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D.11.2.13 findTorsion
Procedure from library control.lib (see control_lib).
- Usage:
- findTorsion(R, I); R an ideal/matrix/module, I an ideal
- Return:
- module
- Purpose:
- computes the Groebner basis of the submodule of R, annihilated by I
- Note:
- especially helpful, when I is the annihilator of the t(R) - the torsion submodule of R. In this case, the result is the explicit presentation of t(R) as
the submodule of R
Example:
| | LIB "control.lib";
// Flexible Rod
ring A = 0,(D1, D2), (c,dp);
module R= [D1, -D1*D2, -1], [2*D1*D2, -D1-D1*D2^2, 0];
module RR = transpose(R);
list L = control(RR);
// here, we have the annihilator:
ideal LAnn = D1; // = L[10]
module Tr = findTorsion(RR,LAnn);
print(RR); // the module itself
==> D1, -D1*D2, -1,
==> 2*D1*D2,-D1*D2^2-D1,0
print(Tr); // generators of the torsion submodule
==> 0,
==> 1
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