This function computes a minimal graded free resolution of the cokernel of M, considered as a map of graded right free modules. M must be homogeneous for this command to work.
As of this version, NCChainComplex (the return type) is still quite simple, though betti still works on them.
i1 : A = skewPolynomialRing(QQ,(-1)_QQ,{x,y,z}) --Calling Bergman for NCGB calculation. Complete! o1 = A o1 : NCQuotientRing |
i2 : M = ncMatrix {{x,y,z}} o2 = | x y z | o2 : NCMatrix |
i3 : Mres = res M --Calling Bergman for NCGB calculation. Complete! --Calling Bergman for NCGB calculation. Complete! --Calling Bergman for NCGB calculation. Complete! 1 3 3 1 o3 = A <-- A <-- A <-- A 0 1 2 3 o3 : NCChainComplex |
i4 : Mres#0 o4 = | x y z | o4 : NCMatrix |
i5 : Mres#1 o5 = | 0 -z -y | | -z 0 -x | | -y -x 0 | o5 : NCMatrix |
i6 : Mres#2 o6 = | -x | | -y | | -z | o6 : NCMatrix |
i7 : betti Mres 0 1 2 3 o7 = total: 1 3 3 1 0: 1 3 3 1 o7 : BettiTally |