| [98] | 1 | ;;; -*- Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*-
|
|---|
| 2 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 3 | ;;;
|
|---|
| 4 | ;;; Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>
|
|---|
| 5 | ;;;
|
|---|
| 6 | ;;; This program is free software; you can redistribute it and/or modify
|
|---|
| 7 | ;;; it under the terms of the GNU General Public License as published by
|
|---|
| 8 | ;;; the Free Software Foundation; either version 2 of the License, or
|
|---|
| 9 | ;;; (at your option) any later version.
|
|---|
| 10 | ;;;
|
|---|
| 11 | ;;; This program is distributed in the hope that it will be useful,
|
|---|
| 12 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|---|
| 13 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|---|
| 14 | ;;; GNU General Public License for more details.
|
|---|
| 15 | ;;;
|
|---|
| 16 | ;;; You should have received a copy of the GNU General Public License
|
|---|
| 17 | ;;; along with this program; if not, write to the Free Software
|
|---|
| 18 | ;;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
|
|---|
| 19 | ;;;
|
|---|
| 20 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 21 |
|
|---|
| [133] | 22 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 23 | ;;
|
|---|
| 24 | ;; Load this file into Maxima to bootstrap the Grobner package
|
|---|
| 25 | ;;
|
|---|
| 26 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 27 |
|
|---|
| [98] | 28 | (in-package :maxima)
|
|---|
| 29 |
|
|---|
| 30 | (macsyma-module cgb-maxima)
|
|---|
| 31 |
|
|---|
| 32 | (eval-when
|
|---|
| 33 | #+gcl (load eval)
|
|---|
| 34 | #-gcl (:load-toplevel :execute)
|
|---|
| 35 | (format t "~&Loading maxima-grobner ~a ~a~%"
|
|---|
| 36 | "$Revision: 2.0 $" "$Date: 2015/06/02 0:34:17 $"))
|
|---|
| 37 |
|
|---|
| 38 | ;;FUNCTS is loaded because it contains the definition of LCM
|
|---|
| 39 | ($load "functs")
|
|---|
| [152] | 40 |
|
|---|
| [157] | 41 | #+gcl (unless (macro-function 'with-compilation-unit)
|
|---|
| 42 | (defmacro with-compilation-unit (a &rest b) `(progn ,@b)))
|
|---|
| [98] | 43 |
|
|---|
| [157] | 44 | (with-compilation-unit nil
|
|---|
| [158] | 45 | ($load "grobner")
|
|---|
| 46 | ($load "monomial")
|
|---|
| 47 | ($load "term")
|
|---|
| 48 | ($load "termlist")
|
|---|
| 49 | ($load "polynomial")
|
|---|
| 50 | ($load "order")
|
|---|
| 51 | ($load "order-mk")
|
|---|
| 52 | ($load "priority-queue")
|
|---|
| 53 | ($load "pair-queue")
|
|---|
| 54 | ($load "utils")
|
|---|
| 55 | ($load "division")
|
|---|
| 56 | ($load "criterion")
|
|---|
| 57 | ($load "buchberger")
|
|---|
| 58 | ($load "gebauer-moeller")
|
|---|
| 59 | ($load "gb-postprocessing")
|
|---|
| 60 | ($load "ideal"))
|
|---|
| [157] | 61 |
|
|---|
| [158] | 62 |
|
|---|
| [98] | 63 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 64 | ;;
|
|---|
| 65 | ;; Maxima expression ring
|
|---|
| 66 | ;;
|
|---|
| 67 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 68 |
|
|---|
| 69 | (defparameter *expression-ring*
|
|---|
| 70 | (make-ring
|
|---|
| 71 | ;;(defun coeff-zerop (expr) (meval1 `(($is) (($equal) ,expr 0))))
|
|---|
| 72 | :parse #'(lambda (expr)
|
|---|
| 73 | (when modulus (setf expr ($rat expr)))
|
|---|
| 74 | expr)
|
|---|
| 75 | :unit #'(lambda () (if modulus ($rat 1) 1))
|
|---|
| 76 | :zerop #'(lambda (expr)
|
|---|
| 77 | ;;When is exactly a maxima expression equal to 0?
