 | (eq signs 5)) |
| | 502 | math-living-dangerously))) |
| | 503 | (math-numberp (car np))) |
| | 504 | (let (d |
| | 505 | (safe t) |
| | 506 | (scalar (math-known-scalarp (car np)))) |
| | 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 |
| | 513 | (math-simplify-one-divisor np dp)))))) |
| | 514 | |
| | 515 | (defun math-simplify-one-divisor (np dp) |
| | 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)))))))) |
| | 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)) |
| | 554 | (list 'frac 1 (math-abs (nth 2 expr)))))))))) |
| | 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)) |
| | 564 | (math-div expr val)))) |
| | 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)) |
| | 577 | (math-gcd (nth 2 a) (nth 2 b))))))) |
| | 578 | |
| | 579 | (math-defsimplify % |
| | 580 | (math-simplify-mod)) |
| | 581 | |
| | 582 | (defun math-simplify-mod () |
| | 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))) |
| | 586 | t1 t2 t3) |
| | 587 | (or (and lin |
| | 588 | (or (math-negp (car lin)) |
| | 589 | (not (Math-lessp (car lin) (nth 2 math-simplify-expr)))) |
| | 590 | (list '% |
| | 591 | (list '+ |
| | 592 | (math-mul (nth 1 lin) (nth 2 lin)) |
| | 593 | (math-mod (car lin) (nth 2 math-simplify-expr))) |
| | 594 | (nth 2 math-simplify-expr))) |
| | 595 | (and lin |
| | 596 | (not (math-equal-int (nth 1 lin) 1)) |
| | 597 | (math-num-integerp (nth 1 lin)) |
| | 598 | (math-num-integerp (nth 2 math-simplify-expr)) |
| | 599 | (setq t1 (calcFunc-gcd (nth 1 lin) (nth 2 math-simplify-expr))) |
| | 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))) |
| | 609 | (math-div (nth 2 math-simplify-expr) t1)))) |
| | 610 | (and (math-equal-int (nth 2 math-simplify-expr) 1) |
| | 611 | (math-known-integerp (if lin |
| | 612 | (math-mul (nth 1 lin) (nth 2 lin)) |
| | 613 | (nth 1 math-simplify-expr))) |
| | 614 | (if lin (math-mod (car lin) 1) 0)))))) |
| | 615 | |
| | 616 | (math-defsimplify (calcFunc-eq calcFunc-neq calcFunc-lt |
| | 617 | calcFunc-gt calcFunc-leq calcFunc-geq) |
| | 618 | (if (= (length math-simplify-expr) 3) |
| | 619 | (math-simplify-ineq))) |
| | 620 | |
| | 621 | (defun math-simplify-ineq () |
| | 622 | (let ((np (cdr math-simplify-expr)) |
| | 623 | n) |
| | 624 | (while (memq (car-safe (setq n (car np))) '(+ -)) |
| | 625 | (math-simplify-add-term (cdr (cdr n)) (cdr (cdr math-simplify-expr)) |
| | 626 | (eq (car n) '-) nil) |
| | 627 | (setq np (cdr n))) |
| | 628 | (math-simplify-add-term np (cdr (cdr math-simplify-expr)) nil |
| | 629 | (eq np (cdr math-simplify-expr))) |
| | 630 | (math-simplify-divide) |
| | 631 | (let ((signs (math-possible-signs (cons '- (cdr math-simplify-expr))))) |
| | 632 | (or (cond ((eq (car math-simplify-expr) 'calcFunc-eq) |
| | 633 | (or (and (eq signs 2) 1) |
| | 634 | (and (memq signs '(1 4 5)) 0))) |
| | 635 | ((eq (car math-simplify-expr) 'calcFunc-neq) |
| | 636 | (or (and (eq signs 2) 0) |
| | 637 | (and (memq signs '(1 4 5)) 1))) |
| | 638 | ((eq (car math-simplify-expr) 'calcFunc-lt) |
| | 639 | (or (and (eq signs 1) 1) |
| | 640 | (and (memq signs '(2 4 6)) 0))) |
| | 641 | ((eq (car math-simplify-expr) 'calcFunc-gt) |
| | 642 | (or (and (eq signs 4) 1) |
| | 643 | (and (memq signs '(1 2 3)) 0))) |
| | 644 | ((eq (car math-simplify-expr) 'calcFunc-leq) |
| | 645 | (or (and (eq signs 4) 0) |
| | 646 | (and (memq signs '(1 2 3)) 1))) |
| | 647 | ((eq (car math-simplify-expr) 'calcFunc-geq) |
| | 648 | (or (and (eq signs 1) 0) |
| | 649 | (and (memq signs '(2 4 6)) 1)))) |
| | 650 | math-simplify-expr)))) |
