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7.5.23.0. doubleExt
Procedure from library purityfiltration.lib (see purityfiltration_lib).
- Usage:
- doubleExt(R,i), R matrix representing the left Module M=D^p/D^q(R^t) over a ring D
int i, less or equal the left projective dimension of M
- Return:
- matrix P, representing the double ext module
- Purpose:
- computes a matrix P, which represents the left module ext^i(ext^i(M,D))
Example:
| | LIB "purityfiltration.lib";
ring D = 0,(x,y,z),dp;
matrix R[7][3]=
0 ,0,1,
1 ,-4*x+z,-z,
-1,8*x-2*z,z,
1 ,0 ,0,
0 ,x-y,0,
0 ,x-y,y,
0 ,0 ,x;
// coker(R) is 2-pure, so all doubleExt are zero
print(doubleExt(transpose(R),0));
==> 1
print(doubleExt(transpose(R),1));
==> 1,0,0,
==> 0,1,0,
==> 0,0,1
print(doubleExt(transpose(R),3));
==> 1
// except of the second
print(doubleExt(transpose(R),2));
==> 4y-z,4x-z
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