|
|---|
| 78 | (cond ((numberp expr)
|
|---|
| 79 | (= expr 0))
|
|---|
| 80 | ((atom expr) nil)
|
|---|
| 81 | (t
|
|---|
| 82 | (case (caar expr)
|
|---|
| 83 | (mrat (eql ($ratdisrep expr) 0))
|
|---|
| 84 | (otherwise (eql ($totaldisrep expr) 0))))))
|
|---|
| 85 | :add #'(lambda (x y) (m+ x y))
|
|---|
| 86 | :sub #'(lambda (x y) (m- x y))
|
|---|
| 87 | :uminus #'(lambda (x) (m- x))
|
|---|
| 88 | :mul #'(lambda (x y) (m* x y))
|
|---|
| 89 | ;;(defun coeff-div (x y) (cadr ($divide x y)))
|
|---|
| 90 | :div #'(lambda (x y) (m// x y))
|
|---|
| 91 | :lcm #'(lambda (x y) (meval1 `((|$LCM|) ,x ,y)))
|
|---|
| 92 | :ezgcd #'(lambda (x y) (apply #'values (cdr ($ezgcd ($totaldisrep x) ($totaldisrep y)))))
|
|---|
| 93 | ;; :gcd #'(lambda (x y) (second ($ezgcd x y)))))
|
|---|
| 94 | :gcd #'(lambda (x y) ($gcd x y))))
|
|---|
| 95 |
|
|---|
| [114] | 96 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 97 | ;;
|
|---|
| 98 | ;; Maxima expression parsing
|
|---|
| 99 | ;;
|
|---|
| 100 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 101 |
|
|---|
| 102 | (defun equal-test-p (expr1 expr2)
|
|---|
| 103 | (alike1 expr1 expr2))
|
|---|
| 104 |
|
|---|
| 105 | (defun coerce-maxima-list (expr)
|
|---|
| 106 | "convert a maxima list to lisp list."
|
|---|
| 107 | (cond
|
|---|
| 108 | ((and (consp (car expr)) (eql (caar expr) 'mlist)) (cdr expr))
|
|---|
| 109 | (t expr)))
|
|---|
| 110 |
|
|---|
| 111 | (defun free-of-vars (expr vars) (apply #'$freeof `(,@vars ,expr)))
|
|---|
| 112 |
|
|---|
| 113 | (defun parse-poly (expr vars &aux (vars (coerce-maxima-list vars)))
|
|---|
| 114 | "Convert a maxima polynomial expression EXPR in variables VARS to internal form."
|
|---|
| 115 | (labels ((parse (arg) (parse-poly arg vars))
|
|---|
| 116 | (parse-list (args) (mapcar #'parse args)))
|
|---|
| 117 | (cond
|
|---|
| 118 | ((eql expr 0) (make-poly-zero))
|
|---|
| 119 | ((member expr vars :test #'equal-test-p)
|
|---|
| 120 | (let ((pos (position expr vars :test #'equal-test-p)))
|
|---|
| 121 | (make-variable *maxima-ring* (length vars) pos)))
|
|---|
| 122 | ((free-of-vars expr vars)
|
|---|
| 123 | ;;This means that variable-free CRE and Poisson forms will be converted
|
|---|
| 124 | ;;to coefficients intact
|
|---|
| 125 | (coerce-coeff *maxima-ring* expr vars))
|
|---|
| 126 | (t
|
|---|
| 127 | (case (caar expr)
|
|---|
| 128 | (mplus (reduce #'(lambda (x y) (poly-add *maxima-ring* x y)) (parse-list (cdr expr))))
|
|---|
| 129 | (mminus (poly-uminus *maxima-ring* (parse (cadr expr))))
|
|---|
| 130 | (mtimes
|
|---|
| 131 | (if (endp (cddr expr)) ;unary
|
|---|
| 132 | (parse (cdr expr))
|
|---|
| 133 | (reduce #'(lambda (p q) (poly-mul *maxima-ring* p q)) (parse-list (cdr expr)))))
|
|---|
| 134 | (mexpt
|
|---|
| 135 | (cond
|
|---|
| 136 | ((member (cadr expr) vars :test #'equal-test-p)
|
|---|
| 137 | ;;Special handling of (expt var pow)
|
|---|
| 138 | (let ((pos (position (cadr expr) vars :test #'equal-test-p)))
|
|---|
| 139 | (make-variable *maxima-ring* (length vars) pos (caddr expr))))
|
|---|
| 140 | ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
|
|---|
| 141 | ;; Negative power means division in coefficient ring
|
|---|
| 142 | ;; Non-integer power means non-polynomial coefficient
|
|---|
| 143 | (mtell "~%Warning: Expression ~%~M~%contains power which is not a positive integer. Parsing as coefficient.~%"
|
|---|
| 144 | expr)
|
|---|
| 145 | (coerce-coeff *maxima-ring* expr vars))
|
|---|
| 146 | (t (poly-expt *maxima-ring* (parse (cadr expr)) (caddr expr)))))
|
|---|
| 147 | (mrat (parse ($ratdisrep expr)))
|
|---|
| 148 | (mpois (parse ($outofpois expr)))
|
|---|
| 149 | (otherwise
|
|---|
| 150 | (coerce-coeff *maxima-ring* expr vars)))))))
|
|---|
| 151 |
|
|---|
| 152 | (defun parse-poly-list (expr vars)
|
|---|
| 153 | (case (caar expr)
|
|---|
| 154 | (mlist (mapcar #'(lambda (p) (parse-poly p vars)) (cdr expr)))
|
|---|
| 155 | (t (merror "Expression ~M is not a list of polynomials in variables ~M."
