FUNCTION : jacnormalid - Renormalizes a sum of jacprods by dividing by the
term with the lowest power of q.
CALLING SEQUENCE : jacnormalid()
jacnormalid(jcombo)
PARAMETERS : jcombo - sum of jacprods
SYNOPSIS :
Renormalizes a sum of jacprods by dividing by the term with the lowest
power of q. In the event of a tie it returns term with the lowest
nops.
EXAMPLES :
> with(qseries):
> with(thetaids):
> jacnormalid();
-------------------------------------------------------------
jacnormalid(jcombo)
Renormalizes a sum of jacprods by dividing by the term
with the lowest power of q.
-------------------------------------------------------------
> E:=n->etaq(q,n,500):
> f:=(a,b,T)->add(a^(j*(j+1)/2)*b^(j*(j-1)/2),j=-T..T):
> CHOIID1:=E(4)^2*E(10)^4*E(20)/E(2)/E(5)^2/E(8)/f(-q^2,-q^18,20)
/f(-q^16,-q^24,20)
-( E(5)*E(10)*f(-q^4,-q^6,20)/f(-q^2,-q^3,20)/f(-q^2,-q^8,20)
-q^3*subs(q=-q^20,E(1))*E(40)*f(-q^8,-q^32,20)/f(q^4,-q^16,20)
/f(-q^16,-q^24,20)
+q^6*E(40)*E(80)*f(-q^8,-q^32,20)/f(-q^16,-q^24,20)
/f(-q^32,-q^48,20)):
> JJ:= qs2jaccombo(CHOIID1,q,200);
9
JJ := JAC(0, 40, infinity) JAC(4, 40, infinity) JAC(10, 40, infinity)
/JAC(20, 40, infinity)\3/2 /
JAC(12, 40, infinity) |---------------------| / (
\JAC(0, 40, infinity) / /
2 2
JAC(2, 40, infinity) JAC(5, 40, infinity) JAC(6, 40, infinity)
2
JAC(14, 40, infinity) JAC(15, 40, infinity) JAC(16, 40, infinity)
3
2 JAC(0, 10, infinity) JAC(4, 10, infinity) 3
JAC(18, 40, infinity) ) - ------------------------------------------ + q
2
JAC(2, 10, infinity) JAC(3, 10, infinity)
2
JAC(4, 80, infinity) JAC(0, 80, infinity) JAC(32, 80, infinity)
/JAC(40, 80, infinity)\1/2 /
JAC(36, 80, infinity) |---------------------| / (
\JAC(0, 80, infinity) / /
2 2
JAC(16, 80, infinity) JAC(24, 80, infinity) ) -
6 2 /JAC(40, 80, infinity)\1/2
q JAC(8, 80, infinity) JAC(0, 80, infinity) |---------------------|
\JAC(0, 80, infinity) /
------------------------------------------------------------------------
JAC(16, 80, infinity) JAC(24, 80, infinity)
> JJ2:=jacnormalid(JJ);
2 9
JJ2 := - JAC(2, 10, infinity) JAC(3, 10, infinity) JAC(0, 40, infinity)
JAC(4, 40, infinity) JAC(10, 40, infinity) JAC(12, 40, infinity)
/JAC(20, 40, infinity)\3/2 / 3
|---------------------| / (JAC(0, 10, infinity) JAC(4, 10, infinity)
\JAC(0, 40, infinity) / /
2 2
JAC(2, 40, infinity) JAC(5, 40, infinity) JAC(6, 40, infinity)
2
JAC(14, 40, infinity) JAC(15, 40, infinity) JAC(16, 40, infinity)
2 2
JAC(18, 40, infinity) ) + 1 - JAC(2, 10, infinity) JAC(3, 10, infinity)
3 2
q JAC(4, 80, infinity) JAC(0, 80, infinity) JAC(32, 80, infinity)
/JAC(40, 80, infinity)\1/2 /
JAC(36, 80, infinity) |---------------------| / (
\JAC(0, 80, infinity) / /
3 2
JAC(0, 10, infinity) JAC(4, 10, infinity) JAC(16, 80, infinity)
2 2 6
JAC(24, 80, infinity) ) + JAC(2, 10, infinity) JAC(3, 10, infinity) q
2 /JAC(40, 80, infinity)\1/2 /
JAC(8, 80, infinity) JAC(0, 80, infinity) |---------------------| /
\JAC(0, 80, infinity) / /
3
(JAC(0, 10, infinity) JAC(4, 10, infinity) JAC(16, 80, infinity)
JAC(24, 80, infinity))
SEE ALSO : jac2eprod, jac2getaprod, jac2getaprod