[Rafael-SOWNet]

The reduced row echelon form of an invertible 4x4 of small rationals had NaN entries, and its Rank threw InvalidCastException. Both forms used GenericTensor's SafeDivision elimination. It keeps every entry as a numerator and a denominator that are never reduced against each other, which suits element types whose division truncates; an Entity divides exactly. Unreduced, the pairs grow with every row operation, and the back substitution squares them. The issue's matrix ended with a denominator near 1e-246, and 0 divided by that is NaN, which is #2277. One 7x7 of small entries took 112 seconds, with 42 NaN entries, and an 8x8 did not return.

Both forms now use the Simple elimination, which divides as it goes.

Input	2.6.0	Now
the issue's 4x4, .Rank	throws InvalidCastException	4
the same, .ReducedRowEchelonForm	throws InvalidCastException	the identity
[[a, b], [c, d]], .RowEchelonForm	[[a, b], [(c * a + -c * a) / a, (d * a + -c * b) / a]]	[[a, b], [c + -c / a * a, d + -c / a * b]]

MatrixTest reduces the issue's matrix, and two more from a random sweep, to the identity with rank 4. It also reduces an 8x8 with determinant -5598, bounded at a minute. All four cases fail on master, the 8x8 by not returning. The suite (18,233), the trio, F#, AOT and the eight harnesses pass locally.

The subagent that traced this ran a sweep against an exact Gauss–Jordan reference. Master gave NaN on 13 of 600 4x4s and on 38 of 200 5x5s; this branch gave none. Symbolic forms change shape but not value: on 13 symbolic matrices it judged, the verdicts were the same on both routes, and 10 of them are wrong on both, because InnerSimplified does not collapse x + -x before taking it as a pivot. That is a separate problem.

This edits the same two lines as #2272, so whichever merges second will need one conflict resolved.

Fixes #2270.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.71%. Comparing base (f570b35) to head (6f0e3b2).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2279      +/-   ##
==========================================
+ Coverage   86.70%   86.71%   +0.01%     
==========================================
  Files         310      310              
  Lines       67869    67869              
  Branches    19701    19701              
==========================================
+ Hits        58843    58854      +11     
+ Misses       4903     4892      -11     
  Partials     4123     4123              

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.26% <100.00%> (+0.01%)	⬆️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
...rces/AngouriMath/Core/Entity/Omni/Entity.Matrix.cs	83.40% <100.00%> (ø)

... and 10 files with indirect coverage changes

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