1;;; -*- Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*- ;;;; 2;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 3;;; The data in this file contains enhancments. ;;;;; 4;;; ;;;;; 5;;; Copyright (c) 1984,1987 by William Schelter,University of Texas ;;;;; 6;;; All rights reserved ;;;;; 7;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 8;;; (c) Copyright 1982 Massachusetts Institute of Technology ;;; 9;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 10 11(in-package :maxima) 12 13(macsyma-module nisimp) 14 15;;;programs for the LET LETSIMP LETRULES and REMLET commands 16;;;these programs use the names LETSIMPTREE and LETRULES on the 17;;;property list of atoms 18;;;except for the top level programs all program names have the prefix NIS 19 20(declare-top (special nistree nisrules nisflag $ratexpand varlist $ratfac)) 21 22(defmvar $letvarsimp nil) 23 24(defmvar $letrat nil) 25 26(defmvar $default_let_rule_package '$default_let_rule_package 27 "The name of the default rule package used by `let' and `letsimp'") 28 29(putprop '$default_let_rule_package 'let-rule-setter 'assign) 30 31(defmvar $current_let_rule_package '$default_let_rule_package 32 "The name of the current rule package used by `let' and `letsimp'") 33 34(putprop '$current_let_rule_package 'let-rule-setter 'assign) 35 36(defmvar $let_rule_packages '((mlist) $default_let_rule_package) 37 "The names of the various let rule simplification packages") 38 39(putprop '$let_rule_packages 'let-rule-setter 'assign) 40 41(setq nisrules nil nistree nil) 42 43(defun let-rule-setter (var val) 44 (cond ((eq var '$default_let_rule_package) 45 (merror (intl:gettext "assignment: cannot assign to default_let_rule_package."))) 46 ((and (eq var '$current_let_rule_package) 47 (not (memalike val (cdr $let_rule_packages)))) 48 (merror (intl:gettext "assignment: ~M is not a rule package.") val)) 49 ((eq var '$let_rule_packages) 50 (merror (intl:gettext "assignment: cannot assign to let_rule_packages.~%assignment: call 'let' to create let rule packages."))))) 51 52(defmspec $let (l) (setq l (cdr l)) 53 (if (null (cdr l)) (wna-err '$let)) 54 ;;LET([PATTERN,REPL,PRED,ARG1,...,ARGN],NAME) 55 (prog (pattern pat replacement treename text $ratfac) 56 ;;LET(PATTERN,REPL,PRED,ARG1,...,ARGN) 57 (cond ((atom (car l)) 58 (setq treename $current_let_rule_package)) 59 ((eq 'mlist (caaar l)) 60 (setq treename (cadr l)) 61 (if (not (symbolp treename)) 62 (improper-arg-err treename '$let)) 63 (setq l (cdar l))) 64 (t (setq treename $current_let_rule_package))) 65 (let ((nistree (mget treename 'letsimptree)) 66 (nisrules (mget treename 'letrules))) 67 (setq pat (strip-lineinfo (meval (car l)))) 68 (setq replacement (cdr l)) 69 (setq pattern (cond ((atom pat) (list pat)) 70 ((eq (caar pat) 'mtimes) 71 (cdr pat)) 72 (t (list pat)))) 73 (setq nistree (nislet nistree pattern replacement)) 74 (cond (treename (mputprop treename 75 nistree 76 'letsimptree) 77 (add2lnc treename $let_rule_packages))) 78 (nonsymchk (caddr l) '$let) 79 (setq text 80 (append (list '(mtext) pat '| --> | ) 81 (cond ((cddr l) 82 (list (cadr l) 83 '#.