QEtaModularEquation(C, AnC)

qetamodeqn.spad line 88 [edit on github]

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 p by 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 d to 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 syms such that eval(pol,syms,gens)=0. It uses (up to) 4 numbers given by the list d to 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 syms such that eval(pol,syms,gens)=0. It uses (up to) 4 numbers given by the list d to 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]).