|
|---|
| 156 | expr vars))))
|
|---|
| 157 | (defun parse-poly-list-list (poly-list-list vars)
|
|---|
| 158 | (mapcar #'(lambda (g) (parse-poly-list g vars)) (coerce-maxima-list poly-list-list)))
|
|---|
| 159 |
|
|---|
| 160 |
|
|---|
| [111] | 161 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 162 | ;;
|
|---|
| 163 | ;; Unary and binary operation definition facility
|
|---|
| 164 | ;;
|
|---|
| 165 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| [98] | 166 |
|
|---|
| [111] | 167 | (defmacro define-unop (maxima-name fun-name
|
|---|
| 168 | &optional (documentation nil documentation-supplied-p))
|
|---|
| 169 | "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
|
|---|
| 170 | `(defun ,maxima-name (p vars
|
|---|
| 171 | &aux
|
|---|
| 172 | (vars (coerce-maxima-list vars))
|
|---|
| 173 | (p (parse-poly p vars)))
|
|---|
| 174 | ,@(when documentation-supplied-p (list documentation))
|
|---|
| 175 | (coerce-to-maxima :polynomial (,fun-name *maxima-ring* p) vars)))
|
|---|
| 176 |
|
|---|
| 177 | (defmacro define-binop (maxima-name fun-name
|
|---|
| 178 | &optional (documentation nil documentation-supplied-p))
|
|---|
| 179 | "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
|
|---|
| 180 | `(defmfun ,maxima-name (p q vars
|
|---|
| 181 | &aux
|
|---|
| 182 | (vars (coerce-maxima-list vars))
|
|---|
| 183 | (p (parse-poly p vars))
|
|---|
| 184 | (q (parse-poly q vars)))
|
|---|
| 185 | ,@(when documentation-supplied-p (list documentation))
|
|---|
| 186 | (coerce-to-maxima :polynomial (,fun-name *maxima-ring* p q) vars)))
|
|---|
| 187 |
|
|---|
| 188 |
|
|---|
| [98] | 189 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 190 | ;;
|
|---|
| 191 | ;; Maxima-level interface functions
|
|---|
| 192 | ;;
|
|---|
| 193 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 194 |
|
|---|
| 195 | ;; Auxillary function for removing zero polynomial
|
|---|
| 196 | (defun remzero (plist) (remove #'poly-zerop plist))
|
|---|
| 197 |
|
|---|
| 198 | ;;Simple operators
|
|---|
| 199 |
|
|---|
| 200 | (define-binop $poly_add poly-add
|
|---|
| 201 | "Adds two polynomials P and Q")
|
|---|
| 202 |
|
|---|
| 203 | (define-binop $poly_subtract poly-sub
|
|---|
| 204 | "Subtracts a polynomial Q from P.")
|
|---|
| 205 |
|
|---|
| 206 | (define-binop $poly_multiply poly-mul
|
|---|
| 207 | "Returns the product of polynomials P and Q.")
|
|---|
| 208 |
|
|---|
| 209 | (define-binop $poly_s_polynomial spoly
|
|---|
| 210 | "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
|
|---|
| 211 |
|
|---|
| 212 | (define-unop $poly_primitive_part poly-primitive-part
|
|---|
| 213 | "Returns the polynomial P divided by GCD of its coefficients.")
|
|---|
| 214 |
|
|---|
| 215 | (define-unop $poly_normalize poly-normalize
|
|---|
| 216 | "Returns the polynomial P divided by the leading coefficient.")
|
|---|
| 217 |
|
|---|
| 218 | ;;Functions
|
|---|
| 219 |
|
|---|
| 220 | (defmfun $poly_expand (p vars)
|
|---|
| 221 | "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
|
|---|
| 222 | If the representation is not compatible with a polynomial in variables VARS,
|
|---|
| 223 | the result is an error."
