FUNCTION: heralg[tau_translate] - the Coxeter transformation of the dimension vector of a module

CALLING SEQUENCE:
tau_translate(x,t,Q)

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

SYNOPSIS:

• The function tau_translate(x,t,Q) applies the t'th power of the Coxeter matrix of the path algebra of the quiver Q to the vector x. Applying the Coxeter matrix to the dimension vector of a module without projective direct summand yields the dimension vector of the Auslander-Reiten translate of this module.

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

EXAMPLES:

> with(heralg):

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

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

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

> tau_translate(v,1,Q);