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BigradedImplicit :: isGoodDegree

isGoodDegree -- verifies if the Z-complex is acyclic in the given degree



The list 'nu' needs to be a 'good degree' for the first parameter '{f0,...,fn}' that can be verified by doing isGoodDegree(polinomialList,nu)

isGoodDegree({f0,...,fn}, nu) verifies if the approximation complex Z associated to the polynomials given is acyclic in degree 'nu'

Given a list of polynomials {f_0,...,f_n}, the approximation complex of cycles is multigraded. This funtion verifies if the strand of degree 'nu' is acyclic.

Precisely, it computes the Euler characteristic of the nu-strand of the Z-complex, by computing the alternate sum of (-1)^i * hilbertFunction(nu+i*d,Z_i)

i1 : A=QQ[s,u,t,v,Degrees=>{{1,1,0},{1,1,0},{1,0,1},{1,0,1}}];
i2 : f0=s*t*u*v+t*u^2*v; f1=s*u*v^2; f2=u*t^2*s+u^2*t^2; f3=s^2*t*v+s*t*u*v;
i6 : isGoodDegree ({f0,f1,f2,f3},{2,1,1})

o6 = true

Ways to use isGoodDegree :