mathics3 9.0.0 does not support to setuptools>=82

[cxzhong]

Description

Since the setuptools>82 remove pkg_resource. Then when we run mathics(nu).BesselK(x).N(20) can not got the correct result

How to Reproduce and Output Given

 sage: def math_bessel_K(nu, x):
 ....:     return mathics(nu).BesselK(x).N(20)
 sage: math_bessel_K(2,I)                      # optional - mathics

Then we got

CompoundExpression[2.7182818284590452354 ^ (-1.0000000000000000000 internals`bessel`u$1) / internals`bessel`u$1 ^ 1.0000000000000000000, internals`bessel`While[True, CompoundExpression[0.50000000000000000000, (-1.0000000000000000000 2.7182818284590452354 ^ (-1.0000000000000000000 internals`bessel`u$1) / internals`bessel`u$1 ^ 2.0000000000000000000 - 1.0000000000000000000 2.7182818284590452354 ^ (-1.0000000000000000000 internals`bessel`u$1) / internals`bessel`u$1 ^ 1.0000000000000000000) / internals`bessel`u$1 ^ 1.0000000000000000000]], 1.7317959997692363070 - 0.37745896303183014917 I]

Expected behavior

-2.5928861754911969782 + 0.18048997206696202663 I

Your Environment

mathics3 9.0.0 sage 10.9 beta8

Workarounds

Priority

Additional context

[cxzhong]

and I think you should release a new version, it seems it has been fixed in the develope branch

[rocky]

and I think you should release a new version, it seems it has been fixed in the develope branch

A new release is in progress.

[cxzhong]

and I test in the master branch's mathics3, the bessel number is wrong in this case

Reproducer

(* Wrong — returns 4.51822... instead of -2.59289... *)
In[1]:= N[BesselK[2, I], 20]
Out[1]= 4.5182194809390058422 - 0.077749407694957219404 I

(* Correct reference value (from mpmath): *)
(* -2.5928861754911969782 + 0.18048997206696202663 I *)

Other affected examples:

(* BesselK[2, 1] returns -3.227*I instead of the correct 1.6248 *)
N[BesselK[2, 1], 20]

(* BesselK[1, I] also wrong *)
N[BesselK[1, I], 20]

Root Cause

In mathics/autoload/rules/Bessel.m, the Rayleigh expansion rules use the condition IntegerQ[2*nu] to detect half-integer orders:

(* Line 35 — intended for half-integer nu only *)
BesselK[nu_/;(nu>0 && IntegerQ[2*nu]), z_] := Module[{u,f,k= nu-1/2}, ...]

The problem is that IntegerQ[2*nu] is True for both half-integers and integers:

nu	2*nu	IntegerQ[2*nu]	Should match?
3/2	3	True	Yes
5/2	5	True	Yes
1	2	True	No
2	4	True	No

When nu is an integer (e.g. 2), the Rayleigh formula is mathematically invalid — it is derived only for half-integer orders. The k = nu - 1/2 loop counter becomes a non-integer (e.g. 3/2), so the While[k > 0, k = k - 1; ...] loop doesn't terminate correctly, and the symbolic result is nonsensical.

All eight rules (two per Bessel function) have the same bug:

Line	Function	Condition
23	BesselI	nu>0 && IntegerQ[2*nu]
24	BesselI	nu<0 && IntegerQ[2*nu]
35	BesselK	nu>0 && IntegerQ[2*nu]
36	BesselK	nu<0 && IntegerQ[2*nu]
45	BesselJ	nu>0 && IntegerQ[2*nu]
46	BesselJ	nu<0 && IntegerQ[2*nu]
58	BesselY	nu>0 && IntegerQ[2*nu]
59	BesselY	nu<0 && IntegerQ[2*nu]

Fix

Add && !IntegerQ[nu] to each condition so the rules only match half-integers:

(* Before *)
BesselK[nu_/;(nu>0 && IntegerQ[2*nu]), z_] := ...

(* After *)
BesselK[nu_/;(nu>0 && IntegerQ[2*nu] && !IntegerQ[nu]), z_] := ...

Apply this change to all eight rules (lines 23, 24, 35, 36, 45, 46, 58, 59).

[rocky]

and I test in the master branch's mathics3, the bessel number is wrong in this case

Reproducer

(* Wrong — returns 4.51822... instead of -2.59289... *)
In[1]:= N[BesselK[2, I], 20]
Out[1]= 4.5182194809390058422 - 0.077749407694957219404 I
....

All of this is useful and interesting information. However, this should be in a separate issue, so that it is tracked separately. People who look at bug reports (whether people fixing or just trying to understand what's reported) should not have to wade through rambling, unrelated bug reports with titles unrelated to the what's reported.

Thanks.

[cxzhong]

I have hided this.

[cxzhong]

and you also needs to test with python 3.14 and 3.14t