Changeset dffd154 in git for Singular/dyn_modules/gfanlib/witness.h
- Timestamp:
- Sep 20, 2014, 1:53:38 AM (10 years ago)
- Branches:
- (u'spielwiese', '5b153614cbc72bfa198d75b1e9e33dab2645d9fe')
- Children:
- 4664b33f793e7e511d9722557720dd523ec89856
- Parents:
- b71400abefd0c9c66c0009063f40ddd5b1f1c4c7
- git-author:
- Yue Ren <ren@mathematik.uni-kl.de>2014-09-20 01:53:38+02:00
- git-committer:
- Yue Ren <ren@mathematik.uni-kl.de>2015-02-06 13:47:05+01:00
- File:
-
- 1 edited
Legend:
- Unmodified
- Added
- Removed
-
Singular/dyn_modules/gfanlib/witness.h
rb71400a rdffd154 5 5 #include <libpolys/polys/simpleideals.h> 6 6 7 /** 8 * Computes a division discarding remainder of f with respect to G. 9 * Given f a polynomial and G={g1,...,gk} a set of polynomials in r, 10 * returns a matrix Q=(q1,...,qk) over r such that 11 * f = q1*g1+...+qk*gk+s 12 * is a determinate division with remainder s. 13 */ 7 14 matrix divisionDiscardingRemainder(const poly f, const ideal G, const ring r); 15 16 /** 17 * Computes a division discarding remainder of F with respect to G. 18 * Given F={f1,...,fl} and G={g1,...,gk} two sets of polynomials in r, 19 * returns a matrix Q=(qij) i=1,..,k j=1,...,l over r such that 20 * fj = q1j*g1+...+qkj*gk+sj 21 * is a determinate division with remainder sj for all j=1,...,l. 22 */ 8 23 matrix divisionDiscardingRemainder(const ideal F, const ideal G, const ring r); 24 25 /** 26 * Let w be the uppermost weight vector in the matrix defining the ordering on r. 27 * Let I be a Groebner basis of an ideal in r, inI its initial form with respect w. 28 * Given an w-homogeneous element m of inI, computes a witness g of m in I, 29 * i.e. g in I such that in_w(g)=m. 30 */ 9 31 poly witness(const poly m, const ideal I, const ideal inI, const ring r); 32 33 /** 34 * Computes witnesses in J for inI 35 * Given inI={h1,...,hl} and J={g1,...,gk} two sets of polynomials in r, 36 * returns a set I={f1,...,fl} of <g1,...,gk> such that 37 * in_w(fj)=hj for all j=1,...,l, 38 * where w denotes the uppoermost weight vector in the matrix defining the ordering on r. 39 * Assumes that hj is an element of <in_w(g1),...,in_w(gk)> 40 */ 10 41 ideal witness(const ideal inI, const ideal J, const ring r); 11 42 12 43 #ifndef NDEBUG 13 44 #include <Singular/ipid.h> 14 15 BOOLEAN dwr0(leftv res, leftv args); 16 BOOLEAN witness0(leftv res, leftv args); 45 BOOLEAN dwrDebug(leftv res, leftv args); 46 BOOLEAN witnessDebug(leftv res, leftv args); 17 47 #endif 18 48
Note: See TracChangeset
for help on using the changeset viewer.