| | 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) |
| | 679 | (setcar dp (setq n (math-neg temp))))))))) |
| | 680 | |
| | 681 | (math-defsimplify calcFunc-sin |
| | 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))))) |
| | 686 | (and (eq calc-angle-mode 'rad) |
| | 687 | (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi)))) |
| | 688 | (and n |
| | 689 | (math-known-sin (car n) (nth 1 n) 120 0)))) |
| | 690 | (and (eq calc-angle-mode 'deg) |
| | 691 | (let ((n (math-integer-plus (nth 1 math-simplify-expr)))) |
| | 692 | (and n |
| | 693 | (math-known-sin (car n) (nth 1 n) '(frac 2 3) 0)))) |
| | 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)) |
| | 699 | (list 'calcFunc-sqrt |
| | 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)))) |
| | 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)) |
| | 709 | (list 'calcFunc-sin a)))))))) |
| | 710 | |
| | 711 | (math-defsimplify calcFunc-cos |
| | 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)))) |
| | 716 | (and (eq calc-angle-mode 'rad) |
| | 717 | (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi)))) |
| | 718 | (and n |
| | 719 | (math-known-sin (car n) (nth 1 n) 120 300)))) |
| | 720 | (and (eq calc-angle-mode 'deg) |
| | 721 | (let ((n (math-integer-plus (nth 1 math-simplify-expr)))) |
| | 722 | (and n |
| | 723 | (math-known-sin (car n) (nth 1 n) '(frac 2 3) 300)))) |
| | 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) |
| | 728 | (math-div 1 |
| | 729 | (list 'calcFunc-sqrt |
| | 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)))) |
| | 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)) |
| | 739 | (list 'calcFunc-sin a)))))))) |
| | 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))) |
| | 753 | m))) |
| | 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))) |
| | 791 | (t nil)))))) |
| | 792 | |
| | 793 | (math-defsimplify calcFunc-tan |
| | 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))))) |
| | 798 | (and (eq calc-angle-mode 'rad) |
| | 799 | (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi)))) |
| | 800 | (and n |
| | 801 | (math-known-tan (car n) (nth 1 n) 120)))) |
| | 802 | (and (eq calc-angle-mode 'deg) |
| | 803 | (let ((n (math-integer-plus (nth 1 math-simplify-expr)))) |
| | 804 | (and n |
| | 805 | (math-known-tan (car n) (nth 1 n) '(frac 2 3))))) |
| | 806 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin) |
| | 807 | (math-div (nth 1 (nth 1 math-simplify-expr)) |
| | 808 | (list 'calcFunc-sqrt |
| | 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) |
| | 811 | (math-div (list 'calcFunc-sqrt |
| | 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)))) |
| | 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))) |
| | 819 | (math-div (list 'calcFunc-sin (nth 1 math-simplify-expr)) |
| | 820 | (list 'calcFunc-cos (nth 1 math-simplify-expr)))))))) |
| | 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)))) |
| | 852 | (t nil)))))) |
| | 853 | |
| | 854 | (math-defsimplify calcFunc-sinh |
| | 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) |
| | 860 | math-living-dangerously |
| | 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) |
| | 864 | math-living-dangerously |
| | 865 | (math-div (nth 1 (nth 1 math-simplify-expr)) |
| | 866 | (list 'calcFunc-sqrt |
| | 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))) |
| | 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)) |
| | 876 | (list 'calcFunc-sinh a))))))))) |
| | 877 | |
| | 878 | (math-defsimplify calcFunc-cosh |
