source: branches/f4grobner/criterion.lisp@ 1534

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;;;  Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>          

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;;

;; Pair selection criteria

;;

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(defpackage "CRITERION"

  (:use :cl :monomial :pair-queue :grobner-debug :polynomial)

  (:export "CRITERION-1"

           "CRITERION-2"

           ))



(in-package :criterion)



(defun criterion-1 (pair)

  "Returns T if the leading monomials of the two polynomials

in G pointed to by the integers in PAIR have disjoint (relatively prime)

monomials. This test is known as the first Buchberger criterion."

  (declare (type pair pair))

  (let ((f (pair-first pair))

        (g (pair-second pair)))

    (when (monom-rel-prime-p (poly-lm f) (poly-lm g))

      (debug-cgb ":1")

      (return-from criterion-1 t))))



(defun criterion-2 (pair b-done partial-basis

                    &aux (f (pair-first pair)) (g (pair-second pair))

                         (place :before))

  "Returns T if the leading monomial of some element P of

PARTIAL-BASIS divides the LCM of the leading monomials of the two

polynomials in the polynomial list PARTIAL-BASIS, and P paired with

each of the polynomials pointed to by the the PAIR has already been

treated, as indicated by the absence in the hash table B-done."

  (declare (type pair pair) (type hash-table b-done)

           (type poly f g))

  ;; In the code below we assume that pairs are ordered as follows: 

  ;; if PAIR is (I J) then I appears before J in the PARTIAL-BASIS.

  ;; We traverse the list PARTIAL-BASIS and keep track of where we

  ;; are, so that we can produce the pairs in the correct order

  ;; when we check whether they have been processed, i.e they

  ;; appear in the hash table B-done

  (dolist (h partial-basis nil)

    (cond

     ((eq h f)

      #+grobner-check(assert (eq place :before))

      (setf place :in-the-middle))

     ((eq h g)

      #+grobner-check(assert (eq place :in-the-middle))

      (setf place :after))

     ((and (monom-divides-monom-lcm-p (poly-lm h) (poly-lm f) (poly-lm g))

           (gethash (case place

                      (:before (list h f))

                      ((:in-the-middle :after) (list f h)))

                    b-done)

           (gethash (case place

                      ((:before :in-the-middle) (list h g))

                      (:after (list g h)))

                    b-done))

      (debug-cgb ":2")

      (return-from criterion-2 t)))))