FUNCTION : mixedajc2jac - converts a sum of quotients of jacprods to a
common base
CALLING SEQUENCE : mixedjac2jac()
mixedjac2jac(jacexp)
PARAMETERS : jacexp - sum of quotients of theta functions written
in terms of JAC(a,b,infinity)
SYNOPSIS : jac2series and jacprodmake (from qseries package)
are used to convert each quotient into a
a quotient with the same base.
This function is used by processjacid.
NOTE: Must contain at least two terms.
EXAMPLES :
> with(thetaids):
> with(qseries):
> mixedjac2jac();
-------------------------------------------------------------
mixedjac2jac(jacexp)
jacexp is a sum of quotients of theta functions written
in terms of JAC(a,b,infinity). jac2series and
jacprodmake is used to convert each quotient into a
a quotient of the same b.
T is chosen large enough for conversion to work.
-------------------------------------------------------------
> J1:=1-1/JAC(0,10,infinity)^2/JAC(0,120,infinity)^3/JAC(1,3,infinity)/JAC(2,6,infinity)
> /JAC(3,10,infinity)/JAC(4,12,infinity)/JAC(8,20,infinity)^2*JAC(0,1,infinity)
> *JAC(0,2,infinity)*JAC(0,5,infinity)^2*JAC(0,8,infinity)*JAC(4,10,infinity)
> *JAC(6,20,infinity)*JAC(16,40,infinity)*JAC(120,360,infinity)^3;
2
J1 := 1 - JAC(0, 1, infinity) JAC(0, 2, infinity) JAC(0, 5, infinity)
JAC(0, 8, infinity) JAC(4, 10, infinity) JAC(6, 20, infinity)
3 / 2
JAC(16, 40, infinity) JAC(120, 360, infinity) / (JAC(0, 10, infinity)
/
3
JAC(0, 120, infinity) JAC(1, 3, infinity) JAC(2, 6, infinity)
2
JAC(3, 10, infinity) JAC(4, 12, infinity) JAC(8, 20, infinity) )
> jacbase(op(2,J1));
360
> J2 := mixedjac2jac(J1);
2 2 2
J2 := 1 - JAC(5, 40, infinity) JAC(6, 40, infinity) JAC(14, 40, infinity)
2 2 /
JAC(15, 40, infinity) JAC(16, 40, infinity) / (JAC(3, 40, infinity)
/
2 3
JAC(7, 40, infinity) JAC(8, 40, infinity) JAC(12, 40, infinity)
JAC(13, 40, infinity) JAC(17, 40, infinity) JAC(20, 40, infinity))
>
> series(jac2series(J2-J1,400),q,400);
400
O(q )
DISCUSSION : We able to convert given jacexp with mixed bases (divisors of 360)
to base 40.
SEE ALSO : jacbase, processjacid