FUNCTION : printJACIDORDStable - print a table of ORDS of a jacprod identity
CALLING SEQUENCE : printJACIDORDStable()
PARAMETERS : none
GLOBAL VARIABLES : none (although it uses global vars as input)
SYNOPSIS :
Print a table of ORDS for each term in a jacprod-identity
using global data produced by the function provemodfuncid.
Table is stored in the matrix bigmat which is returned.
EXAMPLES :
> with(qseries):
> with(thetaids):
> CHOIID1:=
_ETAn(3)*_ETAn(6)*_ETAn(10)^2*_ETAn(12)*_ETAn(20)^3*_ETAn(120)^3*_ETAn(360)*
> _ETAnm(3,1)*_ETAnm(6,2)*_ETAnm(10,3)*_ETAnm(12,4)*_ETAnm(20,8)^3
> -_ETAn(1)*_ETAn(2)*_ETAn(5)^2*_ETAn(8)*_ETAn(20)^2*_ETAn(40)*_ETAn(360)^4
> *_ETAnm(10,4)*_ETAnm(20,6)*_ETAnm(20,8)*_ETAnm(40,16)*_ETAnm(360,120)^3
> +_ETAn(1)*_ETAn(2)*_ETAn(5)^2*_ETAn(8)*_ETAn(20)^2*_ETAn(40)*_ETAn(360)^4
> *_ETAnm(5,2)^2*_ETAnm(20,6)*_ETAnm(20,8)*_ETAnm(40,4)*_ETAnm(360,120)^3;
/749\
|---|
\24 / 3
CHOIID1 := q JAC(0, 10, infinity) JAC(0, 120, infinity)
JAC(0, 360, infinity) JAC(1, 3, infinity) JAC(2, 6, infinity)
749
---
3 24
JAC(3, 10, infinity) JAC(4, 12, infinity) JAC(8, 20, infinity) - q
2
JAC(0, 1, infinity) JAC(0, 2, infinity) JAC(0, 5, infinity)
JAC(0, 8, infinity) JAC(0, 360, infinity) JAC(4, 10, infinity)
JAC(6, 20, infinity) JAC(8, 20, infinity) JAC(16, 40, infinity)
/821\
|---|
3 \24 /
JAC(120, 360, infinity) /JAC(0, 10, infinity) + q JAC(0, 1, infinity)
JAC(0, 2, infinity) JAC(0, 8, infinity) JAC(0, 360, infinity)
2
JAC(2, 5, infinity) JAC(6, 20, infinity) JAC(8, 20, infinity)
3
JAC(4, 40, infinity) JAC(120, 360, infinity)
> NCHOIID1:=processjacid(CHOIID1):
> jcombobase(NCHOIID1);
40
> overrideproofq:=true:
> provemodfuncid(NCHOIID1,40);
"TERM ", 1, "of ", 3, " *****************"
"TERM ", 2, "of ", 3, " *****************"
"TERM ", 3, "of ", 3, " *****************"
"mintotord = ", -24
"TO PROVE the identity we need to show that v[oo](ID) > ", 24
*** There were NO errors.
*** o Each term was modular function on
Gamma1(40).
*** o We also checked that the total order of
each term was zero.
*** o We also checked that the power of q was correct in
each term.
"*** WARNING: some terms were constants. ***"
"See array CONTERMS."
To prove the identity we will need to verify if up to
q^(24).
Do you want to prove the identity? (yes/no)
You entered yes.
We verify the identity to O(q^(104)).
RESULT: The identity holds to O(q^(104)).
CONCLUSION: This proves the identity since we had only
to show that v[oo](ID) > 24.
24
> printJACIDORDStable();
-------------------------------------------------------------
printJACIDORDStable()
Print a table of ORDS for each term in a jacprod-identity
using global data produced by the function provemodfuncid.
Table is stored in the matrix bigmat which is returned.
