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Conjugacy Tests for Matrices

Given two n x n matrices A and B with rational or integral entries, Magma can test whether A is conjugate to B in GLn(Z).

Currently, the implementation is limited to the cases where A, B have finite order or where n=2. This limitation will be removed in future versions.

IsGLZConjugate(A, B) : AlgMatElt, AlgMatElt -> BoolElt, GrpMatElt
IsGLZConjugate(A, B) : GrpMatElt, GrpMatElt -> BoolElt, GrpMatElt
IsSLZConjugate(A, B) : AlgMatElt, AlgMatElt -> BoolElt, GrpMatElt
IsSLZConjugate(A, B) : GrpMatElt, GrpMatElt -> BoolElt, GrpMatElt
Tests whether two rational or integral matrices A and B are conjugate in GLn(Z) or SLn(Z). If so, a matrix x such that Ax = B is also returned.
CentralizerGLZ(A) : AlgMatElt -> GrpMat
CentralizerGLZ(A) : GrpMatElt -> GrpMat
Given a rational or integral matrix A, this function returns its centralizer in GLn(Z). The current implementation is limited to the cases where either A has finite order or A is a 2 x 2 matrix.
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Version: V2.19 of Mon Dec 17 14:40:36 EST 2012