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D.15.10.2 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]:
==>    _[1,1]=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
==> [2]:
==>    _[1,1]=-x(1)*x(3)
==>    _[2,1]=x(1)*x(2)
==> [3]:
==>    _[1,1]=x(2)*D(2)+1
==>    _[2,1]=x(1)*D(1)+2
==>    _[3,1]=-x(3)*D(3)-1
==> [4]:
==>    _[1,1]=0