QEtaModularFormGenerators4ti2 F

qetamodformgens.spad line 204 [edit on github]

• F: with

  *: (%, %) -> %

  ^: (%, NonNegativeInteger) -> %

  maxIndex: () -> PositiveInteger

  qetaGrade: (%, PositiveInteger) -> Integer

QEtaModularFormGenerators4ti2(F) is a package that computes from a samba basis and a modular form a corresponding system of equations and inequations from which (when solved) one can extract the respective generators of modular forms.

modularFormGenerators: (F, F, List F) -> List List F

modularFormGenerators(f,t,bas) returns a the generators of the modular forms in two lists [li,lh] such that any modular form is a linear combination of the form $c*i + sum_{h in lh} ch*h$ for some constant coefficients c and ch and any i from li.

modularFormGenerators: (F, F, List F, Integer) -> List F

modularFormGenerators(f,t,bas,expof) returns a the generators of the modular forms of weight equal to expof*weight(f).

modularFormSolutions: (F, F, List F) -> Record(zinhom: List Vector Integer, zhom: List Vector Integer, zfree: List Vector Integer)

modularFormSystem(f,t,bas) computes from the orders of the expansions of the algebra basis and the orders of the respective t and an the orders of a modular form f a system and solves it via 4ti2's zsolve.

modularFormSolutions: (F, F, List F, Integer) -> Record(zinhom: List Vector Integer, zhom: List Vector Integer, zfree: List Vector Integer)

modularFormSystem(f,t,bas,expof) computes from the orders of the expansions of the algebra basis and the orders of the respective t and an the orders of a modular form f a systemand solves it via 4ti2's zsolve.