[Rafael-SOWNet]

Closes #2346.

	2.6.0 and master	now
[[a, b], [c, d]].Inverse.Simplify()	each entry … provided not a = 0	[[d / (a * d - b * c), -b / (a * d - b * c)], [-c / (a * d - b * c), a / (a * d - b * c)]]
[[cos(t), -sin(t)], [sin(t), cos(t)]].Inverse.Simplify()	[[cos(t), sin(t) provided not cos(t) = 0], [-sin(t) provided not cos(t) = 0, cos(t)]]	[[cos(t), sin(t)], [-sin(t), cos(t)]]
the rotation's inverse at t = π/2, evaluated	NaN	[[0, 1], [-1, 0]]

The inverse was GenericTensor's InvertMatrix. That takes the determinant by elimination, which divides by the first pivot and multiplies it back, so the determinant came to a * (d * a + -c * b) / a, and simplifying its a / a wrote the pivot's condition on every entry. As the issue suggests, the inverse is now the matrix's own Adjugate over its own Determinant, entry by entry. The determinant is a polynomial in the entries (Bareiss' fraction-free elimination, or Laplace), and the adjugate's entries are cofactors. Only the division by the determinant is left, and its condition is the inverse's own.

A matrix of numbers has the inverse it had: the existing inverse tests pass unchanged, and matrixcheck's A A^-1 = I and A adj(A) = det(A) I are clean on 1200 random matrices (seeds 14–16). The cost is the same, since GenericTensor's inversion also went through the adjugate. GenTensorGuard.InvertMatrix had no caller left and is removed.

Tests: AnInverseIsTheAdjugateOverTheDeterminantTest, 7 cases. 4 fail on master; the numeric, singular and adjugate-value cases 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]

Codecov Report

❌ Patch coverage is 75.00000% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 86.78%. Comparing base (40dd98f) to head (1736e19).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
...rces/AngouriMath/Core/Entity/Omni/Entity.Matrix.cs	75.00%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2353      +/-   ##
==========================================
- Coverage   86.79%   86.78%   -0.01%     
==========================================
  Files         312      312              
  Lines       68709    68727      +18     
  Branches    20006    20014       +8     
==========================================
+ Hits        59637    59647      +10     
- Misses       4904     4907       +3     
- Partials     4168     4173       +5     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.33% <75.00%> (-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
Sources/AngouriMath/Functions/GenTensorGuard.cs	100.00% <ø> (ø)
...rces/AngouriMath/Core/Entity/Omni/Entity.Matrix.cs	84.89% <75.00%> (-0.17%)	⬇️

... and 7 files with indirect coverage changes

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