| [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 | ;;
|
|---|
| [268] | 24 | ;; Load this file into Maxima to bootstrap the Grobner package.
|
|---|
| [133] | 25 | ;;
|
|---|
| [268] | 26 | ;; DETAILS: This file implements an interface between the Grobner
|
|---|
| [269] | 27 | ;; basis package NGROBNER and Maxima. NGROBNER for efficiency uses its
|
|---|
| 28 | ;; own representation of polynomials. Thus, it is necessary to convert
|
|---|
| 29 | ;; Maxima representation to the internal representation and back. The
|
|---|
| 30 | ;; facilities to do so are implemented in this file.
|
|---|
| [268] | 31 | ;;
|
|---|
| [270] | 32 | ;; Also, since the NGROBNER package consists of many Lisp files, it is
|
|---|
| [271] | 33 | ;; necessary to load the files. Unfortunately, it is not quite
|
|---|
| 34 | ;; possible to use ASDF for this purpose, although NGROBNER can be
|
|---|
| [272] | 35 | ;; loaded into lisp using ASDF. Perhaps one day... For now,
|
|---|
| 36 | ;; we use LOAD to accomplish this task.
|
|---|
| [270] | 37 | ;;
|
|---|
| [133] | 38 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 39 |
|
|---|
| [98] | 40 | (in-package :maxima)
|
|---|
| 41 |
|
|---|
| 42 | (macsyma-module cgb-maxima)
|
|---|
| 43 |
|
|---|
| 44 | (eval-when
|
|---|
| 45 | #+gcl (load eval)
|
|---|
| 46 | #-gcl (:load-toplevel :execute)
|
|---|
| 47 | (format t "~&Loading maxima-grobner ~a ~a~%"
|
|---|
| 48 | "$Revision: 2.0 $" "$Date: 2015/06/02 0:34:17 $"))
|
|---|
| 49 |
|
|---|
| 50 | ;;FUNCTS is loaded because it contains the definition of LCM
|
|---|
| 51 | ($load "functs")
|
|---|
| [152] | 52 |
|
|---|
| [275] | 53 | #+sbcl(progn (require 'asdf) (load "ngrobner.asd")(asdf:load-system :ngrobner))
|
|---|
| [274] | 54 |
|
|---|
| [229] | 55 | (use-package :ngrobner)
|
|---|
| 56 |
|
|---|
| [98] | 57 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 58 | ;;
|
|---|
| 59 | ;; Maxima expression ring
|
|---|
| 60 | ;;
|
|---|
| 61 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 62 |
|
|---|
| [230] | 63 | (defparameter *maxima-ring*
|
|---|
| 64 | (make-ring
|
|---|
| [98] | 65 | ;;(defun coeff-zerop (expr) (meval1 `(($is) (($equal) ,expr 0))))
|
|---|
| 66 | :parse #'(lambda (expr)
|
|---|
| 67 | (when modulus (setf expr ($rat expr)))
|
|---|
| 68 | expr)
|
|---|
| 69 | :unit #'(lambda () (if modulus ($rat 1) 1))
|
|---|
| 70 | :zerop #'(lambda (expr)
|
|---|
| 71 | ;;When is exactly a maxima expression equal to 0?
