Give the three numeric types one remainder between them (#708)

[Rafael-SOWNet]

Fixes #708.

The three numeric types answered % three different ways, and two of the answers were wrong. Because Integer and Rational are both Real, which one applied depended on the static type at the call site rather than on the values.

	7 % 3	-7 % 3	7 % -3	-7 % -3
Integer before	1	2	throws	throws
Real before	1	-1	1	-1
Rational before (7/2 % 3 etc.)	1/2	5/2	1/2	-7/2
all three, after	1	2	-2	-1

• Integer used EInteger.Mod, which refuses a negative divisor, so Integer.Create(7) % Integer.Create(-3) threw ArithmeticException: Divisor is negative — a public operator throwing on ordinary input.
• Real truncated, taking the sign of the dividend where the other two took the sign of the divisor.
• Rational added the divisor whenever the truncated remainder came out negative. That is the correct truncated-to-floored conversion only when the divisor is positive; for a negative one it moves the answer further from zero. (-7/2) % (-3) came back as -7/2 — larger in magnitude than the divisor, so not a remainder under any convention. The code carried a // TODO: consider the case for the divisor to be negative saying exactly this.

Why floored

All three now compute a - b*floor(a/b), so the remainder takes the sign of the divisor. This is what SymPy, Mathematica and Maxima answer, and the convention under which the residues modulo n are the numbers 0 to n-1.

Checked against SymPy 1.14 rather than asserted, integer and rational alike:

Mod(7/2, 3) = 1/2      Mod(-7/2, 3) = 5/2
Mod(7/2, -3) = -5/2    Mod(-7/2, -3) = -1/2

It is also what the library already does by hand where it needs a remainder it can rely on — ExpressionNumerical.Equality.cs carries a private TrueRemainder that converts C#'s truncation into precisely this.

What actually changes for callers

For Integer and Rational, only the broken cases move: the two that threw, and the one that was wrong.

For Real this is a behaviour change — -7 % 3 was -1 and is now 2. That is the point of the PR rather than a side effect, and it is why #708 is an issue rather than a quiet fix. Worth a maintainer's eye.

Tests

27 new, of which 12 fail without the change. Two are property tests rather than tables, since between them they are the definition of a remainder:

• it is strictly smaller in magnitude than the divisor — which is what the Rational case was failing;
• a - (a % b) is a whole multiple of b.

Suite: Failed: 0, Passed: 4572, Skipped: 14, Total: 4586, with no internal call site disturbed — the places that use % internally all divide by a positive constant.

Independent of #703, which needs a remainder and computes the floored one itself rather than going through these operators. If both land, #703 could be simplified to use % directly; I have left it alone so the two can be reviewed separately.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 81.83%. Comparing base (90c00a8) to head (eb91ede).
⚠️ Report is 82 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #709      +/-   ##
==========================================
+ Coverage   80.99%   81.83%   +0.83%     
==========================================
  Files         155      159       +4     
  Lines       13687    13807     +120     
  Branches     1957     2333     +376     
==========================================
+ Hits        11086    11299     +213     
+ Misses       1990     1854     -136     
- Partials      611      654      +43     

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