QEtaModularLambdaTools CΒΆ
qetamodlambdatool.spad line 198 [edit on github]
QEtaModularLambdaTools provides functions for working with the modular lambda function.
- applyLambdaTransformation: (Matrix Integer, Fraction SparseUnivariatePolynomial C) -> Fraction SparseUnivariatePolynomial C
- By https://fungrim.org/entry/099301/ we can easily get the expansion of the modular lambda function at any cusp/transformation. applyLambdaTransformation( - g,- rf) replaces the variable of- rfby the respective rational function expression according to the transformation matrix- g.
- evalAtModularLambda: Fraction SparseUnivariatePolynomial C -> QEtaLaurentSeries C if C has Field
- evalAtModularLambda(rf)replaces the variable of- rfwith modularLambda() from the QFunctions package. The function caches its result.
- evalAtModularLambda: SparseUnivariatePolynomial C -> QEtaLaurentSeries C
- evalAtModularLambda(pol)replaces the variable of- polwith modularLambda() from the QFunctions package. The function caches its results.
- transformAtModularLambda: (Fraction SparseUnivariatePolynomial C, Matrix Integer, Matrix Integer, Fraction Integer) -> QEtaLaurentSeries C if C has Field
- transformAtModularLambda(r,g,t,w)returns the series $- r(lambda(- g(- ttau)))$ expressed in the variable $- q^{frac{1}{- w}}$ where $- q=exp(pi- itau)$ and $- t$ is the transformation $taumapstofrac{atau}{- d}$ for some integers $a$ and $- d$.