FUNCTION : printtype6 - print of Type 6 identity
CALLING SEQUENCE : printtype6(L, EQNNAME, num, nL)
PARAMETERS : L - list [a,p,c1,N,B]
num - positive integer (no. of identity found by findtype6)
nL - number of identities
GLOBAL VARIABLES : _F
SYNOPSIS :
Prints identity for
G(a) H*(p) + c1 G*(a) H(p)
with equation number (eqn.num)
EXAMPLES :
> with(qseries):
> with(thetaids):
> with(ramarobinsids):
> G:=j->1/GetaL([1],12,j): H:=j->1/GetaL([5],12,j):
> GM:=j->1/MGetaL([1],12,j): HM:=j->1/MGetaL([5],12,j):
> GE:=j->-GetaLEXP([1],12,j): HE:=j->-GetaLEXP([5],12,j):
> proveit:=true: xprint:=false:
> findtype6(6);
*** There were NO errors. Each term was modular function on
Gamma1(24). Also -mintotord=4. To prove the identity
we need to check up to O(q^(6)).
To be on the safe side we check up to O(q^(52)).
*** The identity below is PROVED!
[1, 1, -1]
3 2 2
2 eta(24 tau) eta(6 tau) eta(4 tau)
_G(1) _HM(1) - _GM(1) _H(1) = --------------------------------------
5
eta(12 tau) eta(8 tau) eta(2 tau)
*** There were NO errors. Each term was modular function on
Gamma1(24). Also -mintotord=4. To prove the identity
we need to check up to O(q^(6)).
To be on the safe side we check up to O(q^(52)).
*** The identity below is PROVED!
[1, 1, 1]
2
2 eta(24 tau) eta(8 tau) eta(6 tau) eta(4 tau)
_G(1) _HM(1) + _GM(1) _H(1) = -----------------------------------------------
4
eta(12 tau) eta(2 tau)
WARNING: There were 8 ebasethreshold problems.
See the global array EBL.
[[1, 1, -1], [1, 1, 1]]
> L:=PROVEDFL6[1];
L := [1, 1, -1, 24, -4]
> printtype6(L,3, 5);
3 2 2
2 eta(24 tau) eta(6 tau) eta(4 tau)
G(1) H*(1) - G*(1) H(1) = --------------------------------------, Gamma[1](24),
5
eta(12 tau) eta(8 tau) eta(2 tau)
-B = 4, (3.5)
DISCUSSION :
SEE ALSO :
findtype6,
printtype1, printtype2, printtype3, printtype4,
printtype5, printtype6, printtype7, printtype8,
printtype9, printtype10, printtypelist