Function: qfauto
Section: linear_algebra
C-Name: qfauto0
Prototype: GDG
Help: qfauto(G,{fl}): automorphism group of the positive definite quadratic
form G.
Doc:
$G$ being a square and symmetric matrix with integer entries representing a
positive definite quadratic form, outputs the automorphism group of the
associate lattice.
Since this requires computing the minimal vectors, the computations can
become very lengthy as the dimension grows. $G$ can also be given by an
\kbd{qfisominit} structure.
See \kbd{qfisominit} for the meaning of \var{fl}.
The output is a two-components vector $[o,g]$ where $o$ is the group order
and $g$ is the list of generators (as a vector). For each generator $H$,
the equality $G={^t}H\*G\*H$ holds.
The interface of this function is experimental and will likely change in the
future.
This function implements an algorithm of Plesken and Souvignier, following
Souvignier's implementation.
Variant: The function \fun{GEN}{qfauto}{GEN G, GEN fl} is also available
where $G$ is a vector of \kbd{zm} matrices.