# Singular          #### D.15.11.2 MVComplex

Procedure from library `deRham.lib` (see deRham_lib).

Usage:
MVComplex(L); L a list of polynomials

Assume:
-Basering is a polynomial ring with n vwariables and rational coefficients -L is a list of non-constant polynomials

Return:
ring W: the nth Weyl algebra
W contains a list MV, which represents the Mayer-Vietrois complex (C^i,d^i) of the polynomials contained in L as follows:
the C^i are given by D_n^ncols(C[2*i-1])/im(C[2*i-1]) and the differentials d^i are given by C[2*i]

Example:
 ```LIB "deRham.lib"; ring r = 0,(x,y,z),dp; list L=xy,xz; def C=MVComplex(L); setring C; MV; ==> : ==> _[1,1]=D(3) ==> _[1,2]=0 ==> _[2,1]=x(1)*D(1)+1 ==> _[2,2]=0 ==> _[3,1]=-x(2)*D(2)-1 ==> _[3,2]=0 ==> _[4,1]=0 ==> _[4,2]=D(2) ==> _[5,1]=0 ==> _[5,2]=x(1)*D(1)+1 ==> _[6,1]=0 ==> _[6,2]=-x(3)*D(3)-1 ==> : ==> _[1,1]=-x(1)*x(3) ==> _[2,1]=x(1)*x(2) ==> : ==> _[1,1]=x(2)*D(2)+1 ==> _[2,1]=x(1)*D(1)+2 ==> _[3,1]=-x(3)*D(3)-1 ==> : ==> _[1,1]=0 ```

### Misc 