|
|---|
| 224 | (with-parsed-polynomials ((vars) :polynomials (p)
|
|---|
| 225 | :value-type :polynomial)
|
|---|
| 226 | p))
|
|---|
| 227 |
|
|---|
| 228 | (defmfun $poly_expt (p n vars)
|
|---|
| 229 | (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
|
|---|
| 230 | (poly-expt *maxima-ring* p n)))
|
|---|
| 231 |
|
|---|
| 232 | (defmfun $poly_content (p vars)
|
|---|
| 233 | (with-parsed-polynomials ((vars) :polynomials (p))
|
|---|
| 234 | (poly-content *maxima-ring* p)))
|
|---|
| 235 |
|
|---|
| 236 | (defmfun $poly_pseudo_divide (f fl vars
|
|---|
| 237 | &aux (vars (coerce-maxima-list vars))
|
|---|
| 238 | (f (parse-poly f vars))
|
|---|
| 239 | (fl (parse-poly-list fl vars)))
|
|---|
| 240 | (multiple-value-bind (quot rem c division-count)
|
|---|
| 241 | (poly-pseudo-divide *maxima-ring* f fl)
|
|---|
| 242 | `((mlist)
|
|---|
| 243 | ,(coerce-to-maxima :poly-list quot vars)
|
|---|
| 244 | ,(coerce-to-maxima :polynomial rem vars)
|
|---|
| 245 | ,c
|
|---|
| 246 | ,division-count)))
|
|---|
| 247 |
|
|---|
| 248 | (defmfun $poly_exact_divide (f g vars)
|
|---|
| 249 | (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
|
|---|
| 250 | (poly-exact-divide *maxima-ring* f g)))
|
|---|
| 251 |
|
|---|
| 252 | (defmfun $poly_normal_form (f fl vars)
|
|---|
| 253 | (with-parsed-polynomials ((vars) :polynomials (f)
|
|---|
| 254 | :poly-lists (fl)
|
|---|
| 255 | :value-type :polynomial)
|
|---|
| 256 | (normal-form *maxima-ring* f (remzero fl) nil)))
|
|---|
| 257 |
|
|---|
| 258 | (defmfun $poly_buchberger_criterion (g vars)
|
|---|
| 259 | (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
|
|---|
| 260 | (buchberger-criterion *maxima-ring* g)))
|
|---|
| 261 |
|
|---|
| 262 | (defmfun $poly_buchberger (fl vars)
|
|---|
| 263 | (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
|
|---|
| 264 | (buchberger *maxima-ring* (remzero fl) 0 nil)))
|
|---|
| 265 |
|
|---|
| 266 | (defmfun $poly_reduction (plist vars)
|
|---|
| 267 | (with-parsed-polynomials ((vars) :poly-lists (plist)
|
|---|
| 268 | :value-type :poly-list)
|
|---|
| 269 | (reduction *maxima-ring* plist)))
|
|---|
| 270 |
|
|---|
| 271 | (defmfun $poly_minimization (plist vars)
|
|---|
| 272 | (with-parsed-polynomials ((vars) :poly-lists (plist)
|
|---|
| 273 | :value-type :poly-list)
|
|---|
| 274 | (minimization plist)))
|
|---|
| 275 |
|
|---|
| 276 | (defmfun $poly_normalize_list (plist vars)
|
|---|
| 277 | (with-parsed-polynomials ((vars) :poly-lists (plist)
|
|---|
| 278 | :value-type :poly-list)
|
|---|
| 279 | (poly-normalize-list *maxima-ring* plist)))
|
|---|
| 280 |
|
|---|
| 281 | (defmfun $poly_grobner (f vars)
|
|---|
| 282 | (with-parsed-polynomials ((vars) :poly-lists (f)
|
|---|
| 283 | :value-type :poly-list)
|
|---|
| 284 | (grobner *maxima-ring* (remzero f))))
|
|---|
| 285 |
|
|---|
| 286 | (defmfun $poly_reduced_grobner (f vars)
|
|---|
| 287 | (with-parsed-polynomials ((vars) :poly-lists (f)
|
|---|
| 288 | :value-type :poly-list)
|
|---|
| 289 | (reduced-grobner *maxima-ring* (remzero f))))
|
|---|
| 290 |
|
|---|
| 291 | (defmfun $poly_depends_p (p var mvars
|
|---|
| 292 | &aux (vars (coerce-maxima-list mvars))
|
|---|
| 293 | (pos (position var vars)))
|
|---|
| 294 | (if (null pos)
|
|---|
| 295 | (merror "~%Variable ~M not in the list of variables ~M." var mvars)
|
|---|
| 296 | (poly-depends-p (parse-poly p vars) pos)))
|
|---|
| 297 |
|
|---|
| 298 | (defmfun $poly_elimination_ideal (flist k vars)
|
|---|
| 299 | (with-parsed-polynomials ((vars) :poly-lists (flist)
