QEtaModularEquation(C, AnC)¶
qetamodeqn.spad line 88 [edit on github]
- C: Field 
- AnC: QEtaPowerGradedAlgebra C 
QEtaModularEquation computes a modular polynomial with coefficients in ZZ of two functions with coefficients in C.
- evaluate: (SparseUnivariatePolynomial C, CachedPower AnC) -> AnC
- evaluate(p,c)replace the variable in- pby the series represented by- c. Sloppyly: evaluate(- p,- c) computes- p(- c).
- modularPolynomial: (AnC, AnC) -> Polynomial Integer if C has convert: C -> Integer
- modularPolynomial(x,y)returns modularPolynomial(- x,- y,[]).
- modularPolynomial: (AnC, AnC, List NonNegativeInteger) -> Polynomial Integer if C has convert: C -> Integer
- modularPolynomial(x,y,d)computes a nonzero polynomial pol such that pol(- x,- y) is zero. It uses (up to) 4 numbers given by the list- dto print intermediate debugging. The valuse are given to oneVerboseStep!.
- modularPolynomial: (List AnC, List Symbol) -> Polynomial C
- modularPolynomial(gens,syms)returns modularPolynomial(- gens,- syms,[]).
- modularPolynomial: (List AnC, List Symbol, List NonNegativeInteger) -> Polynomial C
- modularPolynomial(gens,syms,d)assumes that #gens=2=#syms and computes a nonzero polynomial pol in the variables given by- symssuch that eval(pol,- syms,- gens)- =0. It uses (up to) 4 numbers given by the list- dto print intermediate debugging. The valuse are given to oneVerboseStep!.
- modularPolynomial: List AnC -> Polynomial C
- modularPolynomial(gens)returns modularPolynomial(- gens,[“x”::Symbol,”y”::Symbol]).
- modularPolynomialCached: (AnC, AnC) -> Polynomial Integer if C has convert: C -> Integer
- modularPolynomialCached(x,y)returns modularPolynomialCached(- x,- y,[]).
- modularPolynomialCached: (AnC, AnC, List NonNegativeInteger) -> Polynomial Integer if C has convert: C -> Integer
- modularPolynomialCached(x,y,d)returns modularPolynomialCached(- x,- y,[“x”::Symbol,,”y”::Symbol],- d).
- modularPolynomialCached: (AnC, AnC, List Symbol, List NonNegativeInteger) -> Polynomial Integer if C has convert: C -> Integer
- modularPolynomialCached(x,y,syms,d)computes modularPolynomialCached([- x,- y],- syms,- d) and lifts the polynomial into a polynomial with integer coefficients.
- modularPolynomialCached: (List AnC, List Symbol) -> Polynomial C
- modularPolynomialCached(gens,syms)returns modularPolynomialCached(- gens,- syms,[]).
- modularPolynomialCached: (List AnC, List Symbol, List NonNegativeInteger) -> Polynomial C
- modularPolynomialCached(gens,syms,d)assumes that #gens=2=#syms and computes a nonzero polynomial pol in the variables given by- symssuch that eval(pol,- syms,- gens)- =0. It uses (up to) 4 numbers given by the list- dto print intermediate debugging. The valuse are given to oneVerboseStep!. It caches the intermediate products of the computation.
- modularPolynomialCached: List AnC -> Polynomial C
- modularPolynomialCached(gens)returns modularPolynomialCached(- gens,[“x”::Symbol,”y”::Symbol]).