Matrix summation improvements

[sylee957]

References to other Issues or PRs

Brief description of what is fixed or changed

There are some issues with sum involving matrices, which are fixed here.

1. Matrix was casted into MutableDenseMatrix after summation, but now, it will be casted into ImmutableDenseMatrix and ImmutableSparseMatrix respecting the original matrix class.
   I made the behavior not to retain the mutability though, because sympify would already cast mutable matrix into a immutable one.

2. There was inefficient casting of sparse matrices into dense matrices in the original code.

from sympy import *

x = Dummy('x', integer=True)
m = SparseMatrix(200, 200, {(0, 0): 1}) * x

from pyinstrument import Profiler

profiler = Profiler()
profiler.start()

Sum(m, (x, 1, 100)).doit()

profiler.stop()

print(profiler.output_text(unicode=True, color=True))

And the speed had improved as

  _     ._   __/__   _ _  _  _ _/_   Recorded: 18:56:58  Samples:  3315
 /_//_/// /_\ / //_// / //_'/ //     Duration: 3.343     CPU time: 3.344
/   _/                      v3.0.3

  _     ._   __/__   _ _  _  _ _/_   Recorded: 18:56:23  Samples:  284
 /_//_/// /_\ / //_// / //_'/ //     Duration: 0.284     CPU time: 0.266
/   _/                      v3.0.3

3. Matrix expressions were throwing errors in summation because they don't have _mat attribute

from sympy import *

x = Symbol('x')
Sum(Identity(3), (x, 0, 3)).doit()

AttributeError: 'Identity' object has no attribute '_mat'
But after now, it may not be computed because of lack of some formulas, but at least it will return unevaluated.
I've also changed the check like

            if self != expanded:
                return expanded.doit()
            return self

because of the recursion error, if it does not succeed rewriting.

Other comments

Release Notes

• concrete
  • Fixed Sum casting dense matrix into sparse matrix.
  • Sum will cast mutable matrices into immutable variant after computation

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• concrete

  • Fixed Sum casting dense matrix into sparse matrix. (#17241 by @sylee957)

  • Sum will cast mutable matrices into immutable variant after computation (#17241 by @sylee957)

This will be added to https://github.com/sympy/sympy/wiki/Release-Notes-for-1.5.

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#### References to other Issues or PRs
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#### Brief description of what is fixed or changed

There are some issues with `sum` involving matrices, which are fixed here.

1. Matrix was casted into MutableDenseMatrix after summation, but now, it will be casted into `ImmutableDenseMatrix` and `ImmutableSparseMatrix` respecting the original matrix class.
I made the behavior not to retain the mutability though, because `sympify` would already cast mutable matrix into a immutable one.

2. There was inefficient casting of sparse matrices into dense matrices in the original code.
```python
from sympy import *

x = Dummy('x', integer=True)
m = SparseMatrix(200, 200, {(0, 0): 1}) * x

from pyinstrument import Profiler

profiler = Profiler()
profiler.start()

Sum(m, (x, 1, 100)).doit()

profiler.stop()

print(profiler.output_text(unicode=True, color=True))
```
And the speed had improved as
```
  _     ._   __/__   _ _  _  _ _/_   Recorded: 18:56:58  Samples:  3315
 /_//_/// /_\ / //_// / //_'/ //     Duration: 3.343     CPU time: 3.344
/   _/                      v3.0.3
```
```
  _     ._   __/__   _ _  _  _ _/_   Recorded: 18:56:23  Samples:  284
 /_//_/// /_\ / //_// / //_'/ //     Duration: 0.284     CPU time: 0.266
/   _/                      v3.0.3
```

3. Matrix expressions were throwing errors in summation because they don't have `_mat` attribute
```python
from sympy import *

x = Symbol('x')
Sum(Identity(3), (x, 0, 3)).doit()
```
`AttributeError: 'Identity' object has no attribute '_mat'`
But after now, it may not be computed because of lack of some formulas, but at least it will return unevaluated.
I've also changed the check like
```
            if self != expanded:
                return expanded.doit()
            return self
```
because of the recursion error, if it does not succeed rewriting.

#### Other comments


#### Release Notes

<!-- Write the release notes for this release below. See
https://github.com/sympy/sympy/wiki/Writing-Release-Notes for more information
on how to write release notes. The bot will check your release notes
automatically to see if they are formatted correctly. -->

<!-- BEGIN RELEASE NOTES -->

- concrete
  - Fixed `Sum` casting dense matrix into sparse matrix.
  - `Sum` will cast mutable matrices into immutable variant after computation

<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

[oscarbenjamin]

This looks good to me.

[oscargus]

Looks good! Can you try #16989 and add those tests that work? (And if both works, add a fixes to this?)

[sylee957]

I've only added the first case because the second one hangs in jordan form computation.
Some other things may be improved in later, with base on this

[codecov]

Codecov Report

Merging #17241 into master will increase coverage by 0.014%.
The diff coverage is 71.428%.

@@              Coverage Diff              @@
##            master    #17241       +/-   ##
=============================================
+ Coverage   74.549%   74.564%   +0.014%     
=============================================
  Files          623       623               
  Lines       161739    161784       +45     
  Branches     37965     37966        +1     
=============================================
+ Hits        120576    120633       +57     
+ Misses       35817     35800       -17     
- Partials      5346      5351        +5