William Stein <wst...@gmail.com> writes:
> By the way, when using this, I repeatedly felt like I wished the
> command in Sage were "fricas" instead of "axiom" and the file to test
> were "fricas.py" instead of "axiom.py".
I agree. Meanwhile, FriCAS is well established.
By the way, is the following differential equation for the generating function
for integer partitions known to people coming from modular forms? (Dietrich
Burde from Vienna said it "must" be known...)
Sorry about posting this to the wrong forum...
Martin
(1) -> l := [partition n for n in 0..45]
(1)
[1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135,
176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958,
2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310,
14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174,
63261, 75175, 89134]
Type: List(Integer)
(2) -> guessADE(l, homogeneous==4, maxDerivative==4, maxDegree==2).1.function
(2)
[
n
[x ]f(x):
2 3 (iv) 2 2 , 3 ,,,
x f(x) f (x) + (20x f(x) f (x) + 5x f(x) )f (x)
+
2 2 ,, 2
- 39x f(x) f (x)
+
2 , 2 2 , 3 ,,
(12x f(x)f (x) - 15x f(x) f (x) + 4f(x) )f (x)
+
2 , 4 , 3 2 , 2
6x f (x) + 10x f(x)f (x) - 16f(x) f (x)
=
0
,
2 3 4
f(x)= 1 + x + 2x + 3x + O(x )]
Type: Expression(Integer)
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