source: branches/f4grobner/mx-grobner.lisp@ 100

;;; -*-  Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*- 
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;;;                                                                              
;;;  Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>          
;;;                                                                              
;;;  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")


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;;
;; Debugging/tracing
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defmacro debug-cgb (&rest args)
  `(when $poly_grobner_debug (format *terminal-io* ,@args)))



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;;
;; These are provided mostly for debugging purposes To enable
;; verification of grobner bases with BUCHBERGER-CRITERION, do
;; (pushnew :grobner-check *features*) and compile/load this file.
;; With this feature, the calculations will slow down CONSIDERABLY.
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(defun grobner-test (ring g f)
  "Test whether G is a Grobner basis and F is contained in G. Return T
upon success and NIL otherwise."
  (debug-cgb "~&GROBNER CHECK: ")
  (let (($poly_grobner_debug nil)
        (stat1 (buchberger-criterion ring g))
        (stat2
          (every #'poly-zerop
                 (makelist (normal-form ring (copy-tree (elt f i)) g nil)
                           (i 0 (1- (length f)))))))
    (unless stat1 (error "~&Buchberger criterion failed."))
    (unless stat2
      (error "~&Original polys not in ideal spanned by Grobner.")))
  (debug-cgb "~&GROBNER CHECK END")
  t)


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;;
;; Selection of algorithm and pair heuristic
;;
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(defun find-grobner-function (algorithm)
  "Return a function which calculates Grobner basis, based on its
names. Names currently used are either Lisp symbols, Maxima symbols or
keywords."
  (ecase algorithm
    ((buchberger :buchberger $buchberger) #'buchberger)
    ((parallel-buchberger :parallel-buchberger $parallel_buchberger) #'parallel-buchberger)
    ((gebauer-moeller :gebauer_moeller $gebauer_moeller) #'gebauer-moeller)))

(defun grobner (ring f &optional (start 0) (top-reduction-only nil))
  ;;(setf F (sort F #'< :key #'sugar))
  (funcall
   (find-grobner-function $poly_grobner_algorithm)
   ring f start top-reduction-only))

(defun reduced-grobner (ring f &optional (start 0) (top-reduction-only $poly_top_reduction_only))
  (reduction ring (grobner ring f start top-reduction-only)))

(defun set-pair-heuristic (method)
  "Sets up variables *PAIR-KEY-FUNCTION* and *PAIR-ORDER* used
to determine the priority of critical pairs in the priority queue."
  (ecase method
    ((sugar :sugar $sugar)
     (setf *pair-key-function* #'sugar-pair-key
           *pair-order* #'sugar-order))
;     ((minimal-mock-spoly :minimal-mock-spoly $minimal_mock_spoly)
;      (setf *pair-key-function* #'mock-spoly
;          *pair-order* #'mock-spoly-order))
    ((minimal-lcm :minimal-lcm $minimal_lcm)
     (setf *pair-key-function* #'(lambda (p q)
                                   (monom-lcm (poly-lm p) (poly-lm q)))
           *pair-order* #'reverse-monomial-order))
    ((minimal-total-degree :minimal-total-degree $minimal_total_degree)
     (setf *pair-key-function* #'(lambda (p q)
                                   (monom-total-degree
                                    (monom-lcm (poly-lm p) (poly-lm q))))
           *pair-order* #'<))
    ((minimal-length :minimal-length $minimal_length)
     (setf *pair-key-function* #'(lambda (p q)
                                   (+ (poly-length p) (poly-length q)))
           *pair-order* #'<))))




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;;
;; Set up the coefficients to be polynomials
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;; (defun poly-ring (ring vars)
;;   (make-ring 
;;    :parse #'(lambda (expr) (poly-eval ring expr vars))
;;    :unit #'(lambda () (poly-unit ring (length vars)))
;;    :zerop #'poly-zerop
;;    :add #'(lambda (x y) (poly-add ring x y))
;;    :sub #'(lambda (x y) (poly-sub ring x y))
;;    :uminus #'(lambda (x) (poly-uminus ring x))
;;    :mul #'(lambda (x y) (poly-mul ring x y))
;;    :div #'(lambda (x y) (poly-exact-divide ring x y))
;;    :lcm #'(lambda (x y) (poly-lcm ring x y))
;;    :ezgcd #'(lambda (x y &aux (gcd (poly-gcd ring x y)))
;;            (values gcd
;;                    (poly-exact-divide ring x gcd)
;;                    (poly-exact-divide ring y gcd)))
;;    :gcd #'(lambda (x y) (poly-gcd x y))))



