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7.10.4.12 testLift
Procedure from library freegb.lib (see freegb_lib).
- Usage:
- testLift(M,T); module M, matrix T
- Return:
- module
- Purpose:
- assembles the result of the lift procedure
- Assume:
- T is the lift matrix of a submodule of M
- Note:
- the inverse of the lift procedure
Example:
| LIB "freegb.lib";
LIB "freegb.lib";
==> // ** redefining tstfreegb (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining tstfreegb (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining setLetterplaceAttributes (LIB "freegb.lib";) ./examples/\
testLift.sing:2
==> // ** redefining setLetterplaceAttributes (LIB "freegb.lib";) ./examples/\
testLift.sing:2
==> // ** redefining lst2str (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining mod2str (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining vct2str (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining isVar (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining letplaceGBasis (LIB "freegb.lib";) ./examples/testLift.s\
ing:2
==> // ** redefining letplaceGBasis (LIB "freegb.lib";) ./examples/testLift.s\
ing:2
==> // ** redefining lieBracket (LIB "freegb.lib";) ./examples/testLift.sing:\
2
==> // ** redefining lieBracket (LIB "freegb.lib";) ./examples/testLift.sing:\
2
==> // ** redefining lpPrint (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining lpPrint (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining freeGBasis (LIB "freegb.lib";) ./examples/testLift.sing:\
2
==> // ** redefining freeGBasis (LIB "freegb.lib";) ./examples/testLift.sing:\
2
==> // ** redefining crs (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining polylen (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining lpDegBound (LIB "freegb.lib";) ./examples/testLift.sing:\
2
==> // ** redefining lpDegBound (LIB "freegb.lib";) ./examples/testLift.sing:\
2
==> // ** redefining lpVarBlockSize (LIB "freegb.lib";) ./examples/testLift.s\
ing:2
==> // ** redefining lpVarBlockSize (LIB "freegb.lib";) ./examples/testLift.s\
ing:2
==> // ** redefining isFreeAlgebra (LIB "freegb.lib";) ./examples/testLift.si\
ng:2
==> // ** redefining isFreeAlgebra (LIB "freegb.lib";) ./examples/testLift.si\
ng:2
==> // ** redefining lpNcgenCount (LIB "freegb.lib";) ./examples/testLift.sin\
g:2
==> // ** redefining lpNcgenCount (LIB "freegb.lib";) ./examples/testLift.sin\
g:2
==> // ** redefining makeLetterplaceRing (LIB "freegb.lib";) ./examples/testL\
ift.sing:2
==> // ** redefining makeLetterplaceRing (LIB "freegb.lib";) ./examples/testL\
ift.sing:2
==> // ** redefining makeLetterplaceRing1 (LIB "freegb.lib";) ./examples/test\
Lift.sing:2
==> // ** redefining makeLetterplaceRing2 (LIB "freegb.lib";) ./examples/test\
Lift.sing:2
==> // ** redefining makeLetterplaceRing4 (LIB "freegb.lib";) ./examples/test\
Lift.sing:2
==> // ** redefining makeLetterplaceRing3 (LIB "freegb.lib";) ./examples/test\
Lift.sing:2
==> // ** redefining freegbold (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining stringpoly2lplace (LIB "freegb.lib";) ./examples/testLif\
t.sing:2
==> // ** redefining addplaces (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining sent2lplace (LIB "freegb.lib";) ./examples/testLift.sing\
:2
==> // ** redefining testnumber (LIB "freegb.lib";) ./examples/testLift.sing:\
2
==> // ** redefining str2lplace (LIB "freegb.lib";) ./examples/testLift.sing:\
2
==> // ** redefining strpower2rep (LIB "freegb.lib";) ./examples/testLift.sin\
g:2
==> // ** redefining shiftPoly (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining lastBlock (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining test_shift (LIB "freegb.lib";) ./examples/testLift.sing:\
2
==> // ** redefining lp2lstr (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining lp2lstr (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining strList2poly (LIB "freegb.lib";) ./examples/testLift.sin\
g:2
==> // ** redefining file2lplace (LIB "freegb.lib";) ./examples/testLift.sing\
:2
==> // ** redefining lpPower (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining lpNF (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining lpNF (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining lpDivision (LIB "freegb.lib";) ./examples/testLift.sing:\
