FUNCTION: heralg[perp_cm] - the Cartan matrix of the algebra corresponding to the right perpendicular category of a module

CALLING SEQUENCE:
perp_cm(x, Q)

PARAMETERS:
x - a vector
Q - a quiver given by a quiverdata structure

SYNOPSIS:

• The function perp_cm(x, Q) uses the function perpgen (also part of the heralg package) to compute the Cartan matrix of the quiver algebra corresponding to the right perpendicular category of the module of dimension vector x over the path algebra of the quiver Q. This module must be an exceptional module, i.e. an indecomposable module without self extensions.

• The algorithm uses a simple heuristic which will fail if the module considered is a tau-sincere regular module (or too far away from a non sincere, projective or injective module).

• This function is part of the heralg package, and so can be used in the form perp_cm(..) only after performing the command with(heralg) or with(heralg, perp_cm). The function can always be accessed in the long form heralg[perp_cm](..).

EXAMPLES:

> with(heralg):

> perp_cm(array([4,5,0]), [3,[[2,1,2],[3,2]]]);

> Q:= [ 4, [[2,1], [3,1], [3,2], [4,3]]];

> x := array( [ 9,6,6,2 ] );

> perp_cm(x,Q);