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___N__C__Matrix_sp_sl_sl_sp__N__C__Matrix.out
-- -*- M2-comint -*- hash: 17963186949737904910 i1 : B = threeDimSklyanin(QQ,{1,1,-1},{x,y,z}) --Calling Bergman for NCGB calculation. Complete! o1 = B o1 : NCQuotientRing i2 : A = ambient B o2 = A o2 : NCPolynomialRing i3 : g = 2*(-y^3-x*y*z+y*x*z+x^3) 3 3 o3 = -2y +2yxz-2xyz+2x o3 : A i4 : J = (ideal B) + ncIdeal {g} 2 2 2 3 3 o4 = Two-sided ideal {zy+yz-x , zx-y +xz, -z +yx+xy, -2y +2yxz-2xyz+2x } o4 : NCIdeal i5 : B' = A/J -- Factor of sklyanin --Calling Bergman for NCGB calculation. Complete! o5 = B' o5 : NCQuotientRing i6 : k = ncMatrix {{x,y,z}} o6 = | x y z | o6 : NCMatrix i7 : BprimeToB = ncMap(B,B',gens B) -- way to lift back from B' to B o7 = NCRingMap B <--- B' o7 : NCRingMap i8 : M = BprimeToB rightKernelBergman rightKernelBergman k -- second syzygy of k over B --Calling Bergman for NCGB calculation. Complete! --Calling Bergman for NCGB calculation. Complete! --Calling Bergman for NCGB calculation. Complete! --Calling Bergman for NCGB calculation. Complete! --Calling Bergman for NCGB calculation. Complete! --Calling Bergman for NCGB calculation. Complete! o8 = | -z y*z -y^2 -y*x-2*x*y | | x y*x+x*y y*z+x^2 -y^2+3*x*z | | y -x*z -x*y x^2 | | 0 -2*y -2*x -2*z | o8 : NCMatrix i9 : gId = g*(ncMatrix applyTable(entries id_(ZZ^4), i -> promote(i,B))) o9 = | -2*y^3+2*y*x*z-2*x*y*z+2*x^3 0 0 0 | | 0 -2*y^3+2*y*x*z-2*x*y*z+2*x^3 0 0 | | 0 0 -2*y^3+2*y*x*z-2*x*y*z+2*x^3 0 | | 0 0 0 -2*y^3+2*y*x*z-2*x*y*z+2*x^3 | o9 : NCMatrix i10 : assignDegrees(gId,{2,2,2,3},{5,5,5,6}); i11 : M' = gId // M --Calling Bergman for NCGB calculation. Complete! o11 = | -2*y*x 0 -2*y^2+2*x*z y*x*z+x^3 | | -x z -y y^2-x*z | | -y -x z y*z-x^2 | | z y x 0 | o11 : NCMatrix i12 : M*M' == gId o12 = true i13 :
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