FUNCTIONS

MAIN FUNCTIONS

  • cuspmake1 - set of inequivalent cusps for Gamma[1](N)
  • CUSPSANDWIDMAKE1 - set of inequivalent cusps for Gamma[1](N) with corresponding widths
  • cuspwid1 - cusp width in Gamma[1](N)
  • eeta - symbolic form eta(n*tau)
  • egeta - symbolic form eta[n,g](tau)
  • eta2geta - convert from ETA to eta notation
  • eta2jac - convert from ETA to JAC notation
  • _etan - symbolic form eta(n*tau)
  • _ETAn - a symbolic form for eta(n*tau) in terms of JAC
  • _etanm - symbolic form eta[n,m](tau)
  • _ETAnm - a symbolic form of generalized eta-function eta[n,m](tau) in terms of JAC
  • Gamma1ModFunc - Checks whether the generalized eta-quotient corresponding to the geta-list L is a modular function of Gamma[1](N)
  • getacuspord - order of generalized eta-product at a cusp
  • GETAP2getalist - Convert a quotient of generalized eta-products into a (geta)-list
  • getalist2jacprod - Convert a getalist to a jacprod
  • getaprodcuspORDS - ORD of generalized-etaproduct at each cusp
  • getaprodcuspord - invariant order of a generalized-etaproduct at a cusp
  • jac2eprod - Convert a quotient of theta-functions to generalize eta-products
  • jac2getacombo - Convert a linear combination of jacprods into a linear combination of getaprods (using standard eta-notation)
  • jac2getaprod - Convert a quotient of theta-functions to generalize eta-products using eta-notation
  • jacbase - q-base of a jacprod
  • jacnormalid - Renormalizes a sum of jacprods by dividing by the term with the lowest power of q.
  • JACP2jaclist - Convert a quotient of jacprods into a (jac)-list
  • jcombobase - q-base of a sum of jacprods jcombobase(jcombo)
  • mintotORDS - lower bound for sum of ORDS
  • mixedjac2jac - converts a sum of quotients of jacprods to a common base
  • numcuspequiv1 - Number of inequivalent cusps of of Gamma[1](N)
  • printJACIDORDStable - print a table of ORDS of a jacprod identity
  • processjacid - processes jacprod identity
  • provemodfuncid - prove theta-function identity
  • provemodfuncidBATCH - prove theta-function identity
  • thetaidschanges - recent changes in thetaids package
  • thetaidspversion - version of thetaids package

OTHER FUNCTIONS

  • Acmake - the set A[c]
  • Bord - Calculates a order of a theta-function at a cusp
  • cuspequiv1 - determines whether two cusps ate GAMMA[1](N)-equivalent
  • cuspsetinequiv1 - determine Gamma[1](N)-inequivalence of given set of cusps
  • DivCheck - Check certain divisor condition
  • ejac - used in jac2eprod
  • fpart - fractional part
  • gterm2jacprod - Convert list [b,a,c] to corresponding jacprod
  • JACCOF - constant 1
  • lqdegree - lowest degree in q
  • lqdegree0 - power of q in a q-monomial
  • newxy - Compute new x,y mod N
  • phiset - Relatively prime integers
  • qjacdegree - q-degree of a jacterm
  • QP2 - {x}^2 - {x} + 1/6
  • rmcofjac - Remove constant coefficient of a jacterm
  • rmcofnotqjac - Remove constant coefficient of a jacterm
  • Scmake - the set S[c]
  • srep -
  • sset -
  • v0 - 2*ORD(G,0)
  • vinf - 2*ORD(G,oo)

The url of this page is http://qseries.org/fgarvan/qmaple/thetaids/functions.html.
Created by F.G. Garvan (fgarvan@ufl.edu) on Thursday, July 25, 2013.
Last update made Wed Dec 31 12:48:07 PST 2014.

MAIL fgarvan@ufl.edu