2
==> // ** redefining lpDivision (LIB "freegb.lib";) ./examples/testLift.sing:\
2
==> // ** redefining lpGBPres2Poly (LIB "freegb.lib";) ./examples/testLift.si\
ng:2
==> // ** redefining lpGBPres2Poly (LIB "freegb.lib";) ./examples/testLift.si\
ng:2
==> // ** redefining getExpVecs (LIB "freegb.lib";) ./examples/testLift.sing:\
2
==> // ** redefining delSupZero (LIB "freegb.lib";) ./examples/testLift.sing:\
2
==> // ** redefining delSupZeroList (LIB "freegb.lib";) ./examples/testLift.s\
ing:2
==> // ** redefining makeDVec (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining makeDVecL (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining makeDVecI (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining dShiftDiv (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining lpNormalForm1 (LIB "freegb.lib";) ./examples/testLift.si\
ng:2
==> // ** redefining lpNormalForm2 (LIB "freegb.lib";) ./examples/testLift.si\
ng:2
==> // ** redefining isOrderingShiftInvariant (LIB "freegb.lib";) ./examples/\
testLift.sing:2
==> // ** redefining isOrderingShiftInvariant (LIB "freegb.lib";) ./examples/\
testLift.sing:2
==> // ** redefining lpMonomialsWithHoles (LIB "freegb.lib";) ./examples/test\
Lift.sing:2
==> // ** redefining getlpCoeffs (LIB "freegb.lib";) ./examples/testLift.sing\
:2
==> // ** redefining lpReduce (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining entryViolation (LIB "freegb.lib";) ./examples/testLift.s\
ing:2
==> // ** redefining checkAssumptionsLPIV (LIB "freegb.lib";) ./examples/test\
Lift.sing:2
==> // ** redefining checkAssumptions (LIB "freegb.lib";) ./examples/testLift\
.sing:2
==> // ** redefining checkLPRing (LIB "freegb.lib";) ./examples/testLift.sing\
:2
==> // ** redefining checkAssumptionIdeal (LIB "freegb.lib";) ./examples/test\
Lift.sing:2
==> // ** redefining checkAssumptionPoly (LIB "freegb.lib";) ./examples/testL\
ift.sing:2
==> // ** redefining isContainedInVp (LIB "freegb.lib";) ./examples/testLift.\
sing:2
==> // ** redefining extractLinearPart (LIB "freegb.lib";) ./examples/testLif\
t.sing:2
==> // ** redefining isLinearVector (LIB "freegb.lib";) ./examples/testLift.s\
ing:2
==> // ** redefining lpAssumeViolation (LIB "freegb.lib";) ./examples/testLif\
t.sing:2
==> // ** redefining skip0 (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining ivL2lpI (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining ivL2lpI (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining iv2lp (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining iv2lp (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining iv2lpList (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining iv2lpList (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining iv2lpMat (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining iv2lpMat (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining lpId2ivLi (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining lpId2ivLi (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining lp2iv (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining lp2iv (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining lp2ivId (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining lp2ivId (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining testLift (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining testLift (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining testSyz (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining testSyz (LIB "freegb.lib";) ./examples/testLift.sing:2
==> // ** redefining mod_init (LIB "freegb.lib";) ./examples/testLift.sing:2
ring r = 0,(x,y),(c,Dp);
ring R = freeAlgebra(r, 7, 2);
ideal I = std(x*y*x + 1);
print(matrix(I)); // finite two-sided Groebner basis
==> x*y-y*x,y*x*x+1
ideal SI = x*I[1]*y + y*x*I[2], I[1]*y*x + I[2]*y;
matrix T = lift(I, SI); // T is the lifting matrix of SI wrt I
print(T); //
==> y*ncgen(1)*x*x+x*ncgen(1)*y,y*x*ncgen(1)+y*ncgen(1)*x+ncgen(1)*y*x,
==> y*ncgen(2)*x, y*ncgen(2)
print(matrix(SI)); // the original generators of SI as a matrix
==> y*x*y*x*x+x*x*y*y-x*y*x*y+y*x,x*y*y*x+y*x*x*y-y*x*y*x+y
print(matrix(testLift(I,T))); // and the result of testLift
==> y*x*y*x*x+x*x*y*y-x*y*x*y+y*x,x*y*y*x+y*x*x*y-y*x*y*x+y
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