|
|---|
| 72 | (cond ((numberp expr)
|
|---|
| 73 | (= expr 0))
|
|---|
| 74 | ((atom expr) nil)
|
|---|
| 75 | (t
|
|---|
| 76 | (case (caar expr)
|
|---|
| 77 | (mrat (eql ($ratdisrep expr) 0))
|
|---|
| 78 | (otherwise (eql ($totaldisrep expr) 0))))))
|
|---|
| 79 | :add #'(lambda (x y) (m+ x y))
|
|---|
| 80 | :sub #'(lambda (x y) (m- x y))
|
|---|
| 81 | :uminus #'(lambda (x) (m- x))
|
|---|
| 82 | :mul #'(lambda (x y) (m* x y))
|
|---|
| 83 | ;;(defun coeff-div (x y) (cadr ($divide x y)))
|
|---|
| 84 | :div #'(lambda (x y) (m// x y))
|
|---|
| 85 | :lcm #'(lambda (x y) (meval1 `((|$LCM|) ,x ,y)))
|
|---|
| 86 | :ezgcd #'(lambda (x y) (apply #'values (cdr ($ezgcd ($totaldisrep x) ($totaldisrep y)))))
|
|---|
| 87 | ;; :gcd #'(lambda (x y) (second ($ezgcd x y)))))
|
|---|
| 88 | :gcd #'(lambda (x y) ($gcd x y))))
|
|---|
| 89 |
|
|---|
| [369] | 90 | ;; Rebind some global variables for Maxima environment
|
|---|
| 91 | (setf *expression-ring* *maxima-ring*
|
|---|
| [370] | 92 | *ratdisrep-fun* '$ratdisrep
|
|---|
| 93 | )
|
|---|
| [237] | 94 |
|
|---|
| [114] | 95 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 96 | ;;
|
|---|
| 97 | ;; Maxima expression parsing
|
|---|
| 98 | ;;
|
|---|
| 99 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 100 |
|
|---|
| 101 | (defun equal-test-p (expr1 expr2)
|
|---|
| 102 | (alike1 expr1 expr2))
|
|---|
| 103 |
|
|---|
| 104 | (defun coerce-maxima-list (expr)
|
|---|
| 105 | "convert a maxima list to lisp list."
|
|---|
| 106 | (cond
|
|---|
| 107 | ((and (consp (car expr)) (eql (caar expr) 'mlist)) (cdr expr))
|
|---|
| 108 | (t expr)))
|
|---|
| 109 |
|
|---|
| 110 | (defun free-of-vars (expr vars) (apply #'$freeof `(,@vars ,expr)))
|
|---|
| 111 |
|
|---|
| 112 | (defun parse-poly (expr vars &aux (vars (coerce-maxima-list vars)))
|
|---|
| 113 | "Convert a maxima polynomial expression EXPR in variables VARS to internal form."
|
|---|
| 114 | (labels ((parse (arg) (parse-poly arg vars))
|
|---|
| 115 | (parse-list (args) (mapcar #'parse args)))
|
|---|
| 116 | (cond
|
|---|
| 117 | ((eql expr 0) (make-poly-zero))
|
|---|
| 118 | ((member expr vars :test #'equal-test-p)
|
|---|
| 119 | (let ((pos (position expr vars :test #'equal-test-p)))
|
|---|
| [233] | 120 | (make-variable *expression-ring* (length vars) pos)))
|
|---|
| [114] | 121 | ((free-of-vars expr vars)
|
|---|
| 122 | ;;This means that variable-free CRE and Poisson forms will be converted
|
|---|
| 123 | ;;to coefficients intact
|
|---|
| [233] | 124 | (coerce-coeff *expression-ring* expr vars))
|
|---|
| [114] | 125 | (t
|
|---|
| 126 | (case (caar expr)
|
|---|
| [233] | 127 | (mplus (reduce #'(lambda (x y) (poly-add *expression-ring* x y)) (parse-list (cdr expr))))
|
|---|
| 128 | (mminus (poly-uminus *expression-ring* (parse (cadr expr))))
|
|---|
| [114] | 129 | (mtimes
|
|---|
| 130 | (if (endp (cddr expr)) ;unary
|
|---|
| 131 | (parse (cdr expr))
|
|---|
| [233] | 132 | (reduce #'(lambda (p q) (poly-mul *expression-ring* p q)) (parse-list (cdr expr)))))
|
|---|
| [114] | 133 | (mexpt
|
|---|
| 134 | (cond
|
|---|
| 135 | ((member (cadr expr) vars :test #'equal-test-p)
|
|---|
| 136 | ;;Special handling of (expt var pow)
|
|---|
| 137 | (let ((pos (position (cadr expr) vars :test #'equal-test-p)))
|
|---|
| [233] | 138 | (make-variable *expression-ring* (length vars) pos (caddr expr))))
|
|---|
| [114] | 139 | ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
|
|---|
| 140 | ;; Negative power means division in coefficient ring
|
|---|
| 141 | ;; Non-integer power means non-polynomial coefficient
|
|---|
| 142 | (mtell "~%Warning: Expression ~%~M~%contains power which is not a positive integer. Parsing as coefficient.~%"
|
|---|
| 143 | expr)
|
|---|
| [233] | 144 | (coerce-coeff *expression-ring* expr vars))
|
|---|
| 145 | (t (poly-expt *expression-ring* (parse (cadr expr)) (caddr expr)))))
|
|---|
| [114] | 146 | (mrat (parse ($ratdisrep expr)))
|
|---|
| 147 | (mpois (parse ($outofpois expr)))
|
|---|
| 148 | (otherwise
|
|---|
| [233] | 149 | (coerce-coeff *expression-ring* expr vars)))))))
|
|---|
| [114] | 150 |
|
|---|
| 151 | (defun parse-poly-list (expr vars)
|
|---|
| 152 | (case (caar expr)
|
|---|
| 153 | (mlist (mapcar #'(lambda (p) (parse-poly p vars)) (cdr expr)))
|
|---|
| 154 | (t (merror "Expression ~M is not a list of polynomials in variables ~M."
