Singular Manual: testSyz

| #### 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,          y*x*ncgen(1)+y*ncgen(1)*x,
    ==> -x*ncgen(2)+ncgen(2)*x,y*ncgen(2)-ncgen(2)*y
    testSyz(I,S); // returns zero
    ==> _[1]=0
    ==> _[2]=0

User manual for Singular version 4-1-3, 2020, generated by texi2html.