QEtaModularEquationPrimeField(C, trfs)¶

qetamodeqn.spad line 298 [edit on github]

C: Field with

coerce: Integer -> %

convert: % -> Integer
trfs: List Matrix Integer

QEtaModularEquationPrimeField computes a modular polynomial with coefficients in ZZ of two functions with coefficients in C. It does so by projecting the series coefficients down to a prime field C=PrimeField(p) for a given prime and then computing the polynomial in C. Eventually, the coefficients are lifted back to ZZ.

modularPolynomial: (ModularFunctionQSeries(Fraction Integer, trfs), ModularFunctionQSeries(Fraction Integer, trfs)) -> Polynomial Integer: modularPolynomial(x,y) returns modularPolynomial(x,y,[]).

modularPolynomial: (ModularFunctionQSeries(Fraction Integer, trfs), ModularFunctionQSeries(Fraction Integer, trfs), List NonNegativeInteger) -> Polynomial Integer: modularPolynomial(x,y,d) computes a nonzero polynomial pol such that pol(x,y) is zero when considered over C. It uses (up to) 4 numbers given by the list d to print intermediate debugging. The valuse are given to oneVerboseStep!.

modularPolynomial: (ModularFunctionQSeriesConstructor(Fraction Integer, QEtaTruncatedLaurentSeries Fraction Integer, trfs), ModularFunctionQSeriesConstructor(Fraction Integer, QEtaTruncatedLaurentSeries Fraction Integer, trfs)) -> Polynomial Integer: modularPolynomial(x,y) returns modularPolynomial(x,y,[]).

modularPolynomial: (ModularFunctionQSeriesConstructor(Fraction Integer, QEtaTruncatedLaurentSeries Fraction Integer, trfs), ModularFunctionQSeriesConstructor(Fraction Integer, QEtaTruncatedLaurentSeries Fraction Integer, trfs), List NonNegativeInteger) -> Polynomial Integer: modularPolynomial(x,y,d) computes a polynomial pol such that pol(x,y) is zero when considered over C. It uses (up to) 4 numbers given by the list d to print intermediate debugging. The valuse are given to oneVerboseStep!.

project: ModularFunctionQSeries(Fraction Integer, trfs) -> ModularFunctionQSeries(C, trfs): project(x) maps the coefficients of x from QQ to C.

project: ModularFunctionQSeries(Integer, trfs) -> ModularFunctionQSeries(C, trfs): project(x) maps the coefficients of x from ZZ to C.

project: ModularFunctionQSeriesConstructor(Fraction Integer, QEtaTruncatedLaurentSeries Fraction Integer, trfs) -> ModularFunctionQSeriesConstructor(C, QEtaTruncatedLaurentSeries C, trfs): project(x) maps the coefficients of x from QQ to C.

project: ModularFunctionQSeriesConstructor(Integer, QEtaTruncatedLaurentSeries Integer, trfs) -> ModularFunctionQSeriesConstructor(C, QEtaTruncatedLaurentSeries C, trfs): project(x) maps the coefficients of x from ZZ to C.