|
|---|
| 155 | expr vars))))
|
|---|
| 156 | (defun parse-poly-list-list (poly-list-list vars)
|
|---|
| 157 | (mapcar #'(lambda (g) (parse-poly-list g vars)) (coerce-maxima-list poly-list-list)))
|
|---|
| 158 |
|
|---|
| 159 |
|
|---|
| [111] | 160 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 161 | ;;
|
|---|
| [241] | 162 | ;; Conversion from internal form to Maxima general form
|
|---|
| 163 | ;;
|
|---|
| 164 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 165 |
|
|---|
| 166 | (defun maxima-head ()
|
|---|
| 167 | (if $poly_return_term_list
|
|---|
| 168 | '(mlist)
|
|---|
| 169 | '(mplus)))
|
|---|
| 170 |
|
|---|
| 171 | (defun coerce-to-maxima (poly-type object vars)
|
|---|
| 172 | (case poly-type
|
|---|
| 173 | (:polynomial
|
|---|
| 174 | `(,(maxima-head) ,@(mapcar #'(lambda (term) (coerce-to-maxima :term term vars)) (poly-termlist object))))
|
|---|
| 175 | (:poly-list
|
|---|
| 176 | `((mlist) ,@(mapcar #'(lambda (p) (funcall *ratdisrep-fun* (coerce-to-maxima :polynomial p vars))) object)))
|
|---|
| 177 | (:term
|
|---|
| 178 | `((mtimes) ,(funcall *ratdisrep-fun* (term-coeff object))
|
|---|
| 179 | ,@(mapcar #'(lambda (var power) `((mexpt) ,var ,power))
|
|---|
| 180 | vars (monom-exponents (term-monom object)))))
|
|---|
| 181 | ;; Assumes that Lisp and Maxima logicals coincide
|
|---|
| 182 | (:logical object)
|
|---|
| 183 | (otherwise
|
|---|
| 184 | object)))
|
|---|
| 185 |
|
|---|
| 186 |
|
|---|
| 187 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 188 | ;;
|
|---|
| [111] | 189 | ;; Unary and binary operation definition facility
|
|---|
| 190 | ;;
|
|---|
| 191 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| [98] | 192 |
|
|---|
| [111] | 193 | (defmacro define-unop (maxima-name fun-name
|
|---|
| 194 | &optional (documentation nil documentation-supplied-p))
|
|---|
| 195 | "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
|
|---|
| 196 | `(defun ,maxima-name (p vars
|
|---|
| 197 | &aux
|
|---|
| 198 | (vars (coerce-maxima-list vars))
|
|---|
| 199 | (p (parse-poly p vars)))
|
|---|
| 200 | ,@(when documentation-supplied-p (list documentation))
|
|---|
| [233] | 201 | (coerce-to-maxima :polynomial (,fun-name *expression-ring* p) vars)))
|
|---|
| [111] | 202 |
|
|---|
| 203 | (defmacro define-binop (maxima-name fun-name
|
|---|
| 204 | &optional (documentation nil documentation-supplied-p))
|
|---|
| 205 | "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
|
|---|
| 206 | `(defmfun ,maxima-name (p q vars
|
|---|
| 207 | &aux
|
|---|
| 208 | (vars (coerce-maxima-list vars))
|
|---|
| 209 | (p (parse-poly p vars))
|
|---|
| 210 | (q (parse-poly q vars)))
|
|---|
| 211 | ,@(when documentation-supplied-p (list documentation))
|
|---|
| [233] | 212 | (coerce-to-maxima :polynomial (,fun-name *expression-ring* p q) vars)))
|
|---|
| [111] | 213 |
|
|---|
| 214 |
|
|---|
| [219] | 215 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 216 | ;;
|
|---|
| 217 | ;; Facilities for evaluating Grobner package expressions
|
|---|
| 218 | ;; within a prepared environment
|
|---|
| 219 | ;;
|
|---|
| 220 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 221 |
|
|---|
| 222 | (defmacro with-monomial-order ((order) &body body)
|
|---|
| 223 | "Evaluate BODY with monomial order set to ORDER."
