# representationMatrix -- computes the right-most map of the Z-complex in degree nu)

## Synopsis

• Usage:
repMatrix = representationMatrix(polynomialList, nu)
• Inputs:
• polynomialList, a list, polynomialList 'f={f0,...,fn}' defining the rational map
• nu, a list, the multidegree where ti take the homogeneous strand of the map f (i.e.: R_d)
• Outputs:
• repMatrix, , a matrix of linear functions in QQ[X_0,...,X_n] defining a representation Matrix of f

## Description

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

representationMatrix({f0,...,fn},nu) computes the right-most map of the Z-complex in degree nu. Its determinant vanishes on the implicit equation of the image of the map given by (f0:...:fn) in P^n

 `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```