Put the canonicalizers where a caller will look for them, and settle the -ize spelling (#746)

[Rafael-SOWNet]

Both canonicalisers existed only as Transformation objects, reachable by someone who already knew the transformation layer existed. This puts them beside Simplify, Expand and Factorize.

Entity Canonicalize()                     // the commutative structure
Entity? CanonicalizeAsRationalFunction()  // rational functions over Q, or null

Wiring them into the pipeline turned out not to be a thing to do

Simplify already runs CanonicalOrder before its rules — that is what lets a binary rule find sin(x)^2 + cos(x)^2 buried in a longer sum. And Canonicalization is InnerSimplification composed with the sort, so it cannot go inside InnerSimplified without containing itself.

What was missing was reach, not application.

The rational one refuses, and says so by answering nothing

null where the expression is not a rational function over ℚ — the library's own way of saying "no answer", and it keeps the boundary in the signature. A form whose whole value is that equal trees mean equal expressions must not hand back a normalisation that merely resembles one.

Cancelling still carries its condition: x/x is 1 provided not x = 0, and is not equal to the canonical form of 1. There is a test saying exactly that.

Nothing is applied by default

Pinned by a test: InnerSimplified still leaves y + x alone, and Simplify still leaves 1/x + 1/y split. Turning either on by default moves every commutative operand order in every printed answer — a release's decision, not a method's.

And the spelling is settled, in the direction the surface already went

The second commit renames five members so that one operation has one spelling:

Was	Is	Shipped?
Entity.Canonicalise	Canonicalize	no
Entity.CanonicaliseAsRationalFunction	CanonicalizeAsRationalFunction	no
Transformation.Canonicalisation	Canonicalization	no
Transformation.RationalCanonicalisation	RationalCanonicalization	no
Transformation.Rationalisation	Rationalization	v2.1.0
RewriteRules.RationaliseDenominator	RationalizeDenominator	v2.1.0

The rest of the surface is Factorize, Latexize, Stringize, Normalization, Factorization, so the odd ones out were the -ise five.

The last two are in the v2.1.0 tag and so get a BREAKING-CHANGES.md entry. It breaks a build rather than an answer — the compiler names the missing member. The one silent part is the rule set's Name, which comes from nameof, so a caller matching the string "RationaliseDenominator" now sees "RationalizeDenominator".

Prose keeps British spelling. Factorize has always sat beside the word "factorisation" and still does; the convention is about identifiers, not documentation. A private LongDivision.Canonicalise helper predating this work was renamed too, so a grep for the British spelling now returns only prose.

Measured

Suite 7087 passed / 0 failed, 17 of them new, run after the rename. docsamples against a build of the first commit: 84 samples, 0 compile errors, 0 output mismatches, 57 outputs verified. Library, unit tests, benchmark project and the F# wrapper all build under -c Release; the two Windows-only sample projects fail on Linux exactly as they do on master. PublicApi.txt records every addition and rename, and the alphabetical ordering was re-checked because s and z do not sort alike.

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