Add round, min, max and gcd, closing #809

[Rafael-SOWNet]

Closes #809. Follows #827, which added floor and ceil.

Every convention measured, and two were not what the issue assumed

round is half to even

round(1/2)  = 0     round(-1/2) = 0
round(3/2)  = 2     round(-3/2) = -2
round(5/2)  = 2     round(-5/2) = -2

Python, SymPy, Mathematica and IEEE 754 all mean this by rounding, and it is .NET's Math.Round default. It is deliberately not floor(x + 1/2) — the obvious translation, which disagrees at every tie: that sends 1/2 to 1 and 5/2 to 3. There is a test pinning that the two differ, so nobody simplifies the node into it later.

That also decided the SymPy export. SymPy has no symbolic round — RoundFunction is an abstract base that raises, and .round() is a method on a concrete number, not a function of an expression. So ToSymPy builds the tie correction out of floor, frac and Mod rather than emitting the wrong one-liner, and the construction was checked against SymPy's own Rational.round() on ties, non-ties and negatives.

gcd is not integers only

The issue said "only defined on integers" and I repeated it. SymPy's gcd is the polynomial gcd with the integer case inside it:

gcd(12, 18)      = 6
gcd(1/2, 1/3)    = 1/6        rationals, not just integers
gcd(x**2-1, x-1) = x - 1      polynomials

Integers and rationals are computed here. The polynomial case is left as the node rather than half-done — this library already has PolynomialGcd behind the PolynomialGcdCancellation rule set, and wiring that in is its own change.

min and max are nodes, not sugar

Expressible as (a + b ∓ |a − b|)/2, and SymPy still keeps Min/Max as nodes. That is the right call: the closed form is what they simplify to where it helps, not what they should print as — and the round-trip contract would make a sugar spelling permanent, since min(a, b) could then never print as min.

They compare only where the arguments are ordered; an unordered pair is left alone rather than guessed at. Their derivative stays unevaluated, because stating it needs a case split on which argument is smaller — declining is the honest answer there.

Variadic

min, max and gcd take any number of arguments and fold left, as they do everywhere else: min(3, 5, 1) is 1. That needed one new helper, AssertAtLeast, since every existing arity check is for a fixed count.

Tests

5928 passing, 0 failed, 14 skipped. F# 130 passing.

RoundMinMaxGcdTest covers the tie behaviour in both directions, that round differs from floor(x + 1/2), comparison and folding, gcd over integers and rationals, printing, LaTeX, round-trips, derivatives, arity errors and substitution.

Twelve tests in MissingFunctionNamesRefusedTest asserted these names were refused and no longer pass. Same category as last time and worth naming: that is the answer getting better, not a test pinning a fudge. The refusal cases move to trunc, lcm, erf and conjugate, which are what is still missing.

Compatibility

BREAKING-CHANGES.md records it. If you were catching UnrecognizedFunctionParseException around these names, that is dead code now. Bare min, max and floor without a bracket are still ordinary variables, and minimum(x) is still the implicit product.

🤖 Generated with Claude Code