|
|---|
| 224 | `(let ((*monomial-order* (or (find-order ,order) *monomial-order*)))
|
|---|
| 225 | . ,body))
|
|---|
| 226 |
|
|---|
| 227 | (defmacro with-coefficient-ring ((ring) &body body)
|
|---|
| 228 | "Evaluate BODY with coefficient ring set to RING."
|
|---|
| [233] | 229 | `(let ((*expression-ring* (or (find-ring ,ring) *expression-ring*)))
|
|---|
| [219] | 230 | . ,body))
|
|---|
| 231 |
|
|---|
| 232 | (defmacro with-elimination-orders ((primary secondary elimination-order)
|
|---|
| 233 | &body body)
|
|---|
| 234 | "Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
|
|---|
| 235 | `(let ((*primary-elimination-order* (or (find-order ,primary) *primary-elimination-order*))
|
|---|
| 236 | (*secondary-elimination-order* (or (find-order ,secondary) *secondary-elimination-order*))
|
|---|
| 237 | (*elimination-order* (or (find-order ,elimination-order) *elimination-order*)))
|
|---|
| 238 | . ,body))
|
|---|
| 239 |
|
|---|
| 240 |
|
|---|
| [98] | 241 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 242 | ;;
|
|---|
| 243 | ;; Maxima-level interface functions
|
|---|
| 244 | ;;
|
|---|
| 245 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 246 |
|
|---|
| 247 | ;; Auxillary function for removing zero polynomial
|
|---|
| 248 | (defun remzero (plist) (remove #'poly-zerop plist))
|
|---|
| 249 |
|
|---|
| 250 | ;;Simple operators
|
|---|
| 251 |
|
|---|
| 252 | (define-binop $poly_add poly-add
|
|---|
| 253 | "Adds two polynomials P and Q")
|
|---|
| 254 |
|
|---|
| 255 | (define-binop $poly_subtract poly-sub
|
|---|
| 256 | "Subtracts a polynomial Q from P.")
|
|---|
| 257 |
|
|---|
| 258 | (define-binop $poly_multiply poly-mul
|
|---|
| 259 | "Returns the product of polynomials P and Q.")
|
|---|
| 260 |
|
|---|
| 261 | (define-binop $poly_s_polynomial spoly
|
|---|
| 262 | "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
|
|---|
| 263 |
|
|---|
| 264 | (define-unop $poly_primitive_part poly-primitive-part
|
|---|
| 265 | "Returns the polynomial P divided by GCD of its coefficients.")
|
|---|
| 266 |
|
|---|
| 267 | (define-unop $poly_normalize poly-normalize
|
|---|
| 268 | "Returns the polynomial P divided by the leading coefficient.")