| | 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) |
| | 884 | math-living-dangerously |
| | 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) |
| | 888 | math-living-dangerously |
| | 889 | (math-div 1 |
| | 890 | (list 'calcFunc-sqrt |
| | 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))) |
| | 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)) |
| | 900 | (list 'calcFunc-sinh a))))))))) |
| | 901 | |
| | 902 | (math-defsimplify calcFunc-tanh |
| | 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) |
| | 908 | math-living-dangerously |
| | 909 | (math-div (nth 1 (nth 1 math-simplify-expr)) |
| | 910 | (list 'calcFunc-sqrt |
| | 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) |
| | 913 | math-living-dangerously |
| | 914 | (math-div (list 'calcFunc-sqrt |
| | 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))) |
| | 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))) |
| | 922 | (math-div (list 'calcFunc-sinh (nth 1 math-simplify-expr)) |
| | 923 | (list 'calcFunc-cosh (nth 1 math-simplify-expr)))))))) |
| | 924 | |
| | 925 | (math-defsimplify calcFunc-arcsin |
| | 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) |
| | 929 | (math-quarter-circle t)) |
| | 930 | (and (equal (nth 1 math-simplify-expr) '(frac 1 2)) |
| | 931 | (math-div (math-half-circle t) 6)) |
| | 932 | (and math-living-dangerously |
| | 933 | (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sin) |
| | 934 | (nth 1 (nth 1 math-simplify-expr))) |
| | 935 | (and math-living-dangerously |
| | 936 | (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cos) |
| | 937 | (math-sub (math-quarter-circle t) |
| | 938 | (nth 1 (nth 1 math-simplify-expr)))))) |
| | 939 | |
| | 940 | (math-defsimplify calcFunc-arccos |
| | 941 | (or (and (eq (nth 1 math-simplify-expr) 0) |
| | 942 | (math-quarter-circle t)) |
| | 943 | (and (eq (nth 1 math-simplify-expr) -1) |
| | 944 | (math-half-circle t)) |
| | 945 | (and (equal (nth 1 math-simplify-expr) '(frac 1 2)) |
| | 946 | (math-div (math-half-circle t) 3)) |
| | 947 | (and (equal (nth 1 math-simplify-expr) '(frac -1 2)) |
| | 948 | (math-div (math-mul (math-half-circle t) 2) 3)) |
| | 949 | (and math-living-dangerously |
| | 950 | (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cos) |
| | 951 | (nth 1 (nth 1 math-simplify-expr))) |
| | 952 | (and math-living-dangerously |
| | 953 | (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sin) |
| | 954 | (math-sub (math-quarter-circle t) |
| | 955 | (nth 1 (nth 1 math-simplify-expr)))))) |
| | 956 | |
| | 957 | (math-defsimplify calcFunc-arctan |
| | 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) |
| | 961 | (math-div (math-half-circle t) 4)) |
| | 962 | (and math-living-dangerously |
| | 963 | (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-tan) |
| | 964 | (nth 1 (nth 1 math-simplify-expr))))) |
| | 965 | |
| | 966 | (math-defsimplify calcFunc-arcsinh |
| | 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) |
| | 970 | (or math-living-dangerously |
| | 971 | (math-known-realp (nth 1 (nth 1 math-simplify-expr)))) |
| | 972 | (nth 1 (nth 1 math-simplify-expr))))) |
| | 973 | |
| | 974 | (math-defsimplify calcFunc-arccosh |
| | 975 | (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cosh) |
| | 976 | (or math-living-dangerously |
| | 977 | (math-known-realp (nth 1 (nth 1 math-simplify-expr)))) |
| | 978 | (nth 1 (nth 1 math-simplify-expr)))) |
| | 979 | |
| | 980 | (math-defsimplify calcFunc-arctanh |
| | 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) |
