Polynomials relations between modular forms rings generators

This package contains certain utility functions that finds polynomials relations between the generators of the graded ring of modular forms for Gamma0(N).

EXAMPLE:

    sage: load("relations.sage")
    sage: M = ModularFormsRing(Gamma0(6))
    sage: relations(M, 4)
    [    1  2/11  1/11 -1/11     0     0]
    sage: f1,f2,f3,f4,f5,f6 = homogeneous_monomials_of_weight(M, 4)
    sage: (f1 + (2/11)*f2 + (1/11)*f3 - (1/11)*f4).is_zero()
    True

More relations can be found in the file result.txt.

Content of the repo:

• relations.sage: contains all the utility functions;
• script.sage: contains the script that execute the functions defined in relations.sage;
• result.txt: contains the result of the script computations.

After cloning this repo, if you only want to use the utility functions (and don't run the script), you should execute the following command in your SageMath session:

    sage: load('relations.sage')

This will only load the functions defined in relations.sage in your current session. To see the docstring of a given function, you can write name_of_function?.