FUNCTION : CHECKRAMIDF - checks whether an expression in terms of G, H
is a likely etaproduct
CALLING SEQUENCE : CHECKRAMIDF(SYMF,ACC,T)
PARAMETERS : SYMF - symbolic expression in _G, _H
ACC - integer
T - integer
GLOBAL VARIABLES: S,S2,_JFUNC,LDQ,RID,SYMID,
qthreshold,proveit,ebasethreshold,ebtprob,
EBL,PL,CHECKSYMF
SYNOPSIS :
The functions G,H,GM,HM must be defined before CHECKRAMIDF can be used.
CHECKRAMIDF(SYMF,ACC,T) determines whether SYMF is a likely etaproduct.
Here ACC is max abs value of exponents in the formal product. T
is the largest power of q tested.
If suspects an etaproduct a list of exponents is returned, otherwise
NULL is returned.
EXAMPLES :
> with(qseries):
> with(thetaids):
> with(ramarobinsids):
> G:=j->1/GetaL([1],10,j):H:=j->1/GetaL([3],10,j):
> GM:=j->1/MGetaL([1],10,j): HM:=j->1/MGetaL([3],10,j):
> SYMID1:=_G(6)*_H(1)-_G(1)*_H(6);
_G(6) _H(1) - _G(1) _H(6)
> CHECKRAMIDF(SYMID1,10,100);
[0, 0, 0, 1, 1, -1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0,
0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0,
-1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 1, 0, -1, 1, 1, 0, 0, 0, 0, 0,
0, 0, 1, 1, -1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 1, 0, -1, 0]
> series(jac2series(_JFUNC,200)*q^(25/12),q,200):
> etamake(%,q,60);
(25/12) 3
q eta(30 tau) eta(12 tau) eta(5 tau) eta(4 tau)
-------------------------------------------------------
2 2
eta(60 tau) eta(15 tau) eta(10 tau) eta(6 tau)
EXAMPLES :
It seems that when G(1)=1/eta[10,1](tau), H(1)=1/eta[10,3](tau)
G(6)H(1) - G(1)H(6) is an eta-product.
SEE ALSO :