|
|---|
| 269 |
|
|---|
| [222] | 270 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 271 | ;;
|
|---|
| 272 | ;; Macro facility for writing Maxima-level wrappers for
|
|---|
| 273 | ;; functions operating on internal representation
|
|---|
| 274 | ;;
|
|---|
| 275 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
|---|
| 276 |
|
|---|
| 277 | (defmacro with-parsed-polynomials (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
|
|---|
| 278 | &key (polynomials nil)
|
|---|
| 279 | (poly-lists nil)
|
|---|
| 280 | (poly-list-lists nil)
|
|---|
| 281 | (value-type nil))
|
|---|
| 282 | &body body
|
|---|
| 283 | &aux (vars (gensym))
|
|---|
| 284 | (new-vars (gensym)))
|
|---|
| 285 | `(let ((,vars (coerce-maxima-list ,maxima-vars))
|
|---|
| 286 | ,@(when new-vars-supplied-p
|
|---|
| 287 | (list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
|
|---|
| 288 | (coerce-to-maxima
|
|---|
| 289 | ,value-type
|
|---|
| 290 | (with-coefficient-ring ($poly_coefficient_ring)
|
|---|
| 291 | (with-monomial-order ($poly_monomial_order)
|
|---|
| 292 | (with-elimination-orders ($poly_primary_elimination_order
|
|---|
| 293 | $poly_secondary_elimination_order
|
|---|
| 294 | $poly_elimination_order)
|
|---|
| 295 | (let ,(let ((args nil))
|
|---|
| 296 | (dolist (p polynomials args)
|
|---|
| 297 | (setf args (cons `(,p (parse-poly ,p ,vars)) args)))
|
|---|
| 298 | (dolist (p poly-lists args)
|
|---|
| 299 | (setf args (cons `(,p (parse-poly-list ,p ,vars)) args)))
|
|---|
| 300 | (dolist (p poly-list-lists args)
|
|---|
| 301 | (setf args (cons `(,p (parse-poly-list-list ,p ,vars)) args))))
|
|---|
| 302 | . ,body))))
|
|---|
| 303 | ,(if new-vars-supplied-p
|
|---|
| 304 | `(append ,vars ,new-vars)
|
|---|
| 305 | vars))))
|
|---|
| 306 |
|
|---|
| 307 |
|
|---|
| [98] | 308 | ;;Functions
|
|---|
| 309 |
|
|---|
| 310 | (defmfun $poly_expand (p vars)
|
|---|
| 311 | "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
|
|---|
| 312 | If the representation is not compatible with a polynomial in variables VARS,
|
|---|
| 313 | the result is an error."
|
|---|
| 314 | (with-parsed-polynomials ((vars) :polynomials (p)
|
|---|
| 315 | :value-type :polynomial)
|
|---|
| 316 | p))
|
|---|
| 317 |
|
|---|
| 318 | (defmfun $poly_expt (p n vars)
|
|---|
| 319 | (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
|
|---|
| [233] | 320 | (poly-expt *expression-ring* p n)))
|
|---|
| [98] | 321 |
|
|---|
| 322 | (defmfun $poly_content (p vars)
|
|---|
| 323 | (with-parsed-polynomials ((vars) :polynomials (p))
|
|---|
| [233] | 324 | (poly-content *expression-ring* p)))
|
|---|
| [98] | 325 |
|
|---|
| 326 | (defmfun $poly_pseudo_divide (f fl vars
|
|---|
| 327 | &aux (vars (coerce-maxima-list vars))
|
|---|
| 328 | (f (parse-poly f vars))
|
|---|
| 329 | (fl (parse-poly-list fl vars)))
|
|---|
| 330 | (multiple-value-bind (quot rem c division-count)
|
|---|
| [233] | 331 | (poly-pseudo-divide *expression-ring* f fl)
|
|---|
| [98] | 332 | `((mlist)
|
|---|
| 333 | ,(coerce-to-maxima :poly-list quot vars)
|
|---|
| 334 | ,(coerce-to-maxima :polynomial rem vars)
|
|---|
| 335 | ,c
|
|---|
| 336 | ,division-count)))
|
|---|
| 337 |
|
|---|
