FUNCTION: pst_alg - convert intermediary format into a (bound) poset algebra

CALLING SEQUENCE:
pst_alg(a)

PARAMETERS:
a - an algebra given by get_alg intermediary format

SYNOPSIS:

• The function pst_alg forces an algebra a given in the intermediary format as used by the function get_alg into the format of a bound poset algebra.

• The format conversion is done by first interpreting the quiver a[quiver] as the Hasse diagram of a poset. For this the quiver has to be directed. Should this not be the case, the results are bound to be strange.

• Only such relations contained in the data structure of the argument a are taken into account that consist of a single path. Linear combinations of more than one path are ignored. The single paths then are imposed upon the posetalgebra as zero relations.

• In the data structure for a posetalgebra, commutativity relations are implicit. Thus when using the functions get_alg and pst_alg together for input of a (bound) poset algebra, no commutativity relations need to be specified.

EXAMPLES:

> a:=get_alg(): # interactive input via the get_alg interface

> a[quiver];

> a[relations];

> p:=pst_alg(a);