(intern (format nil " ~A " 'where)) 84 (cons (list (caddr l)) 85 (cdddr l)))) 86 (t replacement)))) 87 (setq nisrules (append (list text) nisrules)) 88 (cond (treename (mputprop treename 89 nisrules 90 'letrules))) 91 (return text)))) 92 93(defun nislet (tree list function) 94 (prog (permlist) 95 (setq permlist (nispermutations list)) 96 step (cond ((eq nil permlist) (return tree))) 97 (setq tree (nistreebuilder tree (car permlist) function)) 98 (setq permlist (cdr permlist)) 99 (go step))) 100 101(defun nispermutations (llist) 102 (cond 103 ((null (cdr llist)) (list llist)) 104 (t 105 (prog (permlist a) 106 step (setq permlist 107 (append 108 (nisaddon (car llist) 109 (nispermutations (append a (cdr llist)))) 110 permlist)) 111 (if (null (cdr llist)) (return permlist)) 112 (push (car llist) a) 113 (setq llist (cdr llist)) 114 (go step))))) 115 116(defun nisaddon (x llist) 117 (if llist (cons (cons x (car llist)) (nisaddon x (cdr llist))))) 118 119(defun nistreebuilder (tree perm function) 120 (cond ((null perm) (cons (list function) tree)) 121 ((null tree) 122 (list (cons (car perm) 123 (nistreebuilder nil (cdr perm) function)))) 124 ((equal (car perm) (caar tree)) 125 (nisswcar tree 126 (nisswcdr (car tree) 127 (nistreebuilder (cdar tree) 128 (cdr perm) 129 function)))) 130 (t (nisswcdr tree 131 (nistreebuilder (cdr tree) 132 perm 133 function))))) 134 135(defun nisswcar (x y) 136 (cons y (cdr x))) 137 138(defun nisswcdr (x y) 139 (cons (car x) y)) 140 141(defmspec $remlet (x) 142 (setq x (cdr x)) 143 ;; REMLET(PROD,NAME) REMLET(PROD) REMLET() REMLET(FALSE,NAME) 144 (prog (pattern text treename) 145 (cond ((cddr x) (wna-err '$remlet)) 146 ((null (cdr x)) (setq treename $current_let_rule_package)) 147 (t (setq treename (cadr x)) 148 (if (not (symbolp treename)) 149 (improper-arg-err treename '$remlet)))) 150 (setq pattern (strip-lineinfo (meval (car x)))) 151 (when (or (not pattern) (eq '$all pattern)) 152 (setq nisrules nil nistree nil) 153 (unless (eq treename '$default_let_rule_package) 154 (setq $let_rule_packages (delete treename $let_rule_packages :count 1 :test #'eq))) 155 (go a)) 156 (setq nistree (mget treename 'letsimptree)) 157 (if (setq text (nisremlet pattern)) (return text)) 158 (if nistree 159 (setq nisrules 160 (nistreelister (mget treename 'letrules) pattern)) 161 (setq nisrules nil)) 162 a (mputprop treename nistree 'letsimptree) 163 (mputprop treename nisrules 'letrules) 164 (return '$done))) 165 166(defun nistreelister (llist pattern) 167 (prog (x) 168 a (if (alike1 pattern (cadar llist)) (return (append x (cdr llist)))) 169 (setq x (append x (list (car llist))) llist (cdr llist)) 170 (go a))) 171 172(defun nisremlet (pat) 173 (prog (llist permlist x) 174 (setq llist (if (mtimesp pat) (cdr pat) (ncons pat))) 175 (setq nisflag t x nistree) 176 (setq permlist (nispermutations llist)) 177 step (when (null permlist) (setq nistree x) (return nil)) 178 (setq x (nistreetrimmer (car permlist) x)) 179 (if (null nisflag) (merror (intl:gettext "remlet: no rule found: ~M") pat)) 180 (setq permlist (cdr permlist)) 181 (go step))) 182 183(defun nistreetrimmer (perm tree) 184 (cond ((null perm) 185 (cond ((null tree) (setq nisflag nil)) 186 ((null (cdar tree)) 187 (setq nisflag (caar tree)) (cdr tree)) 188 (t (nisswcdr tree (nistreetrimmer nil (cdr tree)))))) 189 ((null tree) (setq nisflag nil)) 190 ((equal (car perm) (caar tree)) 191 (prog (x) 192 (setq x (nistreetrimmer (cdr perm) (cdar tree))) 193 (if (null x) (return (cdr tree))) 194 (return (nisswcar tree (nisswcdr (car tree) x))))) 195 (t (nisswcdr tree (nistreetrimmer perm (cdr tree)))))) 196 197(defmspec $letrules (name) 198 (setq name (cdr name)) ;LETRULES(NAME) 199 (let ((treename (if name (car name) $current_let_rule_package))) 200 (if (not (symbolp treename)) (improper-arg-err treename '$letrules)) 201 (setq nistree (mget treename 'letsimptree) 202 nisrules (mget treename 'letrules)) 203 (apply #'$disp nisrules))) 204 205(defmspec $letsimp (form) ;letsimp(expr,tree1,...,treen) 206 (setq form (cdr form)) 207 (let* ((expr (strip-lineinfo (meval (pop form)))) 208 (sw ($ratp expr)) 209 $ratfac) 210 (progv (unless sw '(varlist genvar)) 211 (unless sw (list varlist genvar)) 212 (when (and sw (member 'trunc (cdar expr) :test #'eq)) 213 (setq expr ($taytorat expr))) 214 (dolist (rulepackage (or form (list $current_let_rule_package)) 215 (if sw (ratf expr) expr)) 216 (unless (symbolp rulepackage) 217 (improper-arg-err rulepackage '$letsimp)) 218 (when (setq nistree (mget rulepackage 'letsimptree)) 219 ;; Whereas nisletsimp returns an expression in general 220 ;; representation, the original expr might be in CRE form. 221 ;; Regardless, we use ratf to make sure varlist and genvar 222 ;; know of expr's kernels. 223 (setq expr (nisletsimp (if (atom expr) 224 expr 225 (ratf expr))))))))) 226 227(defun nisletsimp (e) 228 (let (x) 229 (cond ((mnump e) e) 230 ((or (and (atom e) (setq x (ncons e))) 231 (and (eq (caar e) 'mtimes) (setq x (cdr e)))) 232 (setq x (nisnewlist x)) 233 (if x (nisletsimp ($ratexpand (cons '(mtimes) x))) e)) 234 ((member (caar e) '(mplus mequal mlist $matrix) :test #'eq) 235 (cons (if (eq (caar e) 'mplus) '(mplus) (car e)) 236 (mapcar #'nisletsimp (cdr e)))) 237 ((or (eq (caar e) 'mrat) 238 (and (eq (caar e) 'mquotient) (setq e (ratf e)))) 239 (nisletsimprat e)) 240 (t ;; A kernel (= product of 1 element) 241 (setq x (nisnewlist (ncons e))) 242 (if x (nisletsimp ($ratexpand (cons '(mtimes) x))) e))))) 243 244(defun nisletsimprat (e) 245 (let ((num (cadr e)) (denom (cddr e)) $ratexpand) 246 (if $letvarsimp (setq varlist (mapcar #'nisletsimp varlist))) 247 (let (($ratexpand t)) 248 (setq num (nisletsimp (pdis num)) denom (nisletsimp (pdis denom)))) 249 (setq e (list '(mquotient) num denom)) 250 (if $letrat (nisletsimp ($ratexpand e)) e))) 251 252(defun nisnewlist (llist) 253 (let ((x (nissearch llist nistree nil))) (if x (nisreplace llist x)))) 254 255(defun nissearch (x y z) 256 (cond ((null y) nil) 257 ((nisinnernull y) (nisfix (nisinnernull y) z)) 258 ((null x) nil) 259 (t (prog (xx yy path bind) 260 (setq yy y) 261 a (setq xx x) 262 b (cond ((and (setq bind (nismatch (car xx) 263 (caar yy) 264 z)) 265 (setq path 266 (nissearch (cdr xx) 267 (cdar yy) 268 (cdr bind)))) 269 (return (cons (car bind) path)))) 270 (setq xx (cdr xx)) 271 (cond (xx (go b))) 272 (setq yy (cdr yy)) 273 (cond ((null yy) (return nil))) 274 (go a))))) 275 276(defun nisinnernull (x) 277 (cond ((null x) nil) 278 ((null (cdar x)) (caar x)) 279 (t (nisinnernull (cdr x))))) 280 281(defun nisfix (funperd argasslist) 282 (prog (function args bindings perd flag) 283 (if (not argasslist) (return (car funperd))) 284 (setq argasslist (nisnumberpicker argasslist)) 285 (setq args (maplist 'caar argasslist)) 286 (setq bindings (maplist 'cdar argasslist)) 287 (mbinding (args bindings) 288 (setq function (car funperd)) 289 (if (setq perd (cdr funperd)) 290 (if (not (meval perd)) (setq flag t))) 291 (if (null flag) (setq function (meval function)))) 292 (return (if flag nil (list function))))) 293 294(defun nisnumberpicker (x) 295 (cond ((null x) nil) 296 ((or (not (symbolp (caar x))) 297 (kindp (caar x) '$constant)) 298 ;; Skip over numbers and constants 299 (nisnumberpicker (cdr x))) 300 (t (nisswcdr x (nisnumberpicker (cdr x)))))) 301 302(defun nismatch (a b c) 303 (prog (x y newexpt) 304 (setq x (nisextract a)) 305 (setq y (nisextract b)) 306 (cond 307 ((cadr y) 308 (cond ((and (equal (car x) (car y)) 309 (setq newexpt (nisexpocheck (cddr x) 310 (cddr y) 311 c)) 312 (setq c (nisargschecker (cadr x) 313 (cadr y) 314 c))) 315 (cond ((equal '(rat) (car newexpt)) 316 (return (cons (cons a (nisbuild x newexpt)) 317 c))) 318 (t (return (cons (cons a '(dummy 0 (0 0))) 319 newexpt))))) 