| 338 | (defmfun $poly_exact_divide (f g vars)
|
|---|
| 339 | (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
|
|---|
| [233] | 340 | (poly-exact-divide *expression-ring* f g)))
|
|---|
| [98] | 341 |
|
|---|
| 342 | (defmfun $poly_normal_form (f fl vars)
|
|---|
| 343 | (with-parsed-polynomials ((vars) :polynomials (f)
|
|---|
| 344 | :poly-lists (fl)
|
|---|
| 345 | :value-type :polynomial)
|
|---|
| [233] | 346 | (normal-form *expression-ring* f (remzero fl) nil)))
|
|---|
| [98] | 347 |
|
|---|
| 348 | (defmfun $poly_buchberger_criterion (g vars)
|
|---|
| 349 | (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
|
|---|
| [233] | 350 | (buchberger-criterion *expression-ring* g)))
|
|---|
| [98] | 351 |
|
|---|
| 352 | (defmfun $poly_buchberger (fl vars)
|
|---|
| 353 | (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
|
|---|
| [233] | 354 | (buchberger *expression-ring* (remzero fl) 0 nil)))
|
|---|
| [98] | 355 |
|
|---|
| 356 | (defmfun $poly_reduction (plist vars)
|
|---|
| 357 | (with-parsed-polynomials ((vars) :poly-lists (plist)
|
|---|
| 358 | :value-type :poly-list)
|
|---|
| [233] | 359 | (reduction *expression-ring* plist)))
|
|---|
| [98] | 360 |
|
|---|
| 361 | (defmfun $poly_minimization (plist vars)
|
|---|
| 362 | (with-parsed-polynomials ((vars) :poly-lists (plist)
|
|---|
| 363 | :value-type :poly-list)
|
|---|
| 364 | (minimization plist)))
|
|---|
| 365 |
|
|---|
| 366 | (defmfun $poly_normalize_list (plist vars)
|
|---|
| 367 | (with-parsed-polynomials ((vars) :poly-lists (plist)
|
|---|
| 368 | :value-type :poly-list)
|
|---|
| [233] | 369 | (poly-normalize-list *expression-ring* plist)))
|
|---|
| [98] | 370 |
|
|---|
| 371 | (defmfun $poly_grobner (f vars)
|
|---|
| 372 | (with-parsed-polynomials ((vars) :poly-lists (f)
|
|---|
| 373 | :value-type :poly-list)
|
|---|
| [233] | 374 | (grobner *expression-ring* (remzero f))))
|
|---|
| [98] | 375 |
|
|---|
| 376 | (defmfun $poly_reduced_grobner (f vars)
|
|---|
| 377 | (with-parsed-polynomials ((vars) :poly-lists (f)
|
|---|
| 378 | :value-type :poly-list)
|
|---|
| [233] | 379 | (reduced-grobner *expression-ring* (remzero f))))
|
|---|
| [98] | 380 |
|
|---|
| 381 | (defmfun $poly_depends_p (p var mvars
|
|---|
| 382 | &aux (vars (coerce-maxima-list mvars))
|
|---|
| 383 | (pos (position var vars)))
|
|---|
| 384 | (if (null pos)
|
|---|
| 385 | (merror "~%Variable ~M not in the list of variables ~M." var mvars)
|
|---|
| 386 | (poly-depends-p (parse-poly p vars) pos)))
|
|---|
| 387 |
|
|---|
| 388 | (defmfun $poly_elimination_ideal (flist k vars)
|
|---|
| 389 | (with-parsed-polynomials ((vars) :poly-lists (flist)
|
|---|
| 390 | :value-type :poly-list)
|
|---|
| [233] | 391 | (elimination-ideal *expression-ring* flist k nil 0)))
|
|---|
| [98] | 392 |
|
|---|
| 393 | (defmfun $poly_colon_ideal (f g vars)
|
|---|
| 394 | (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
|
|---|
| [233] | 395 | (colon-ideal *expression-ring* f g nil)))
|
|---|
| [98] | 396 |
|
|---|
| 397 | (defmfun $poly_ideal_intersection (f g vars)
|
|---|
| 398 | (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
|
|---|
| [233] | 399 | (ideal-intersection *expression-ring* f g nil)))
|
|---|
