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