The list 'nu' needs to be a 'good degree' for the first parameter '{f0,...,fn}' that can be verified by doing isGoodDegree(polinomialList,nu)
degreeImplicitEq({f0,...,fn}, nu) computes the degree of the gcd of the maximal minors of the matrix representation of {f0,...,fn} in degree 'nu', equivalently, the degree of determinant of the Z-complex associated to {f0,...,fn} in degree 'nu'. This is:
degreeImplicitEq({f0,...,fn}, nu)=deg(representationMatrix({f0,...,fn},nu)=deg(det((Z(f0,...,fn))_nu))
Given a list of polynomials {f_0,...,f_n}, it computes the degree of the gcd of the maximal minors of the right-most map of the strand of degree 'nu'.
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 : degreeImplicitEq ({f0,f1,f2,f3},{2,1,1})
o6 = 3
|