Euler numbers via flint

[fchapoton]

euler numbers currently use the slow maxima pexpect interface

they can be much faster using flint

for a possible follow-up, see #17770

CC: @tscrim @jm58660

Component: combinatorics

Author: Frédéric Chapoton

Branch/Commit: 510a91d

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/20763

[fchapoton]

Commit: 510a91d

[fchapoton]

New commits:

510a91d

use flint for euler numbers

[fchapoton]

Description changed:

--- 
+++ 
@@ -1,3 +1,5 @@
 euler numbers currently use the slow maxima pexpect interface
 
 they can be much faster using flint
+
+for a possible follow-up, see #17770

[fchapoton]

Branch: u/chapoton/20763

[tscrim]

comment:2

Can you give some reasoning why it is 1000 for the cut-off for sig_on/sig_off?

[fchapoton]

comment:3

I just copied that from the code of another function in flint/arith.

[tscrim]

comment:4

Guess they consider that a good cutoff bound for speed for small values. Nor can I fault it:

sage: %time euler_number(10000)
CPU times: user 46.3 ms, sys: 0 ns, total: 46.3 ms
Wall time: 46.2 ms
# Too long to put here

[tscrim]

Reviewer: Travis Scrimshaw