Maple ETA Package (Version 0.3) - Installation Instructions - UNDER CONSTRUCTION
These instructions are for Windows (64 bit) and Maple 2019.
If you are using a different version of Maple just change "2019"
to whatever.
- STEP 1
Create a Homelib directory for your maple lib (dotm) files.
My directory is called mylib and is located here:
C:\cygwin64\home\fgarv\maple\mylib
This is what I did to create it:
You should now have a new directory called mylib.
- STEP 2
Set up a maple.ini file.
This file should be created in the directory:
C:\Users\fgarv
and it should contain two lines of code resembling something like:
### 06.29.2019
Homelib:="C:\\cygwin64/home/fgarv/maple/mylib":
libname := libname, Homelib:
The value of Homelib should correspond to your Homelib.
One way to do this is to use the following Maple worksheet.
Now you should have a file maple.ini
containing two lines of code.
- STEP 3
Download the file
This file contains MAPLE code for setting up and saving the
package. Save this file in a place where you keep your MAPLE
programs. I saved it in a special directory:
"C:\cygwin64\home\fgarv\maple\mypackages\ETA\w-setup"
This program saves the ETA package in the mylib directory.
If you want to save it in a different place you will need to
edit the file.
- STEP 4
Install the ETA package.
Start MAPLE and do something like the following.
> libname;
"C:\Program Files\Maple 2019\lib", ".", "C:\cygwin64\home\fgarv\maple\mylib"
> currentdir("C:\\cygwin64\\home\\fgarv\\maple\\mypackages\\ETA\\w-setup");
"C:\cygwin64\home\fgarv\maple\mypackages\ETA\w-setup"
> currentdir();
"C:\cygwin64\home\fgarv\maple\mypackages\ETA\w-setup"
> read "wprog-eta-06-29-2019-HOMEPC.txt":
>
You will need to change "C:....w-setup" to the appropriate place.
This program saves
package as a file ETA.mla in the mylib dir.
See
-
INSTALL THETAIDS
[MW |
[PDF]
- STEP 5
Exit MAPLE and restart it to test the package:
> with(qseries):
> with(ETA):
> gpA1:=[1,2,4,3,2,-5,50,5,25,-2,100,-3]:
> epA1:=gp2etaprod(gpA1);
2 3 5
eta(tau) eta(4 tau) eta(50 tau)
epA1 := --------------------------------------
5 2 3
eta(2 tau) eta(25 tau) eta(100 tau)
> A1q:=etaprodtoqseries(epA1,1000):
> gpa1:=[1,2,10,4,2,-4,5,-2]:
gpa1 := [1, 2, 10, 4, 2, -4, 5, -2]
> epa1:=gp2etaprod(gpa1);
2 4
eta(tau) eta(10 tau)
epa1 := -----------------------
4 2
eta(2 tau) eta(5 tau)
> aq1:=etaprodtoqseries(epa1,2000):
> gprho:=[2,2,20,4,4,-4,10,-2]:
> eprho:=gp2etaprod(gprho);
2 4
eta(2 tau) eta(20 tau)
eprho := ------------------------
4 2
eta(4 tau) eta(10 tau)
> G1a:=etaprodtoqseries(eprho,1001):
> G1:=convert(series(1-G1a,q,1020),polynom):
> etamake(G1,q,100);
3
eta(10 tau) eta(2 tau)
-----------------------
3
eta(20 tau) eta(4 tau)
> U01:=sift(A1q,q,5,0,2000):
> etacombo:=findlincombo(U01,[seq( aq1^k,k=-2..5),seq( aq1^k*(G1),k=-2..5)],[seq( etamake((aq1)^k,q,100),k=-2..5),seq( etamake((aq1)^k*G1,q,100),k=-2..5)],q,0);
nx = , 16
# of terms , 37
2 4
53 eta(tau) eta(10 tau)
etacombo := - -------------------------
4 2
eta(2 tau) eta(5 tau)
8 4 12 6
350 eta(10 tau) eta(tau) 1050 eta(10 tau) eta(tau)
+ -------------------------- - ----------------------------
4 8 6 12
eta(5 tau) eta(2 tau) eta(5 tau) eta(2 tau)
16 8 20 10
1375 eta(10 tau) eta(tau) 625 eta(10 tau) eta(tau)
+ ---------------------------- - ----------------------------
8 16 10 20
eta(5 tau) eta(2 tau) eta(5 tau) eta(2 tau)
3
13 eta(10 tau) eta(2 tau)
+ --------------------------
3
eta(20 tau) eta(4 tau)
7 2
75 eta(10 tau) eta(tau)
- -----------------------------------------------
2 3 3
eta(20 tau) eta(5 tau) eta(4 tau) eta(2 tau)
11 4
175 eta(10 tau) eta(tau)
+ -----------------------------------------------
4 3 7
eta(20 tau) eta(5 tau) eta(4 tau) eta(2 tau)
15 6
125 eta(10 tau) eta(tau)
- ------------------------------------------------
6 3 11
eta(20 tau) eta(5 tau) eta(4 tau) eta(2 tau)
;
> provemodfuncGAMMA0UpETAid(epA1,5,etacombo,20);
*** There were NO errors.
*** o EP is an MF on Gamma[0](100)
*** o Each term in the etacombo is a modular function on
Gamma0(20).
*** o We also checked that the total order of
each term etacombo was zero.
*** To prove the identity U[5](EP)=etacombo we need to show
that v[oo](ID) > 9 This means checking up to q^(10).
Do you want to prove the identity? (yes/no)
You entered yes.
We verify the identity to O(q^(49)).
We find that LHS - RHS is
/ 49\
O\q /
RESULT: The identity holds to O(q^(49)).
CONCLUSION: This proves the identity since we had only
to show that v[oo](ID) > 9.
Do you get this? See
The url of this page is http://qseries.org/fgarvan/qmaple/ETA/install-v0p3.html.
Created by
F.G. Garvan
(fgarvan@ufl.edu) on
Saturday, June 29, 2019.
Last update made Sun Jun 30 11:13:54 EDT 2019.
fgarvan@ufl.edu
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