| | 984 | (or math-living-dangerously |
| | 985 | (math-known-realp (nth 1 (nth 1 math-simplify-expr)))) |
| | 986 | (nth 1 (nth 1 math-simplify-expr))))) |
| | 987 | |
| | 988 | (math-defsimplify calcFunc-sqrt |
| | 989 | (math-simplify-sqrt)) |
| | 990 | |
| | 991 | (defun math-simplify-sqrt () |
| | 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))))) |
| | 1000 | (and fac (not (eq fac 1)) |
| | 1001 | (math-mul (math-normalize (list 'calcFunc-sqrt fac)) |
| | 1002 | (math-normalize |
| | 1003 | (list 'calcFunc-sqrt |
| | 1004 | (math-cancel-common-factor |
| | 1005 | (nth 1 math-simplify-expr) fac)))))) |
| | 1006 | (and math-living-dangerously |
| | 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)))) |
| | 1012 | 'calcFunc-sin) |
| | 1013 | (list 'calcFunc-cos |
| | 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)))) |
| | 1016 | 'calcFunc-cos) |
| | 1017 | (list 'calcFunc-sin |
| | 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)))) |
| | 1025 | 'calcFunc-cosh) |
| | 1026 | (list 'calcFunc-sinh |
| | 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)))) |
| | 1031 | (and (or (and (math-equal-int a 1) |
| | 1032 | (setq a b b (nth 1 (nth 1 math-simplify-expr)))) |
| | 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))))))))) |
| | 1041 | (and (eq (car-safe (nth 1 math-simplify-expr)) '^) |
| | 1042 | (list '^ |
| | 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))) |
| | 1053 | (let ((f (calcFunc-factors (calcFunc-expand |
| | 1054 | (nth 1 math-simplify-expr))))) |
| | 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 |
| | 1074 | (math-mul sums rest)))))))))))) |
| | 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)))) |
| | 1087 | fac))) |
| | 1088 | |
| | 1089 | (math-defsimplify calcFunc-exp |
| | 1090 | (math-simplify-exp (nth 1 math-simplify-expr))) |
| | 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)) |
| | 1118 | (list '+ c (list '* s '(var i var-i)))))))) |
| | 1119 | |
| | 1120 | (math-defsimplify calcFunc-ln |
| | 1121 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-exp) |
| | 1122 | (or math-living-dangerously |
| | 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)) |
| | 1127 | (or math-living-dangerously |
| | 1128 | (math-known-realp (nth 2 (nth 1 math-simplify-expr)))) |
| | 1129 | (nth 2 (nth 1 math-simplify-expr))) |
| | 1130 | (and calc-symbolic-mode |
| | 1131 | (math-known-negp (nth 1 math-simplify-expr)) |
| | 1132 | (math-add (list 'calcFunc-ln (math-neg (nth 1 math-simplify-expr))) |
| | 1133 | '(* (var pi var-pi) (var i var-i)))) |
| | 1134 | (and calc-symbolic-mode |
| | 1135 | (math-known-imagp (nth 1 math-simplify-expr)) |
| | 1136 | (let* ((ip (calcFunc-im (nth 1 math-simplify-expr))) |
| | 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)) |
| | 1143 | '(/ (* (var pi var-pi) (var i var-i)) 2)))))))) |
| | 1144 | |
| | 1145 | (math-defsimplify ^ |
| | 1146 | (math-simplify-pow)) |
| | 1147 | |
| | 1148 | (defun math-simplify-pow () |
| | 1149 | (or (and math-living-dangerously |
| | 1150 | (or (and (eq (car-safe (nth 1 math-simplify-expr)) '^) |
| | 1151 | (list '^ |
| | 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) |
| | 1156 | (list '^ |
| | 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) |
| | 1171 | (not math-integrating) |
| | 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)) |
| | 1175 | (math-imaginary-i) |
| | 1176 | (math-num-integerp (nth 2 math-simplify-expr)) |
| | 1177 | (let ((x (math-mod (math-trunc (nth 2 math-simplify-expr)) 4))) |
| | 1178 | (cond ((eq x 0) 1) |
