From: nagachika00@...
Date: 2021-04-15T01:50:08+00:00
Subject: [ruby-core:103458] [Ruby master Bug#17521] [Matrix stdlib] Zero matrix to the power of zero

Issue #17521 has been updated by nagachika (Tomoyuki Chikanaga).

Backport changed from 2.5: UNKNOWN, 2.6: UNKNOWN, 2.7: UNKNOWN, 3.0: UNKNOWN to 2.6: UNKNOWN, 2.7: UNKNOWN, 3.0: WONTFIX

Even though nobody filled the Backport field yet, I will set "WONTFIX".
Such a long long standing bug could be thought as an spec, and some application could be depended by current behavior.
usa-san, do you have any opinion?

And the related test in rubyspec is failing on ruby_3_0 branch because the test seems expected this change is going to be backported into 3.0.x.
I will send a pull request to ruby/spec repo soon.

----------------------------------------
Bug #17521: [Matrix stdlib] Zero matrix to the power of zero
https://bugs.ruby-lang.org/issues/17521#change-91553

* Author: Kache (Kevin Cheng)
* Status: Closed
* Priority: Normal
* Assignee: marcandre (Marc-Andre Lafortune)
* ruby -v: ruby 2.7.2p137 (2020-10-01 revision 5445e04352) [x86_64-msys]
* Backport: 2.6: UNKNOWN, 2.7: UNKNOWN, 3.0: WONTFIX
----------------------------------------
Just like `0**0 == 1`, `Matrix.zero(n)**0 == Matrix.identity(n)` should be true for all `n`:

https://math.stackexchange.com/questions/699740/zero-matrix-to-the-power-of-0

However:

```
$ ruby -e "require 'matrix'; Matrix.zero(1)**0"
Traceback (most recent call last):
        5: from -e:1:in `<main>'
        4: from /usr/lib/ruby/2.7.0/matrix.rb:1227:in `**'
        3: from /usr/lib/ruby/2.7.0/matrix.rb:1165:in `inverse'
        2: from /usr/lib/ruby/2.7.0/matrix.rb:1173:in `inverse_from'
        1: from /usr/lib/ruby/2.7.0/matrix.rb:1173:in `upto'
/usr/lib/ruby/2.7.0/matrix.rb:1183:in `block in inverse_from': Not Regular Matrix (ExceptionForMatrix::ErrNotRegular)
```

`Matrix.zero(n)**0.0` happens to work properly, but it should work for integers as well.
Wasn't able to test in Ruby 3.0, but its source code suggests it also behaves this way.

For comparison, [Python's numpy](https://numpy.org/doc/stable/reference/generated/numpy.linalg.matrix_power.html):

```
Python 3.8.2 (default, Feb 26 2020, 02:56:10)
>> import numpy as np
>> np.linalg.matrix_power(np.array([[0,0],[0,0]]), 0)
array([[1, 0],
       [0, 1]])
```



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