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;;
;; Conversion from internal to infix form
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(defun coerce-to-infix (poly-type object vars)
  (case poly-type
    (:termlist
     `(+ ,@(mapcar #'(lambda (term) (coerce-to-infix :term term vars)) object)))
    (:polynomial
     (coerce-to-infix :termlist (poly-termlist object) vars))
    (:poly-list
     `([ ,@(mapcar #'(lambda (p) (coerce-to-infix :polynomial p vars)) object)))
    (:term
     `(* ,(term-coeff object)
         ,@(mapcar #'(lambda (var power) `(expt ,var ,power))
                   vars (monom-exponents (term-monom object)))))
    (otherwise
     object)))



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;;
;; 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.")


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;;
;; Order utilities
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defun find-order (order)
  "This function returns the order function bases on its name."
  (cond
   ((null order) nil)
   ((symbolp order)
    (case order
      ((lex :lex $lex) #'lex>) 
      ((grlex :grlex $grlex) #'grlex>)
      ((grevlex :grevlex $grevlex) #'grevlex>)
      ((invlex :invlex $invlex) #'invlex>)
      ((elimination-order-1 :elimination-order-1 elimination_order_1) #'elimination-order-1)
      (otherwise
       (mtell "~%Warning: Order ~M not found. Using default.~%" order))))
   (t
    (mtell "~%Order specification ~M is not recognized. Using default.~%" order)
    nil)))

(defun find-ring (ring)
  "This function returns the ring structure bases on input symbol."
  (cond
   ((null ring) nil)
   ((symbolp ring)
    (case ring
      ((expression-ring :expression-ring $expression_ring) *expression-ring*) 
      ((ring-of-integers :ring-of-integers $ring_of_integers) *ring-of-integers*) 
      (otherwise
       (mtell "~%Warning: Ring ~M not found. Using default.~%" ring))))
   (t
    (mtell "~%Ring specification ~M is not recognized. Using default.~%" ring)
    nil)))

(defmacro with-monomial-order ((order) &body body)
  "Evaluate BODY with monomial order set to ORDER."
  `(let ((*monomial-order* (or (find-order ,order) *monomial-order*)))
     . ,body))

(defmacro with-coefficient-ring ((ring) &body body)
  "Evaluate BODY with coefficient ring set to RING."
  `(let ((*maxima-ring* (or (find-ring ,ring) *maxima-ring*)))
     . ,body))

(defmacro with-elimination-orders ((primary secondary elimination-order)
                                   &body body)
  "Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
  `(let ((*primary-elimination-order* (or (find-order ,primary)  *primary-elimination-order*))
         (*secondary-elimination-order* (or (find-order ,secondary) *secondary-elimination-order*))
         (*elimination-order* (or (find-order ,elimination-order) *elimination-order*)))
     . ,body))



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;;
;; Conversion from internal form to Maxima general form
;;
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(defun maxima-head ()
  (if $poly_return_term_list
      '(mlist)
    '(mplus)))

(defun coerce-to-maxima (poly-type object vars)
  (case poly-type
    (:polynomial 
     `(,(maxima-head) ,@(mapcar #'(lambda (term) (coerce-to-maxima :term term vars)) (poly-termlist object))))
    (:poly-list
     `((mlist) ,@(mapcar #'(lambda (p) ($ratdisrep (coerce-to-maxima :polynomial p vars))) object)))
    (:term
     `((mtimes) ,($ratdisrep (term-coeff object))
       ,@(mapcar #'(lambda (var power) `((mexpt) ,var ,power))
                 vars (monom-exponents (term-monom object)))))
    ;; Assumes that Lisp and Maxima logicals coincide
    (:logical object)
    (otherwise
     object)))



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;;
;; 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*)))))))