• In dealing with graded sheaf theory TUBULAR uses several specific data formats:

• Elements of the grading group Lp are encoded as lists of t+1 integers (t=number of weights); with operations of Lp defined.

• Elements of K₀X are internally coded as vectors of Z^N (where N = `N$` equals the Z-rank of K₀X.) - For the convenience of the user however, the datatype "quiver" has been introduced: Using "show" instead of "print" allows to visualize classes in a "canonical algebra" shape (Cf. to help page for show . Several operations such as grade shifts, coxeter transformation, euler characteristic are user-accessible with arguments as well as results being entered using datatype "quiver". The user has the option to encode each class with respect to three different "canonical" bases: (Lambda denotes the canonical algebra corresponding to the entered weight sequence.)
  • the basis `@O` of indec. projective Lambda-modules:
    
    O, O(x₁),O(2x₁),..,O((p₁-1)x₁), ... , O(x_t),..,O((p_t-1)x_t), O(c)
    
    
  • the basis `@E` of simple Lambda-modules:
    
    chosen subject to the same order as for the indec. projective Lambda-modules above, where each indec. projective module is replaced by the corresponding(!) simple module.
    
    
  • the "simple sheaves" basis `@S`:
    
    O, S_1,1,S_1,2,..,S_1,p1-1, ... , S_t,1,..,S_t,pt-1, S
    
    where S_i,j denotes the cokernel of O(j x_i) ---> O((j+1)x_i) .

• For the t u b u l a r canonical algebras there is a special datatype "tub_enc" encoding objects with respect to the tubular family and their position within it; one of the central aspects of the TUBULAR package is the conversion between this data type and ordinary class representation "quiver" described above.

SEE ALSO: tubular/Lp, show, change, enter, get_class, get_tub