[Rafael-SOWNet]

Closes #2423.

|v| of a column vector was sqrt(sum v_k^2). That is the norm only where every component is real. A complex component gave NaN, a different number, or 0, and a symbol, which may take a complex value, was squared as though it could not. The norm is now sqrt(sum |v_k|^2):

• a Complex number contributes re^2 + im^2, so an exact norm stays exact;
• a component whose codomain is real, such as domain(x, RR), is squared as it is, since that is the same value;
• anything else contributes abs(v)^2.

A row vector is now a vector too. abs([1 + i, 2]T) was taken entry by entry, [[abs(1 + i), 2]], where the column gives its norm. A general matrix is still taken entry by entry.

Absf.InnerSimplify is the only place that turns abs of a vector into a norm. Evaled and Simplify both reach it, and the LINQ compiler compiles the simplified form, so the compiled norm over Complex follows. FastExpression refuses a matrix, as before.

Expression	2.6.0	master	this branch	true
abs([1 + i, 2]).Evaled	NaN	NaN	2.449489742783178…	sqrt(6)
abs([1 + i, 2]).Simplify()	NaN	NaN	sqrt(6)	sqrt(6)
abs([3 * i, 4]).Simplify()	sqrt(7)	sqrt(7)	5	5
abs([1 + i, 1 - i]).Simplify()	0	0	2	2
abs([x, y]).Simplify()	sqrt(x^2 + y^2)	same	sqrt(abs(x)^2 + abs(y)^2)	sqrt(|x|^2 + |y|^2)
abs([x, y]) at x = i, y = 0, evaluated / LINQ over Complex	NaN / i	same	1 / 1	1
abs([1 + i, 2]T).Simplify(), a row vector	[[abs(1 + i), 2]]	same	sqrt(6)	sqrt(6)
abs([3, 4]), abs([sqrt(2), -1]), LINQ over double	right	right	unchanged

The rows are in BREAKING-CHANGES.md, measured on the 2.6.0 package.

Checked on this branch:

• Tests: UnitTests 19382 passed, plus the MCP, Terminal, InteractiveWrapper and F# wrapper suites, and the AOT smoke test. A new test checks norms worked out by hand at real, negative and complex points, through Evaled, Simplify and LINQ over Complex and double, and components declared real.
• Harnesses: BoundCheck, RootCheck, CasBench, PropCheck, SimpSweep, RuleCheck, CanonCheck and Confluence all pass.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.81%. Comparing base (2eea2e9) to head (faa575d).

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2431      +/-   ##
==========================================
- Coverage   86.81%   86.81%   -0.01%     
==========================================
  Files         312      312              
  Lines       69551    69561      +10     
  Branches    20316    20320       +4     
==========================================
+ Hits        60383    60389       +6     
- Misses       4932     4935       +3     
- Partials     4236     4237       +1     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.35% <100.00%> (-0.01%)	⬇️
fsharp	32.97% <ø> (ø)
interactive	39.81% <ø> (ø)

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Files with missing lines	Coverage Δ
...nuous/Evaluation.Continuous.Arithmetics.Classes.cs	88.13% <100.00%> (+0.12%)	⬆️

... and 1 file with indirect coverage changes

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