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7.10.4.13 testSyz

Procedure from library freegb.lib (see freegb_lib).

Usage:
testSyz(M,S); module M, S

Return:
module

Purpose:
tests the result of the syz procedure

Assume:
S is the syzygy bimodule of M

Example:
 
LIB "freegb.lib";
LIB "freegb.lib";
==> // ** redefining tstfreegb (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining tstfreegb (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining setLetterplaceAttributes (LIB "freegb.lib";) ./examples/\
   testSyz.sing:2
==> // ** redefining setLetterplaceAttributes (LIB "freegb.lib";) ./examples/\
   testSyz.sing:2
==> // ** redefining lst2str (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining mod2str (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining vct2str (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining isVar (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining letplaceGBasis (LIB "freegb.lib";) ./examples/testSyz.si\
   ng:2
==> // ** redefining letplaceGBasis (LIB "freegb.lib";) ./examples/testSyz.si\
   ng:2
==> // ** redefining lieBracket (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lieBracket (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lpPrint (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lpPrint (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining freeGBasis (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining freeGBasis (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining crs (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining polylen (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lpDegBound (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lpDegBound (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lpVarBlockSize (LIB "freegb.lib";) ./examples/testSyz.si\
   ng:2
==> // ** redefining lpVarBlockSize (LIB "freegb.lib";) ./examples/testSyz.si\
   ng:2
==> // ** redefining isFreeAlgebra (LIB "freegb.lib";) ./examples/testSyz.sin\
   g:2
==> // ** redefining isFreeAlgebra (LIB "freegb.lib";) ./examples/testSyz.sin\
   g:2
==> // ** redefining lpNcgenCount (LIB "freegb.lib";) ./examples/testSyz.sing\
   :2
==> // ** redefining lpNcgenCount (LIB "freegb.lib";) ./examples/testSyz.sing\
   :2
==> // ** redefining makeLetterplaceRing (LIB "freegb.lib";) ./examples/testS\
   yz.sing:2
==> // ** redefining makeLetterplaceRing (LIB "freegb.lib";) ./examples/testS\
   yz.sing:2
==> // ** redefining makeLetterplaceRing1 (LIB "freegb.lib";) ./examples/test\
   Syz.sing:2
==> // ** redefining makeLetterplaceRing2 (LIB "freegb.lib";) ./examples/test\
   Syz.sing:2
==> // ** redefining makeLetterplaceRing4 (LIB "freegb.lib";) ./examples/test\
   Syz.sing:2
==> // ** redefining makeLetterplaceRing3 (LIB "freegb.lib";) ./examples/test\
   Syz.sing:2
==> // ** redefining freegbold (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining stringpoly2lplace (LIB "freegb.lib";) ./examples/testSyz\
   .sing:2
==> // ** redefining addplaces (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining sent2lplace (LIB "freegb.lib";) ./examples/testSyz.sing:\
   2
==> // ** redefining testnumber (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining str2lplace (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining strpower2rep (LIB "freegb.lib";) ./examples/testSyz.sing\
   :2
==> // ** redefining shiftPoly (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lastBlock (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining test_shift (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lp2lstr (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lp2lstr (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining strList2poly (LIB "freegb.lib";) ./examples/testSyz.sing\
   :2
==> // ** redefining file2lplace (LIB "freegb.lib";) ./examples/testSyz.sing:\
   2
==> // ** redefining lpPower (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lpNF (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lpNF (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lpDivision (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lpDivision (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lpGBPres2Poly (LIB "freegb.lib";) ./examples/testSyz.sin\
   g:2
==> // ** redefining lpGBPres2Poly (LIB "freegb.lib";) ./examples/testSyz.sin\
   g:2
==> // ** redefining getExpVecs (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining delSupZero (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining delSupZeroList (LIB "freegb.lib";) ./examples/testSyz.si\
   ng:2
==> // ** redefining makeDVec (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining makeDVecL (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining makeDVecI (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining dShiftDiv (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lpNormalForm1 (LIB "freegb.lib";) ./examples/testSyz.sin\
   g:2
==> // ** redefining lpNormalForm2 (LIB "freegb.lib";) ./examples/testSyz.sin\
   g:2
==> // ** redefining isOrderingShiftInvariant (LIB "freegb.lib";) ./examples/\
   testSyz.sing:2
==> // ** redefining isOrderingShiftInvariant (LIB "freegb.lib";) ./examples/\
   testSyz.sing:2
==> // ** redefining lpMonomialsWithHoles (LIB "freegb.lib";) ./examples/test\
   Syz.sing:2
==> // ** redefining getlpCoeffs (LIB "freegb.lib";) ./examples/testSyz.sing:\
   2
==> // ** redefining lpReduce (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining entryViolation (LIB "freegb.lib";) ./examples/testSyz.si\
   ng:2
==> // ** redefining checkAssumptionsLPIV (LIB "freegb.lib";) ./examples/test\
   Syz.sing:2
==> // ** redefining checkAssumptions (LIB "freegb.lib";) ./examples/testSyz.\
   sing:2
==> // ** redefining checkLPRing (LIB "freegb.lib";) ./examples/testSyz.sing:\
   2
==> // ** redefining checkAssumptionIdeal (LIB "freegb.lib";) ./examples/test\
   Syz.sing:2
==> // ** redefining checkAssumptionPoly (LIB "freegb.lib";) ./examples/testS\
   yz.sing:2
==> // ** redefining isContainedInVp (LIB "freegb.lib";) ./examples/testSyz.s\
   ing:2
==> // ** redefining extractLinearPart (LIB "freegb.lib";) ./examples/testSyz\
   .sing:2
==> // ** redefining isLinearVector (LIB "freegb.lib";) ./examples/testSyz.si\
   ng:2
==> // ** redefining lpAssumeViolation (LIB "freegb.lib";) ./examples/testSyz\
   .sing:2
==> // ** redefining skip0 (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining ivL2lpI (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining ivL2lpI (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining iv2lp (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining iv2lp (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining iv2lpList (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining iv2lpList (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining iv2lpMat (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining iv2lpMat (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lpId2ivLi (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lpId2ivLi (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lp2iv (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lp2iv (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lp2ivId (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining lp2ivId (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining testLift (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining testLift (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining testSyz (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining testSyz (LIB "freegb.lib";) ./examples/testSyz.sing:2
==> // ** redefining mod_init (LIB "freegb.lib";) ./examples/testSyz.sing:2
ring r = 0,(x,y),(c,Dp);
ring R = freeAlgebra(r, 7, 2);
ideal I = twostd(x*y*x + 1);
print(matrix(I));
==> x*y-y*x,y*x*x+1
module S = syz(I);
print(S);
==> ncgen(1)*x*x,S[1,2],S[1,3],S[1,4],S[1,5],
==> S[2,1],      S[2,2],S[2,3],S[2,4],S[2,5] 
testSyz(I,S); // returns zero
==> _[1]=0
==> _[2]=0
==> _[3]=0
==> _[4]=0
==> _[5]=0