|
|---|
| 300 | :value-type :poly-list)
|
|---|
| 301 | (elimination-ideal *maxima-ring* flist k nil 0)))
|
|---|
| 302 |
|
|---|
| 303 | (defmfun $poly_colon_ideal (f g vars)
|
|---|
| 304 | (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
|
|---|
| 305 | (colon-ideal *maxima-ring* f g nil)))
|
|---|
| 306 |
|
|---|
| 307 | (defmfun $poly_ideal_intersection (f g vars)
|
|---|
| 308 | (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
|
|---|
| 309 | (ideal-intersection *maxima-ring* f g nil)))
|
|---|
| 310 |
|
|---|
| 311 | (defmfun $poly_lcm (f g vars)
|
|---|
| 312 | (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
|
|---|
| 313 | (poly-lcm *maxima-ring* f g)))
|
|---|
| 314 |
|
|---|
| 315 | (defmfun $poly_gcd (f g vars)
|
|---|
| 316 | ($first ($divide (m* f g) ($poly_lcm f g vars))))
|
|---|
| 317 |
|
|---|
| 318 | (defmfun $poly_grobner_equal (g1 g2 vars)
|
|---|
| 319 | (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
|
|---|
| 320 | (grobner-equal *maxima-ring* g1 g2)))
|
|---|
| 321 |
|
|---|
| 322 | (defmfun $poly_grobner_subsetp (g1 g2 vars)
|
|---|
| 323 | (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
|
|---|
| 324 | (grobner-subsetp *maxima-ring* g1 g2)))
|
|---|
| 325 |
|
|---|
| 326 | (defmfun $poly_grobner_member (p g vars)
|
|---|
| 327 | (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
|
|---|
| 328 | (grobner-member *maxima-ring* p g)))
|
|---|
| 329 |
|
|---|
| 330 | (defmfun $poly_ideal_saturation1 (f p vars)
|
|---|
| 331 | (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
|
|---|
| 332 | :value-type :poly-list)
|
|---|
| 333 | (ideal-saturation-1 *maxima-ring* f p 0)))
|
|---|
| 334 |
|
|---|
| 335 | (defmfun $poly_saturation_extension (f plist vars new-vars)
|
|---|
| 336 | (with-parsed-polynomials ((vars new-vars)
|
|---|
| 337 | :poly-lists (f plist)
|
|---|
| 338 | :value-type :poly-list)
|
|---|
| 339 | (saturation-extension *maxima-ring* f plist)))
|
|---|
| 340 |
|
|---|
| 341 | (defmfun $poly_polysaturation_extension (f plist vars new-vars)
|
|---|
| 342 | (with-parsed-polynomials ((vars new-vars)
|
|---|
| 343 | :poly-lists (f plist)
|
|---|
| 344 | :value-type :poly-list)
|
|---|
| 345 | (polysaturation-extension *maxima-ring* f plist)))
|
|---|
| 346 |
|
|---|
| 347 | (defmfun $poly_ideal_polysaturation1 (f plist vars)
|
|---|
| 348 | (with-parsed-polynomials ((vars) :poly-lists (f plist)
|
|---|
| 349 | :value-type :poly-list)
|
|---|
| 350 | (ideal-polysaturation-1 *maxima-ring* f plist 0 nil)))
|
|---|
| 351 |
|
|---|
| 352 | (defmfun $poly_ideal_saturation (f g vars)
|
|---|
| 353 | (with-parsed-polynomials ((vars) :poly-lists (f g)
|
|---|
| 354 | :value-type :poly-list)
|
|---|
| 355 | (ideal-saturation *maxima-ring* f g 0 nil)))
|
|---|
| 356 |
|
|---|
| 357 | (defmfun $poly_ideal_polysaturation (f ideal-list vars)
|
|---|
| 358 | (with-parsed-polynomials ((vars) :poly-lists (f)
|
|---|
| 359 | :poly-list-lists (ideal-list)
|
|---|
| 360 | :value-type :poly-list)
|
|---|
| 361 | (ideal-polysaturation *maxima-ring* f ideal-list 0 nil)))
|
|---|
| 362 |
|
|---|
| 363 | (defmfun $poly_lt (f vars)
|
|---|
| 364 | (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
|
|---|
| 365 | (make-poly-from-termlist (list (poly-lt f)))))
|
|---|
| 366 |
|
|---|
| 367 | (defmfun $poly_lm (f vars)
|
|---|
| 368 | (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
|
|---|
| 369 | (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit *maxima-ring*)))))))
|
|---|
| 370 |
|
|---|