| | 1179 | ((eq x 1) (nth 1 math-simplify-expr)) |
| | 1180 | ((eq x 2) -1) |
| | 1181 | ((eq x 3) (math-neg (nth 1 math-simplify-expr)))))) |
| | 1182 | (and math-integrating |
| | 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)) |
| | 1188 | (math-sub 1 |
| | 1189 | (math-sqr |
| | 1190 | (list 'calcFunc-sin |
| | 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)) |
| | 1195 | (math-add 1 |
| | 1196 | (math-sqr |
| | 1197 | (list 'calcFunc-sinh |
| | 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)))) |
| | 1205 | (and (not (Math-zerop flr)) |
| | 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) |
| | 1210 | (let ((temp (math-simplify-sqrt))) |
| | 1211 | (and temp |
| | 1212 | (list '^ temp (math-mul (nth 2 math-simplify-expr) 2))))))) |
| | 1213 | |
| | 1214 | (math-defsimplify calcFunc-log10 |
| | 1215 | (and (eq (car-safe (nth 1 math-simplify-expr)) '^) |
| | 1216 | (math-equal-int (nth 1 (nth 1 math-simplify-expr)) 10) |
| | 1217 | (or math-living-dangerously |
| | 1218 | (math-known-realp (nth 2 (nth 1 math-simplify-expr)))) |
| | 1219 | (nth 2 (nth 1 math-simplify-expr)))) |
| | 1220 | |
| | 1221 | |
| | 1222 | (math-defsimplify calcFunc-erf |
| | 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))))))) |
| | 1228 | |
| | 1229 | (math-defsimplify calcFunc-erfc |
| | 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))))))) |
| | 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)) |
| | 1243 | (and always (list expr 0)))) |
| | 1244 | |
| | 1245 | (defun math-multiple-of (expr term) |
| | 1246 | (let ((p (math-linear-in expr term))) |
| | 1247 | (and p |
| | 1248 | (math-zerop (car p)) |
| | 1249 | (nth 1 p)))) |
| | 1250 | |
| | 1251 | ; not perfect, but it'll do |
| | 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))))) |
| | 1263 | (t nil))) |
| | 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 |
| | 1286 | (cons 0 coef))))) |
| | 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)) |
| | 1312 | (and always |
| | 1313 | (list 1 expr))))) |
| | 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")) |
| | 1322 | (cons 'vec res)))) |
| | 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")) |
| | 1331 | (cons 'vec res)))) |
| | 1332 | |
| | 1333 | (defun calcFunc-islin (expr &optional var) |
| | 1334 | (if (and (Math-objvecp expr) (not var)) |
| | 1335 | 0 |
| | 1336 | (calcFunc-lin expr var) |
| | 1337 | 1)) |
| | 1338 | |
| | 1339 | (defun calcFunc-islinnt (expr &optional var) |
| | 1340 | (if (Math-objvecp expr) |
| | 1341 | 0 |
| | 1342 | (calcFunc-linnt expr var) |
| | 1343 | 1)) |
| | 1344 | |
| | 1345 | |
| | 1346 | |
| | 1347 | |
| | 1348 | ;;; Simple operations on expressions. |
| | 1349 | |
| | 1350 | ;;; Return number of occurrences of thing in expr, or nil if none. |
| | 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) |
| | 1360 | num))))) |
| | 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)))) |
| | 1368 | expr))) |
| | 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))))) |
| | 1377 | thing)) |
| | 1378 | |
| | 1379 | ;;; Substitute all occurrences of old for new in expr (non-destructive). |
| | 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) |
| | 1387 | (math-expr-subst-rec expr)) |
| | 1388 | |
| | 1389 | (defalias 'calcFunc-subst 'math-expr-subst) |
| | 1390 | |
| | 1391 | (defun math-expr-subst-rec (expr) |
| | 1392 | (cond ((equal expr math-expr-subst-old) math-expr-subst-new) |
| | 1393 | ((Math-primp expr) expr) |
| | 1394 | ((memq (car expr) '(calcFunc-deriv |
| | 1395 | calcFunc-tderiv)) |
