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Matrix Groups Over Z
and Q
The intrinsics described in this section have been implemented by Marcus
Kirschmer (Aachen) unless noted otherwise.
New Features:
- Given a matrix A
of finite order in
GL(n,Z)
, a much improved
algorithm is used to implement the intrinsic CentralizerGLZ(A
)
which computes the centralizer of A
in
GL(n,Z)
.
- The intrinsic CentralizerGLZ(A
)) may now be used to compute the
centraliser of a matrix A
in
GL(2,Z)
, when A
has infinite order.
The algorithm and code was developed by D. Husert (University of Paderborn).
- A new intrinsic IsGLZConjugate(A, B)
tests whether two rational
or integral matrices A
and B
having finite order are conjugate in
GL(n,Z)
or
SL(n,Z)
.
- The intrinsic IsGLZConjugate(A, B)
may be used to test conjugacy
of matrices A
and B
in
GL(2,Z)
, when A
and B
have infinite order.
The method and code are due to D. Husert.
- Given a finite subgroup G
of
GL(n,Z)
, a much improved algorithm is
used to implement the intrinsic NormalizerGLZ(G)
which computes the
normalizer of G
in
GL(n,Z)
.
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