320 (t (return nil))))) 321 (cond ((and (setq c (nisargmatch (niskernel a) (car y) c)) 322 (setq newexpt (nisexpocheck (cddr x) 323 (cddr y) 324 c))) 325 (cond ((equal '(rat) (car newexpt)) 326 (return (cons (cons a (nisbuild x newexpt)) 327 c))) 328 (t (return (cons (cons a '(dummy 0 (0 0))) 329 newexpt)))))) 330 (return nil))) 331 332(defun niskernel (a) 333 (if (mexptp a) (cadr a) a)) 334 335(defun nisextract (x) 336 (cond ((or (atom x) (eq (caar x) 'rat)) 337 (cons x (cons nil 1))) 338 ((eq 'mexpt (caar x)) 339 (cond ((atom (cadr x)) 340 (cons (cadr x) (cons nil (caddr x)))) 341 (t (cons (if (member 'array (cdaadr x) :test #'eq) 342 (list (caaadr x) 'array) 343 (caaadr x)) 344 (cons (cdadr x) (caddr x)))))) 345 (t (cons (if (member 'array (cdar x) :test #'eq) 346 (list (caar x) 'array) 347 (caar x)) 348 (cons (cdr x) 1))))) 349 350(defun nisargschecker (listargs treeargs argasslist) 351 (prog (c) 352 (cond ((and listargs treeargs) (go check)) 353 ((or listargs treeargs) (return nil)) 354 (t (return argasslist))) 355 check(setq c (nisargmatch (car listargs) 356 (car treeargs) 357 argasslist)) 358 (cond (c (return (nisargschecker (cdr listargs) 359 (cdr treeargs) 360 c))) 361 (t (return nil))))) 362 363(defun nisexpocheck (listpower treepower argasslist) 364 (prog (p q r s a b xx) 365 (cond ((atom treepower) 366 (cond ((numberp treepower) 367 (prog2 (setq r treepower s 1) (go math))) 368 (t (return (nisargmatch listpower 369 treepower 370 argasslist)))))) 371 (setq r (cadr treepower) s (caddr treepower)) 372 (if (not (numberp s)) (return nil)) 373 math (cond ((numberp listpower) (setq p listpower q 1)) 374 ((atom listpower) (return nil)) 375 ((eq 'rat (caar listpower)) 376 (setq p (cadr listpower) q (caddr listpower))) 377 (t (return nil))) 378 (setq xx (* (* q s) (- (* p s) (* q r)))) 379 (setq a (< (* r s) 0)) 380 (setq b (< xx 0)) 381 (cond ((or (not (or a b)) (and a (or b (equal 0 xx)))) 382 (return (list '(rat) xx (* q s))))) 383 (return nil))) 384 385(defun nisargmatch (x y c) 386 (prog (w) 387 (setq w c) 388 up (if (null w) (go down)) 389 (cond ((eq (caar w) y) 390 (cond ((alike1 (cdar w) x) (return c)) 391 (t (return nil))))) 392 (setq w (cdr w)) 393 (go up) 394 down (setq w (mget y 'matchdeclare)) 395 (cond ((null w) (if (equal x y) (go out) (return nil))) 396 ((member (car w) '($true t) :test #'eq) (go out)) 397 ((and (atom (car w)) 398 (meval (cons (ncons (car w)) 399 (append (cdr w) (list x))))) 400 (go out)) 401 ((and (not (atom (car w))) 402 (not (atom (caar w))) 403 (atom (caaar w)) 404 ; If we arrive here, (CAR W) is a Maxima expression like ((FOO) ...) 405 ; If (CAR W) is a Maxima lambda expression, evaluate it via MFUNCALL. 406 ; Otherwise, append X and call MEVAL. 407 ; Note that "otherwise" includes Maxima lambda expressions with missing arguments; 408 ; in that case the expression is ((MQAPPLY) ((LAMBDA) ...)) and MEVAL is the way to go. 409 (if (eq (caaar w) 'lambda) 410 (mfuncall (car w) x) 411 (meval (append (car w) (list x))))) 412 (go out)) 413 (t (return nil))) 414 out (return (cons (cons y x) c)))) 415 416(defun nisbuild (x newexpt) 417 (list '(mexpt) 418 (if (cadr x) 419 (cons (if (symbolp (car x)) (ncons (car x)) (car x)) 420 (cadr x)) 421 (car x)) 422 newexpt)) 423 424(defun nisreplace (llist asslist) 425 (cond ((eq (cdr asslist) nil) (cons (car asslist) llist)) 426 ((equal (car llist) (caar asslist)) 427 (cond ((equal 0 (cadar (cdddar asslist))) 428 (nisreplace (cdr llist) (cdr asslist))) 429 (t (cons (cdar asslist) 430 (nisreplace (cdr llist) (cdr asslist)))))) 431 (t (cons (car llist) (nisreplace (cdr llist) asslist))))) 432