| | 1396 | (if (= (length expr) 2) |
| | 1397 | (if (equal (nth 1 expr) math-expr-subst-old) |
| | 1398 | (append expr (list math-expr-subst-new)) |
| | 1399 | expr) |
| | 1400 | (list (car expr) (nth 1 expr) |
| | 1401 | (math-expr-subst-rec (nth 2 expr))))) |
| | 1402 | (t |
| | 1403 | (cons (car expr) |
| | 1404 | (mapcar 'math-expr-subst-rec (cdr expr)))))) |
| | 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))))) |
| | 1413 | w))) |
| | 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))))) |
| | 1421 | (1+ h)))) |
| | 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)) |
| | 1433 | expr))) |
| | 1434 | |
| | 1435 | ;;; If expr is of the form "a + bx + cx^2 + ...", return the list (a b c ...), |
| | 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)) |
| | 1447 | math-poly-base-variable)) |
| | 1448 | (poly (math-is-poly-rec expr math-poly-neg-powers))) |
| | 1449 | (and (or (null math-is-poly-degree) |
| | 1450 | (<= (length poly) (1+ math-is-poly-degree))) |
| | 1451 | poly))) |
| | 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 |
| | 1498 | (or (null math-is-poly-degree) |
| | 1499 | (<= (* (1- (length p1)) n) math-is-poly-degree)) |
| | 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 |
| | 1527 | (or (null math-is-poly-degree) |
| | 1528 | (<= (- (+ (length p1) (length p2)) 2) |
| | 1529 | math-is-poly-degree)) |
| | 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)) |
| | 1549 | math-is-poly-loose) |
| | 1550 | (not (eq (car expr) 'vec)) |
| | 1551 | (list expr))))) |
| | 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) |
| | 1577 | (t 0))) |
| | 1578 | |
| | 1579 | (defun math-poly-depends (expr var) |
| | 1580 | (if math-poly-base-variable |
| | 1581 | (math-expr-contains expr math-poly-base-variable) |
| | 1582 | (math-expr-depends expr var))) |
| | 1583 | |
| | 1584 | ;;; Find the variable (or sub-expression) which is the base of polynomial expr. |
| | 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 | |
| | 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) |
| | 1595 | (or math-poly-base-pred |
| | 1596 | (setq math-poly-base-pred (function (lambda (base) (math-polynomial-p |
| | 1597 | math-poly-base-top-expr base))))) |
| | 1598 | (or (let ((math-poly-base-const-ok nil)) |
| | 1599 | (math-polynomial-base-rec math-poly-base-top-expr)) |
| | 1600 | (let ((math-poly-base-const-ok t)) |
| | 1601 | (math-polynomial-base-rec math-poly-base-top-expr)))) |
| | 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))) |
| | 1614 | (and (or math-poly-base-const-ok (math-expr-contains-vars mpb-expr)) |
| | 1615 | (funcall math-poly-base-pred mpb-expr) |
| | 1616 | mpb-expr)))) |
| | 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))))) |
| | 1625 | expr)))) |
| | 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) |
| | 1637 | p))) |
| | 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)) |
| | 1645 | (math-poly-mix (cdr a) ac (cdr b) bc)))) |
| | 1646 | |
| | 1647 | (defun math-poly-zerop (a) |
| | 1648 | (or (null a) |
| | 1649 | (and (null (cdr a)) (Math-zerop (car a))))) |
| | 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) |
| | 1655 | (math-poly-mul (cdr a) (cons 0 b)) 1))) |
| | 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)) |
| | 1681 | 0)) |
| | 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))))))) |
| | 1693 | f)) |
| | 1694 | |
| | 1695 | ;;; arch-tag: 52e7dcdf-9688-464d-a02b-4bbe789348d0 |
| | 1696 | ;;; calc-alg.el ends here |
HCoop / bpt / emacs.git / blame_incremental