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D.15.21.2 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";
==> // ** redefining `safeVarName` **
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
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