-------------------------------------------------------------
ORDS Table for the jacprod identity
_G = _F[1] - _F[2] + _F[3] = 0
where
_F[1] =
1
_F[2] =
2 2 2 2 2 /
GETA(40, 5) GETA(40, 6) GETA(40, 14) GETA(40, 15) GETA(40, 16) / (
/
2 3
GETA(40, 3) GETA(40, 7) GETA(40, 8) GETA(40, 12) GETA(40, 13)
GETA(40, 17) GETA(40, 20))
_F[3] =
2 2
GETA(40, 2) GETA(40, 3) GETA(40, 5) GETA(40, 6) GETA(40, 7) GETA(40, 13)
2 2
GETA(40, 14) GETA(40, 15) GETA(40, 17) GETA(40, 18) /(GETA(40, 12)
GETA(40, 20))
[cusp ORD(_F[1]) ORD(_F[2]) ORD(_F[3]) ORD(_G)]
[ ]
[ oo 0 0 3 0 ]
[ ]
[ 0 0 0 1 0 ]
[ ]
[1/2 0 0 0 0 ]
[ ]
[1/3 0 0 1 0 ]
[ ]
[1/4 0 -2 -2 -2 ]
[ ]
[1/5 0 3 0 0 ]
[ ]
[1/6 0 0 0 0 ]
[ ]
[1/7 0 0 1 0 ]
[ ]
[1/8 0 1 0 0 ]
[ ]
[1/9 0 0 1 0 ]
[ ]
[1/10 0 -4 -4 -4 ]
[ ]
[1/11 0 0 1 0 ]
[ ]
[1/12 0 -2 -2 -2 ]
[ ]
[1/13 0 0 1 0 ]
[ ]
[1/14 0 0 0 0 ]
[ ]
[1/15 0 3 0 0 ]
[ ]
[1/16 0 1 0 0 ]
[ ]
[1/17 0 0 1 0 ]
[ ]
[1/18 0 0 0 0 ]
[ ]
[1/19 0 0 1 0 ]
[ ]
[1/20 0 0 0 0 ]
[ ]
[2/5 0 0 1 0 ]
[ ]
[3/4 0 -2 -2 -2 ]
[ ]
[3/5 0 0 1 0 ]
[ ]
[3/8 0 1 0 0 ]
[ ]
[3/10 0 -2 -2 -2 ]
[ ]
[3/16 0 1 0 0 ]
[ ]
[3/20 0 -2 -2 -2 ]
[ ]
[3/40 0 1 0 0 ]
[ ]
[4/5 0 3 0 0 ]
[ ]
[4/15 0 3 0 0 ]
[ ]
[5/8 0 1 0 0 ]
[ ]
[7/8 0 1 0 0 ]
[ ]
[7/10 0 -2 -2 -2 ]
[ ]
[7/12 0 -2 -2 -2 ]
[ ]
[7/15 0 0 1 0 ]
[ ]
[7/16 0 1 0 0 ]
[ ]
[7/20 0 -2 -2 -2 ]
[ ]
[7/40 0 1 0 0 ]
[ ]
[9/10 0 -4 -4 -4 ]
[ ]
[9/20 0 0 0 0 ]
[ ]
[9/40 0 0 3 0 ]
[ ]
[ 11 ]
[ -- 0 0 3 0 ]
[ 40 ]
[ ]
[ 13 ]
[ -- 0 0 1 0 ]
[ 15 ]
[ ]
[ 13 ]
[ -- 0 1 0 0 ]
[ 16 ]
[ ]
[ 13 ]
[ -- 0 1 0 0 ]
[ 40 ]
[ ]
[ 17 ]
[ -- 0 1 0 0 ]
[ 40 ]
[ ]
[ 19 ]
[ -- 0 0 3 0 ]
[ 40 ]
This confirms the calculation done by provemodfuncid.
The last column of the table gives a lower bound for
ORDS of _G. By summing this last column (except for oo)
we see that the identity can be proved by showing that
the coefficients of
q^0, q^1, ... q^25 are all zero.
This confirms the calculation done by provemodfuncid.
bigmat
DISCUSSION : See above.
SEE ALSO : provemodfuncid