• Computes the dataset (cf. help page for type/tub_enc) for a given K₀ X -class of type quiver, representing an indecomposable sheaf.

• is only defined for one of the tubular weight-sequences, i.e. (2,3,6), (3,3,3), (2,2,2,2) and (2,4,4).

• get_tub(f) returns the dataset encoding the relevant tubular data for the given Grothendieck-class, in terms of the type "tub_enc". In a certain sense it is the "inverse" to the procedure "get_class".

• However, it is also possible to apply "get_tub" to some K₀ X class of type quiver which has been entered directly using "enter" (cf. one of the examples below).

• Note that any class in K₀ X representing an indecomposable sheaf must neccessarily be a positive root of the quadratic form induced by the Euler-characteristic, or lie in the radical.

• If f is a positive root, then its encoding with rescpect to the tubular structure will be computed, and the result of type "tub_enc" will be returned.

• If f is positive lying in the radical, then a continuous family of sheaves (parametrized over X) will be mapped to the class f. In that case (cf. to the second example given below), in the encoding corresponding to the type "tub_enc" the expression "cont" will replace the second entry (normally indicating the tube-number), and the third entry (quasi-socle-index) will be set to zero. The quasi-length l given in the fourth entry will refer to a sheaf (with K₀ class f) lying in a string tube. Please note that in this case in each exceptional tube of rank pi there will be pi indecomposable sheaves of quasi-length pi*l which are also represented by the class f in K₀ X.

SEE ALSO: show, enter, telescope, get_class, type/tub_enc