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7.5.17.0. allExtOfLeft
Procedure from library purityfiltration.lib (see purityfiltration_lib).
- Usage:
- allExtOfLeft(M),
- Return:
- list, entries are ext-modules
- Assume:
- M presents a left module of finite left projective dimension n
- Purpose:
- For a left module presented by M over the basering D,
compute a list T, whose entry T[i+1] is a matrix, presenting the right module Ext^i_D(M,D) for i=0..n
Example:
| | LIB "purityfiltration.lib";
ring D = 0,(x,y,z),dp;
matrix R[6][4]=
0,-2*x,z-2*y-x,-1,
0,z-2*x,2*y-3*x,1,
z,-6*x,-2*y-5*x,-1,
0,y-x,y-x,0,
y,-x,-y-x,0,
x,-x,-2*x,0;
// coker(R) consider the left module M=D^6/D^4R
list T=allExtOfLeft(transpose(R));
print(T[1]);
==> 0
print(T[2]);
==> 1,0,0,
==> 0,1,0,
==> 0,0,1
print(T[3]);
==> 0,0, z,4y-z,4x-z,
==> 0,-2,1,0, 0,
==> 1,0, 0,0, 0,
==> 0,1, 0,0, 0
print(T[4]);
==> z,y,x
// right modules coker(T[i].)!!
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