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 inp
by the series represented byc
. Sloppyly: evaluate(p
,c
) computesp
(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 listd
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 bysyms
such that eval(pol,syms
,gens
)=0
. It uses (up to) 4 numbers given by the listd
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 bysyms
such that eval(pol,syms
,gens
)=0
. It uses (up to) 4 numbers given by the listd
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]).