SymbolicEtaQuotientGamma

qetasymb.spad line 545 [edit on github]

SymbolicEtaQuotientGamma holds data to compute an eta quotient expansion of $p_{{bar{r},m,t}(gamma tau)$. See eqref{eq:p_r-m-t(gamma*tau)} and eqref{eq:p_rbar-m-t(gamma*tau)}.

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm

from CoercibleTo OutputForm

definingSpecification: % -> QEtaSpecification

If x=etaQuotient(spec,m,t,gamma), then definingSpecification(x) returns purify(spec).

elt: (%, NonNegativeInteger) -> SymbolicEtaQuotientLambdaGamma

x.lambda returns the data corresponding to the respective lambda.

etaQuotient: (QEtaSpecification, Matrix Integer) -> %

etaQuotient(rspec, gamma) returns etaQuotient(rspec,1,0,gamma).

etaQuotient: (QEtaSpecification, PositiveInteger, NonNegativeInteger, Matrix Integer) -> %

etaQuotient(rspec, m, t, gamma) represents the expansion of $p_{bar{r},m,t}(gamma tau)$ where $bar{r}$ is given by rspec.

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

latex: % -> String

from SetCategory

minimalRootOfUnity: % -> PositiveInteger

minimalRootOfUnity(x) returns the smallest positive integer n such that the expansion of the function $p_{r,m,t}(gammatau)$ corresponding to x=etaQuotient(mm,divs,r,m,t,gamma) (neglecting the (c*tau+d)^* factor) lives in Q[w][[z]] where w is a n-th root of unity and z a fractional q power.

multiplier: % -> PositiveInteger

If x=etaQuotient(spec,m,t,gamma), then multiplier(x) returns m.

offset: % -> NonNegativeInteger

If x=etaQuotient(spec,m,t,gamma), then offset(x) returns t. offset(x) returns the subsequence offset.

one?: % -> Boolean

one?(x) returns true if the eta-quotient corresponding to x represents 1. This is the case if one?(specification(x)), i.e. if the representation is trivial.

qExponentMin: % -> Fraction Integer

qExponentMin(x) returns the order of the q-expansion in terms of the original q. Note that this exponent is only a lower bound for the q-expansion. The coefficient corresponding to this q-power may be zero.

transformationMatrix: % -> Matrix Integer

If x=etaQuotient(spec,m,t,gamma), then transformationMatrix(x) returns gamma.

unityExponent: % -> Fraction Integer

If x=etaQuotient(spec,m,t,gamma), then unityExponent(x) returns -(24*t + hat{r})/(24*m).

BasicType

CoercibleTo OutputForm

SetCategory