[ruby-core:101994] [Ruby master Bug#17521] [Matrix stdlib] Zero matrix to the power of zero

Issue #17521 has been updated by marcandre (Marc-Andre Lafortune).

Assignee set to marcandre (Marc-Andre Lafortune)
Status changed from Open to Assigned

Congratulations on finding the oldest bug in Ruby ever! 

This bug will be 23 years old in a week; it dates from the commit "Initial revision" 3db12e8b23

I should have realized this when I refactored it later on and added the spec though.

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Bug #17521: [Matrix stdlib] Zero matrix to the power of zero
https://bugs.ruby-lang.org/issues/17521#change-89843

* Author: Kache (Kevin Cheng)
* Status: Assigned
* Priority: Normal
* Assignee: marcandre (Marc-Andre Lafortune)
* ruby -v: ruby 2.7.2p137 (2020-10-01 revision 5445e04352) [x86_64-msys]
* Backport: 2.5: UNKNOWN, 2.6: UNKNOWN, 2.7: UNKNOWN, 3.0: UNKNOWN
----------------------------------------
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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