FUNCTION : jac2getacombo - Convert a linear combination of jacprods into
a linear combination of getaprods (using
standard eta-notation)
CALLING SEQUENCE : jac2getacombo()
jac2getacombo(jcombo)
PARAMETERS : jcombo - sum of jacprods
SYNOPSIS :
This function uses jac2getaprod to convert a linear combination of jacprods
into a linear combination of getaprods (using standard eta-notation)
EXAMPLES :
> with(thetaids):
> with(qseries):
> jac2getacombo();
-------------------------------------------------------------
jac2getacombo(JJ)
This function converts a combination of jacprods into a
combination of getaprods.
-------------------------------------------------------------
> 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);
15/2
JJ := JAC(0, 40, infinity) JAC(4, 40, infinity) JAC(10, 40, infinity)
3/2 / 2
JAC(12, 40, infinity) JAC(20, 40, infinity) / (JAC(2, 40, infinity)
/
2
JAC(5, 40, infinity) JAC(6, 40, infinity) JAC(14, 40, infinity)
2 2
JAC(15, 40, infinity) JAC(16, 40, infinity) JAC(18, 40, infinity) )
3
JAC(0, 10, infinity) JAC(4, 10, infinity) 3
- ------------------------------------------ + q JAC(4, 80, infinity)
2
JAC(2, 10, infinity) JAC(3, 10, infinity)
3/2
JAC(0, 80, infinity) JAC(32, 80, infinity) JAC(36, 80, infinity)
1/2 / 2 2
JAC(40, 80, infinity) / (JAC(16, 80, infinity) JAC(24, 80, infinity)
/
)
6 3/2 1/2
q JAC(8, 80, infinity) JAC(0, 80, infinity) JAC(40, 80, infinity)
- ------------------------------------------------------------------------
JAC(16, 80, infinity) JAC(24, 80, infinity)
> JJ2:=jacnormalid(JJ);
2 15/2
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)
3/2 / 3
JAC(20, 40, infinity) / (JAC(0, 10, infinity) JAC(4, 10, 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 3
JAC(18, 40, infinity) ) + 1 - JAC(2, 10, infinity) JAC(3, 10, infinity) q
3/2
JAC(4, 80, infinity) JAC(0, 80, infinity) JAC(32, 80, infinity)
1/2 / 3
JAC(36, 80, infinity) JAC(40, 80, infinity) / (JAC(0, 10, infinity)
/
2 2
JAC(4, 10, infinity) JAC(16, 80, infinity) JAC(24, 80, infinity) ) +
2 6
JAC(2, 10, infinity) JAC(3, 10, infinity) q JAC(8, 80, infinity)
3/2 1/2 / 3
JAC(0, 80, infinity) JAC(40, 80, infinity) / (JAC(0, 10, infinity)
/
JAC(4, 10, infinity) JAC(16, 80, infinity) JAC(24, 80, infinity))
> jac2getacombo(JJ2);
2
- eta[10, 2](tau) eta[10, 3](tau) eta(40 tau) eta[40, 4](tau) eta[40, 10](tau)
3/2 /
eta[40, 12](tau) eta[40, 20](tau) / (eta(10 tau) eta[10, 4](tau)
/
2 2
eta[40, 2](tau) eta[40, 5](tau) eta[40, 6](tau) eta[40, 14](tau)
2 2
eta[40, 15](tau) eta[40, 16](tau) eta[40, 18](tau) ) + 1 -
2
eta[10, 2](tau) eta[10, 3](tau) eta[80, 4](tau) eta(80 tau)
1/2 /
eta[80, 32](tau) eta[80, 36](tau) eta[80, 40](tau) / (eta(10 tau)
/
2 2 2
eta[10, 4](tau) eta[80, 16](tau) eta[80, 24](tau) ) + eta[10, 2](tau)
1/2
eta[10, 3](tau) eta[80, 8](tau) eta(80 tau) eta[80, 40](tau) /(
eta(10 tau) eta[10, 4](tau) eta[80, 16](tau) eta[80, 24](tau))
> JJ3:=mixedjac2jac(JJ2):
> jac2getacombo(JJ3);
2 3
- eta[40, 3](tau) eta[40, 7](tau) eta[40, 8](tau) eta[40, 12](tau)
/ 2
eta[40, 13](tau) eta[40, 17](tau) eta[40, 20](tau) / (eta[40, 5](tau)
/
2 2 2 2
eta[40, 6](tau) eta[40, 14](tau) eta[40, 15](tau) eta[40, 16](tau) ) + 1
3 2 2
- eta[80, 32](tau) eta[80, 8](tau) eta[80, 2](tau) eta[80, 3](tau)
2
eta[80, 7](tau) eta[80, 12](tau) eta[80, 13](tau) eta[80, 17](tau)
2 2
eta[80, 18](tau) eta[80, 22](tau) eta[80, 23](tau) eta[80, 27](tau)
2 2 /
eta[80, 28](tau) eta[80, 33](tau) eta[80, 37](tau) eta[80, 38](tau) / (
/
3 3
eta[80, 16](tau) eta[80, 24](tau) eta[80, 6](tau) eta[80, 10](tau)
eta[80, 14](tau) eta[80, 20](tau) eta[80, 26](tau) eta[80, 30](tau)
2 3 2
eta[80, 34](tau)) + eta[80, 32](tau) eta[80, 8](tau) eta[80, 2](tau)
2
eta[80, 3](tau) eta[80, 7](tau) eta[80, 12](tau) eta[80, 13](tau)
2 2
eta[80, 17](tau) eta[80, 18](tau) eta[80, 22](tau) eta[80, 23](tau)
2
eta[80, 27](tau) eta[80, 28](tau) eta[80, 33](tau) eta[80, 37](tau)
2 / 2 2
eta[80, 38](tau) / (eta[80, 4](tau) eta[80, 16](tau) eta[80, 24](tau)
/
eta[80, 36](tau) eta[80, 6](tau) eta[80, 10](tau) eta[80, 14](tau)
eta[80, 20](tau) eta[80, 26](tau) eta[80, 30](tau) eta[80, 34](tau))
SEE ALSO : jac2eprod, jac2getaprod, jacnormalid