[Rafael-SOWNet]

Closes #2345.

The row echelon forms were GenericTensor's, whose elimination asks whether a pivot is the literal 0. An entry the elimination makes itself, like c + -c / a * a, is 0 without being written so. It was chosen and divided by.

	2.6.0 and master	now
[[a, b], [2a, 2b]].Rank	2	1
[[a, b, c], [d, f, g], [a + d, b + f, c + g]].Rank	3	2
[[x, x^2], [1, x]].Rank	2	1
[[sin(t)^2 + cos(t)^2, 1], [1, 1]].Rank	2	1
[[a, b], [c, d]].ReducedRowEchelonForm.Simplify()	NaN	[[1, 0], [0, 1]]
[[a, b], [2a, 2b]].ReducedRowEchelonForm.Simplify()	NaN	[[1, b / a], [0, 0]]

• The elimination is written over the entries, as the determinant's Laplace expansion already was (det, dot, cross, transpose and resultant as functions in an expression #2147). It takes GenericTensor's steps: the first entry of a column from the current row down that is not 0 is the pivot, rows are swapped up, and in the reduced form each pivot row is divided by its pivot. So a matrix of numbers comes out as it did. The 177 matrix tests pass unchanged, and matrixcheck is clean on 1200 random matrices (seeds 14–16).
• Every entry it makes is normalised. A rational function over the rationals goes to RationalFunction's canonical quotient, where 0 is the literal 0. Anything else (sin, pi, more than 8 symbols) is simplified when asked whether it is 0, with a provided on the zero set aside.
• Rank counts the elimination's pivots, so a symbolic matrix's rank is its rank for general values of its symbols. The issue's "0 where a = b = 0" is not something an int can say, and the doc comment states which rank it is.
• Conditions. A symbolic pivot divides, so a reduced form holds where its pivots are not 0. Where a simplification can see that, it says so ([[x, x^2], [1, x]] reduces to [[1, x provided not x = 0], [0, 0]]). Whether the reduced form should instead carry the conditions as a whole, or decline, as the issue's second bullet raises, is left open; NaN is gone either way.

Tests: ASymbolicPivotIsDecidedBeforeItIsChosenTest, 13 cases. 11 fail on master; the two independent ranks pass on both. The full suite, AOT and the nine harnesses pass. There is a BREAKING-CHANGES entry, measured on 2.6.0.

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Codecov Report

❌ Patch coverage is 97.72727% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 86.79%. Comparing base (0e96927) to head (d574b0b).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
...rces/AngouriMath/Core/Entity/Omni/Entity.Matrix.cs	97.72%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2350      +/-   ##
==========================================
- Coverage   86.79%   86.79%   -0.01%     
==========================================
  Files         312      312              
  Lines       68664    68709      +45     
  Branches    19987    20006      +19     
==========================================
+ Hits        59595    59633      +38     
- Misses       4902     4907       +5     
- Partials     4167     4169       +2     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.33% <97.72%> (-0.01%)	⬇️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

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Files with missing lines	Coverage Δ
...rces/AngouriMath/Core/Entity/Omni/Entity.Matrix.cs	85.05% <97.72%> (+1.65%)	⬆️

... and 6 files with indirect coverage changes

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