| [98] | 400 |
|
|---|
| 401 | (defmfun $poly_lcm (f g vars)
|
|---|
| 402 | (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
|
|---|
| [233] | 403 | (poly-lcm *expression-ring* f g)))
|
|---|
| [98] | 404 |
|
|---|
| 405 | (defmfun $poly_gcd (f g vars)
|
|---|
| 406 | ($first ($divide (m* f g) ($poly_lcm f g vars))))
|
|---|
| 407 |
|
|---|
| 408 | (defmfun $poly_grobner_equal (g1 g2 vars)
|
|---|
| 409 | (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
|
|---|
| [233] | 410 | (grobner-equal *expression-ring* g1 g2)))
|
|---|
| [98] | 411 |
|
|---|
| 412 | (defmfun $poly_grobner_subsetp (g1 g2 vars)
|
|---|
| 413 | (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
|
|---|
| [233] | 414 | (grobner-subsetp *expression-ring* g1 g2)))
|
|---|
| [98] | 415 |
|
|---|
| 416 | (defmfun $poly_grobner_member (p g vars)
|
|---|
| 417 | (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
|
|---|
| [233] | 418 | (grobner-member *expression-ring* p g)))
|
|---|
| [98] | 419 |
|
|---|
| 420 | (defmfun $poly_ideal_saturation1 (f p vars)
|
|---|
| 421 | (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
|
|---|
| 422 | :value-type :poly-list)
|
|---|
| [233] | 423 | (ideal-saturation-1 *expression-ring* f p 0)))
|
|---|
| [98] | 424 |
|
|---|
| 425 | (defmfun $poly_saturation_extension (f plist vars new-vars)
|
|---|
| 426 | (with-parsed-polynomials ((vars new-vars)
|
|---|
| 427 | :poly-lists (f plist)
|
|---|
| 428 | :value-type :poly-list)
|
|---|
| [233] | 429 | (saturation-extension *expression-ring* f plist)))
|
|---|
| [98] | 430 |
|
|---|
| 431 | (defmfun $poly_polysaturation_extension (f plist vars new-vars)
|
|---|
| 432 | (with-parsed-polynomials ((vars new-vars)
|
|---|
| 433 | :poly-lists (f plist)
|
|---|
| 434 | :value-type :poly-list)
|
|---|
| [233] | 435 | (polysaturation-extension *expression-ring* f plist)))
|
|---|
| [98] | 436 |
|
|---|
| 437 | (defmfun $poly_ideal_polysaturation1 (f plist vars)
|
|---|
| 438 | (with-parsed-polynomials ((vars) :poly-lists (f plist)
|
|---|
| 439 | :value-type :poly-list)
|
|---|
| [233] | 440 | (ideal-polysaturation-1 *expression-ring* f plist 0 nil)))
|
|---|
| [98] | 441 |
|
|---|
| 442 | (defmfun $poly_ideal_saturation (f g vars)
|
|---|
| 443 | (with-parsed-polynomials ((vars) :poly-lists (f g)
|
|---|
| 444 | :value-type :poly-list)
|
|---|
| [233] | 445 | (ideal-saturation *expression-ring* f g 0 nil)))
|
|---|
| [98] | 446 |
|
|---|
| 447 | (defmfun $poly_ideal_polysaturation (f ideal-list vars)
|
|---|
| 448 | (with-parsed-polynomials ((vars) :poly-lists (f)
|
|---|
| 449 | :poly-list-lists (ideal-list)
|
|---|
| 450 | :value-type :poly-list)
|
|---|
| [233] | 451 | (ideal-polysaturation *expression-ring* f ideal-list 0 nil)))
|
|---|
| [98] | 452 |
|
|---|
| 453 | (defmfun $poly_lt (f vars)
|
|---|
| 454 | (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
|
|---|
| 455 | (make-poly-from-termlist (list (poly-lt f)))))
|
|---|
| 456 |
|
|---|
| 457 | (defmfun $poly_lm (f vars)
|
|---|
| 458 | (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
|
|---|
| [233] | 459 | (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit *expression-ring*)))))))
|
|---|
| [98] | 460 |
|
|---|
