FUNCTION: heralg[homol_blf] - the homological bilinear form of two dimension vectors of modules

CALLING SEQUENCE:
homol_blf(x,y,Q)

PARAMETERS:
x, y - vectors
Q - a quiver given by a quiverdata structure

SYNOPSIS:

• The function homol_blf(x,y,Q) applies the homological bilinear form of the path algebra of the quiver Q to the vectors x and y. This bilinear form is determined by the inverse of the Cartan matrix of the algebra. If x and y are dimension vectors of modules X and Y, the bilinear form gives the difference dim Hom (X,Y) - dim Ext¹(X,Y).

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

EXAMPLES:

> with(heralg):

> homol_blf( array([1,0]), array([0,1]), [2,[[1,2,r]]] );

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

> v := array([0,1,2]);

> w := array([3,3,4]);

> homol_blf(v,w,Q);