Factor polynomials with whole roots (#177)

[Rafael-SOWNet]

Closes #177: x^2 + 2x + 1
stayed as it was written.

x^2 + 2x + 1          →  (1 + x)^2
x^3 + 3x^2 + 3x + 1   →  (1 + x)^3
x^3 - 6x^2 + 11x - 6  →  (x - 1) * (x - 2) * (x - 3)
2x^2 + 4x + 2         →  2 * (1 + x)^2
x^2 + 2x              →  x * (2 + x)

A polynomial in one variable with rational coefficients has its rational roots found by
the rational root theorem — divisors of the constant term over divisors of the leading
one — each checked by exact evaluation and divided out by exact synthetic division. No
floating point is involved, so a root is either exact or not a root.

The factored form is handed to the simplifier as one more candidate, not as a
decision. It sits alongside the other forms already collected and the complexity metric
picks, which is why (1 + x)^2 wins while x^2 - 1 stays as it is.

Deliberately narrow, on two counts

Both are load-bearing — an earlier draft that only required a root to be found
regressed real cases.

Rational roots only. Factoring through every root would answer (x - i)(x + i) for
x^2 + 1 and (x - sqrt(2))(x + sqrt(2)) for x^2 - 2, which is not what factoring
those means. Tests assert those are left alone.

And only when it splits completely into whole roots. A partly factored answer is not
obviously better than the sum it came from, and fractional roots turn up mostly in the
output of calculus, where the expanded form is the conventional one — the antiderivative
of x^2 + x reads better as x^3/3 + x^2/2 than as x^2 * (x + 3/2) / 3. That was a
real regression in the earlier draft, and there is a test for it now.

Multivariate expressions are untouched and still go to the term-collecting rules.

Two existing tests change, and one is removed

• BigSimple1 asserted the expanded form of (1 + x)^4. It now gets (1 + x)^4,
  which is what it was asking for.

• FactorialXM1OverFactorialXM3 gets the same two factors in the other order.

• TestPowerSubstitution's second case is removed, because it was pinning a wrong
  answer:

  ∫ 3x²(x³+2)² dx  →  C - 5/4·x⁶ + (x³+2)(x⁶/2 + 2x³)
  

  That is not an antiderivative of the integrand. At x = 2 the integrand is 1200
  and the derivative of that answer is 1536. The true antiderivative is
  (x³+2)³/3, which differentiates back exactly. I checked this on a stock master
  build — it is not caused by this PR; this PR only perturbs a wrong answer into a
  differently wrong one, which is what surfaced it.

  Rather than update the expectation to another wrong string, the case is restated as
  what it should assert — that differentiating the answer returns the integrand — and
  left Skipped, matching how the other unfinished integration cases in that file are
  handled. It is checked at points rather than symbolically, because the difference is
  zero but Simplify does not reduce it to zero.

  It passes once Fix two Simplify hangs, an integration stack overflow, and incomplete factoring (#403, #531, #178, #205) #665 is also applied. I bisected this: neither Fix two Simplify hangs, an integration stack overflow, and incomplete factoring (#403, #531, #178, #205) #665 nor this PR
  fixes it alone, but together they do — with factoring available, the Simplify(1)
  inside the integrator produces a form that lets u-substitution succeed, so the
  integrand takes the correct route instead of the faulty by-parts one. The by-parts
  defect is presumably still there, just no longer reached for this integrand. Once
  both land, the skip can come off.

Testing

UnitTests 3675 passed / 0 failed. On the 117-problem corpus this branch is 76 solved
against master's 75, with one fewer wrong answer.

18 new tests: the factored cases, value preservation for each (including the ones that
deliberately do not factor), the irrational and complex cases being left alone, the
partial-split case, the antiderivative case, and the multivariate case.

Independent of #663 through #668; touches no file any of them touch.

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Codecov Report

❌ Patch coverage is 92.06349% with 10 lines in your changes missing coverage. Please review.
✅ Project coverage is 79.95%. Comparing base (90c00a8) to head (6453674).
⚠️ Report is 48 commits behind head on master.

Files with missing lines	Patch %	Lines
...th/Functions/Simplification/PolynomialFactoring.cs	91.86%	4 Missing and 6 partials ⚠️
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Additional details and impacted files

@@            Coverage Diff             @@
##           master     #669      +/-   ##
==========================================
- Coverage   80.99%   79.95%   -1.05%     
==========================================
  Files         155      156       +1     
  Lines       13687    12602    -1085     
  Branches     1957     2055      +98     
==========================================
- Hits        11086    10076    -1010     
+ Misses       1990     1932      -58     
+ Partials      611      594      -17     

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[Happypig375]

Needs an update

[Rafael-SOWNet]

Updated, and rebased onto current master.

The skipped test is gone rather than updated. It only ever existed because this branch, on its own, perturbed 3 * x2 * (x3 + 2) ^ 2 from one wrong antiderivative into a different wrong one, and I did not want to pin either — so I moved the case out of the theory into a skipped test asserting what it should give.

#670 fixed the actual cause (Variable.CreateUnique handing back a name already in use), and its version of TestPowerSubstitution now covers that case in the theory with the closed form C + (x ^ 3 + 2) ^ 3 / 3. So the stand-in has nothing left to stand in for, and master's theory is kept as-is.

Suite is green on the rebase: 3841 passed, 0 failed.