;;; -*- Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*- ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;; ;;; Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik ;;; ;;; This program is free software; you can redistribute it and/or modify ;;; it under the terms of the GNU General Public License as published by ;;; the Free Software Foundation; either version 2 of the License, or ;;; (at your option) any later version. ;;; ;;; This program is distributed in the hope that it will be useful, ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ;;; GNU General Public License for more details. ;;; ;;; You should have received a copy of the GNU General Public License ;;; along with this program; if not, write to the Free Software ;;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. ;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; (in-package :maxima) (macsyma-module cgb-maxima) (eval-when #+gcl (load eval) #-gcl (:load-toplevel :execute) (format t "~&Loading maxima-grobner ~a ~a~%" "$Revision: 2.0 $" "$Date: 2015/06/02 0:34:17 $")) ;;FUNCTS is loaded because it contains the definition of LCM ($load "functs") ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; ;; Maxima expression ring ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; (defparameter *expression-ring* (make-ring ;;(defun coeff-zerop (expr) (meval1 `(($is) (($equal) ,expr 0)))) :parse #'(lambda (expr) (when modulus (setf expr ($rat expr))) expr) :unit #'(lambda () (if modulus ($rat 1) 1)) :zerop #'(lambda (expr) ;;When is exactly a maxima expression equal to 0? (cond ((numberp expr) (= expr 0)) ((atom expr) nil) (t (case (caar expr) (mrat (eql ($ratdisrep expr) 0)) (otherwise (eql ($totaldisrep expr) 0)))))) :add #'(lambda (x y) (m+ x y)) :sub #'(lambda (x y) (m- x y)) :uminus #'(lambda (x) (m- x)) :mul #'(lambda (x y) (m* x y)) ;;(defun coeff-div (x y) (cadr ($divide x y))) :div #'(lambda (x y) (m// x y)) :lcm #'(lambda (x y) (meval1 `((|$LCM|) ,x ,y))) :ezgcd #'(lambda (x y) (apply #'values (cdr ($ezgcd ($totaldisrep x) ($totaldisrep y))))) ;; :gcd #'(lambda (x y) (second ($ezgcd x y))))) :gcd #'(lambda (x y) ($gcd x y)))) (defvar *maxima-ring* *expression-ring* "The ring of coefficients, over which all polynomials are assumed to be defined.") ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; ;; Macro facility for writing Maxima-level wrappers for ;; functions operating on internal representation ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; (defmacro with-parsed-polynomials (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p)) &key (polynomials nil) (poly-lists nil) (poly-list-lists nil) (value-type nil)) &body body &aux (vars (gensym)) (new-vars (gensym))) `(let ((,vars (coerce-maxima-list ,maxima-vars)) ,@(when new-vars-supplied-p (list `(,new-vars (coerce-maxima-list ,maxima-new-vars))))) (coerce-to-maxima ,value-type (with-coefficient-ring ($poly_coefficient_ring) (with-monomial-order ($poly_monomial_order) (with-elimination-orders ($poly_primary_elimination_order $poly_secondary_elimination_order $poly_elimination_order) (let ,(let ((args nil)) (dolist (p polynomials args) (setf args (cons `(,p (parse-poly ,p ,vars)) args))) (dolist (p poly-lists args) (setf args (cons `(,p (parse-poly-list ,p ,vars)) args))) (dolist (p poly-list-lists args) (setf args (cons `(,p (parse-poly-list-list ,p ,vars)) args)))) . ,body)))) ,(if new-vars-supplied-p `(append ,vars ,new-vars) vars)))) (defmacro define-unop (maxima-name fun-name &optional (documentation nil documentation-supplied-p)) "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME." `(defun ,maxima-name (p vars &aux (vars (coerce-maxima-list vars)) (p (parse-poly p vars))) ,@(when documentation-supplied-p (list documentation)) (coerce-to-maxima :polynomial (,fun-name *maxima-ring* p) vars))) (defmacro define-binop (maxima-name fun-name &optional (documentation nil documentation-supplied-p)) "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME." `(defmfun ,maxima-name (p q vars &aux (vars (coerce-maxima-list vars)) (p (parse-poly p vars)) (q (parse-poly q vars))) ,@(when documentation-supplied-p (list documentation)) (coerce-to-maxima :polynomial (,fun-name *maxima-ring* p q) vars))) ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; ;; Maxima-level interface functions ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; Auxillary function for removing zero polynomial (defun remzero (plist) (remove #'poly-zerop plist)) ;;Simple operators (define-binop $poly_add poly-add "Adds two polynomials P and Q") (define-binop $poly_subtract poly-sub "Subtracts a polynomial Q from P.") (define-binop $poly_multiply poly-mul "Returns the product of polynomials P and Q.") (define-binop $poly_s_polynomial spoly "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.") (define-unop $poly_primitive_part poly-primitive-part "Returns the polynomial P divided by GCD of its coefficients.") (define-unop $poly_normalize poly-normalize "Returns the polynomial P divided by the leading coefficient.") ;;Functions (defmfun $poly_expand (p vars) "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial. If the representation is not compatible with a polynomial in variables VARS, the result is an error." (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial) p)) (defmfun $poly_expt (p n vars) (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial) (poly-expt *maxima-ring* p n))) (defmfun $poly_content (p vars) (with-parsed-polynomials ((vars) :polynomials (p)) (poly-content *maxima-ring* p))) (defmfun $poly_pseudo_divide (f fl vars &aux (vars (coerce-maxima-list vars)) (f (parse-poly f vars)) (fl (parse-poly-list fl vars))) (multiple-value-bind (quot rem c division-count) (poly-pseudo-divide *maxima-ring* f fl) `((mlist) ,(coerce-to-maxima :poly-list quot vars) ,(coerce-to-maxima :polynomial rem vars) ,c ,division-count))) (defmfun $poly_exact_divide (f g vars) (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial) (poly-exact-divide *maxima-ring* f g))) (defmfun $poly_normal_form (f fl vars) (with-parsed-polynomials ((vars) :polynomials (f) :poly-lists (fl) :value-type :polynomial) (normal-form *maxima-ring* f (remzero fl) nil))) (defmfun $poly_buchberger_criterion (g vars) (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical) (buchberger-criterion *maxima-ring* g))) (defmfun $poly_buchberger (fl vars) (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list) (buchberger *maxima-ring* (remzero fl) 0 nil))) (defmfun $poly_reduction (plist vars) (with-parsed-polynomials ((vars) :poly-lists (plist) :value-type :poly-list) (reduction *maxima-ring* plist))) (defmfun $poly_minimization (plist vars) (with-parsed-polynomials ((vars) :poly-lists (plist) :value-type :poly-list) (minimization plist))) (defmfun $poly_normalize_list (plist vars) (with-parsed-polynomials ((vars) :poly-lists (plist) :value-type :poly-list) (poly-normalize-list *maxima-ring* plist))) (defmfun $poly_grobner (f vars) (with-parsed-polynomials ((vars) :poly-lists (f) :value-type :poly-list) (grobner *maxima-ring* (remzero f)))) (defmfun $poly_reduced_grobner (f vars) (with-parsed-polynomials ((vars) :poly-lists (f) :value-type :poly-list) (reduced-grobner *maxima-ring* (remzero f)))) (defmfun $poly_depends_p (p var mvars &aux (vars (coerce-maxima-list mvars)) (pos (position var vars))) (if (null pos) (merror "~%Variable ~M not in the list of variables ~M." var mvars) (poly-depends-p (parse-poly p vars) pos))) (defmfun $poly_elimination_ideal (flist k vars) (with-parsed-polynomials ((vars) :poly-lists (flist) :value-type :poly-list) (elimination-ideal *maxima-ring* flist k nil 0))) (defmfun $poly_colon_ideal (f g vars) (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list) (colon-ideal *maxima-ring* f g nil))) (defmfun $poly_ideal_intersection (f g vars) (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list) (ideal-intersection *maxima-ring* f g nil))) (defmfun $poly_lcm (f g vars) (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial) (poly-lcm *maxima-ring* f g))) (defmfun $poly_gcd (f g vars) ($first ($divide (m* f g) ($poly_lcm f g vars)))) (defmfun $poly_grobner_equal (g1 g2 vars) (with-parsed-polynomials ((vars) :poly-lists (g1 g2)) (grobner-equal *maxima-ring* g1 g2))) (defmfun $poly_grobner_subsetp (g1 g2 vars) (with-parsed-polynomials ((vars) :poly-lists (g1 g2)) (grobner-subsetp *maxima-ring* g1 g2))) (defmfun $poly_grobner_member (p g vars) (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g)) (grobner-member *maxima-ring* p g))) (defmfun $poly_ideal_saturation1 (f p vars) (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p) :value-type :poly-list) (ideal-saturation-1 *maxima-ring* f p 0))) (defmfun $poly_saturation_extension (f plist vars new-vars) (with-parsed-polynomials ((vars new-vars) :poly-lists (f plist) :value-type :poly-list) (saturation-extension *maxima-ring* f plist))) (defmfun $poly_polysaturation_extension (f plist vars new-vars) (with-parsed-polynomials ((vars new-vars) :poly-lists (f plist) :value-type :poly-list) (polysaturation-extension *maxima-ring* f plist))) (defmfun $poly_ideal_polysaturation1 (f plist vars) (with-parsed-polynomials ((vars) :poly-lists (f plist) :value-type :poly-list) (ideal-polysaturation-1 *maxima-ring* f plist 0 nil))) (defmfun $poly_ideal_saturation (f g vars) (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list) (ideal-saturation *maxima-ring* f g 0 nil))) (defmfun $poly_ideal_polysaturation (f ideal-list vars) (with-parsed-polynomials ((vars) :poly-lists (f) :poly-list-lists (ideal-list) :value-type :poly-list) (ideal-polysaturation *maxima-ring* f ideal-list 0 nil))) (defmfun $poly_lt (f vars) (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial) (make-poly-from-termlist (list (poly-lt f))))) (defmfun $poly_lm (f vars) (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial) (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit *maxima-ring*)))))))