Re: Question about the use of mfslashexpansion

Hello,

Thank you for your reply. I agree that P[2] = 2, but this code gives incorrect output for eta(z)^8 * eta(2z)^8 | U_2 using any of the two methods:

a = mffrometaquo([1, 8; 2, 8]);
b = mfinit(a);
c = 8 * (mfslashexpansion(b, a, [1, 0; 0, 2], 50, 1, &P) + mfslashexpansion(b, a, [1, 1; 0, 2], 50, 1, &P)

[0, 16, -128, 192, 1024, -3360, -1536, 16256, -8192, -32688, 26880, 17472, 12288, 22112, -130048, -40320, 65536, 235296, 261504, -639040, -215040, 195072, -139776, 1099392, -98304, -544400, -176896, -812160, 1040384, -1641120, 322560, 3640832, -524288, 209664, -1882368, -3413760, -2092032, 2568416, 5112320, 265344, 1720320, 173472, -1560576, -10091968, 1118208, 6864480, -8795136, 7562496, 786432, 3339408, 4355200]

a = mffrometaquo([1, 8; 2, 8]);
b = mfinit(a);
c = 8 * (mfslashexpansion(b, a, [1, 0; 0, 2], 50, 0) + mfslashexpansion(b, a, [1, 1; 0, 2], 50, 0)

[0, 0, -8, 0, 64, 0, -96, 0, -512, 0, 1680, 0, 768, 0, -8128, 0, 4096, 0, 16344, 0, -13440, 0, -8736, 0, -6144, 0, -11056, 0, 65024, 0, 20160, 0, -32768, 0, -117648, 0, -130752, 0, 319520, 0, 107520, 0, -97536, 0, 69888, 0, -549696, 0, 49152, 0, 272200]

Expected:

[0, -8, 64, -96, ....]

I did another example:

y(l) = {mffrometaquo([l, l; 1, -1; 2 * l, l; 2, -1]);}

z(l) = {mfinit(y(l));}

mfslashexpansion(z(5), y(5), [1, 0; 0, 5], 50, 1) + mfslashexpansion(z(5), y(5), [1, 1; 0, 5], 50, 1) + mfslashexpansion(z(5), y(5), [1, 2; 0, 5], 50, 1) + mfslashexpansion(z(5), y(5), [1, 3; 0, 5], 50, 1) + mfslashexpansion(z(5), y(5), [1, 4; 0, 5], 50, 1);

Output:

[0, 0, 0, 5, 5, 15, 20, 45, 35, 90, 80, 170, 140, 290, 220, 455, 295, 620, 480, 900, 585, 1230, 840, 1535, 1060, 2000, 1440, 2630, 1640, 3140, 2260, 3790, 2415, 4800, 3120, 5515, 3545, 6510, 4400, 7810, 4695, 8910, 6160, 10205, 6340, 12105, 7780, 13325, 8420, 15170, 10000]

Expected:

[0,3,16,91....]

I am not sure what am I missing here?

Swati

"An equation for me has no meaning unless it expresses a thought of God"— Srinivasa Ramanujan.

From: Cohen Henri <Henri.Cohen@math.u-bordeaux.fr>
Sent: Monday, August 4, 2025 5:18 PM
To: LNU, Swati <S10@email.sc.edu>
Cc: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>; pari-users@pari.math.u-bordeaux.fr <pari-users@pari.math.u-bordeaux.fr>
Subject: Re: Question about the use of mfslashexpansion

a = mffrometaquo([1, 8; 2, 8]);
b = mfinit(a);
c = 8 * (mfslashexpansion(b, a, [1, 0; 0, 2], 50, 1, &P) + mfslashexpansion(b, a, [1, 1; 0, 2], 50, 1, &P))

Output:

Since you included the parameter P, you will see that P[2]=2, which means that the actual variable is q^2 and not q.