FUNCTION: tubetest - test for tubular extensions of E^~_n

CALLING SEQUENCE:
tubetest(p)
tubetest(p,sap)
tubetest(p,sap,tc)

PARAMETERS:
p - a bound poset algebra
sap, tc - optional arguments evaluating to a name

SYNOPSIS:

• tubetest tests whether the bound poset algebra p is a tubular extension of a tame concealed algebra of type E^~_n. If so, the function returns the tubular type of the algebra, else the value 'false'.

• Testing is done in several steps. The results of the intermediary steps can be obtained via the optional arguments sap and tc.

• In case p is a branch extension over the support algebra of the postprojective component of p, this support algebra will be returned via the optional argument sap. (Otherwise, if an optionl argument ist given, sap will get the value 'false'.)

• Also, in case p is a branch algebra over the support algebra of the postprojective component of p, the optional argument tc will tell whether this support algebra is tame concealed of type E^~_n.

EXAMPLES:

> p:=[8,{[1,2,3,4],[2,5,8],[3,6,8],[4,7,8]}];

> tubetest(p,'sap','tc');

> print(sap);

> iscriticale(sap);

-----------------------------------------------------------------------------

> p:=[8,{[1,2,3],[2,4],[3,4],[5,2],[6,3],[7,4],[2,8]},{[6,8],[7,8]}];

> tubetest(p,'sap','tc');

> print(sap);

> print(tc);

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> p:=[10,{[1,2,3,4],[2,5,8],[3,6,8],[4,7,8],[8,9,10]}];

> tubetest(p,'sap','tc');

> print(sap);