The extremum of an expression over a set, as a binder

[Rafael-SOWNet]

Part of #1212 — question I.6, and the extremum item of the plan there. The fourth of the agreed nodes, after divides (#1220) and card (#1221). Independent of both: cut from master, one mechanical conflict round on BREAKING-CHANGES.md and the public-API record with whichever lands first.

What it is

Four binders — Maximumf, Minimumf, Argmaxf, Argminf — reading max(f, t in S), min, argmax, argmin.

• Grammar: max and min already took two values; when the second argument is variable in set (an Inf whose element is a variable) they now bind instead, and argmax/argmin are new and require that shape. max(a, b), max(x, y), max(x, 1 in S) all stay the two-value form. Printed the same words back; \max_{t \in S} f and \operatorname{argmax}_{t \in S} f in LaTeX; sympy.maximum(f, t, S) in the SymPy export (argmax has none there and declines). MathS.Maximum/Minimum/Argmax/Argmin in code. The variable is bound over the expression and the set.
• The value (ExtremumOverSet) is answered over a finite set of numbers, by evaluating at each and comparing; and over a closed interval with numeric ends, by comparing the closed endpoints with the stationary points inside — the derivative's zeros, which the solver gives, with a periodic family c + p n enumerated where it lands in the interval.
• Two guards, because a wrong maximum is worse than none. The expression has to be smooth on the reals (sums, products, whole non-negative powers, sines, cosines, exponentials with a positive base) so that every interior extremum is a stationary point — abs and 1/x are declined. And the best candidate is checked against the expression sampled along the interval: the solver's zero-list is not guaranteed complete, and a sample that beats the best candidate means one was missed, on which the question is left as written. A sample can miss a narrow peak, so this is a guard, not a proof — what it rules out is the confident wrong answer.
• Left as written: an open endpoint (max(x, x in [0; 1)) has no maximum), a symbolic set or end, a pole, a kink, a set with a symbol in it, RR and the special sets.
• Threaded through substitution (the variable is bound, renamed as a summation's index is), sort keys, JSON, FreeVariables (the variable is bound), the inverter (declined), the public-API record. Not buildable-as-a-pattern, like the other binders, so the node census is unchanged.

One thing the measurement caught: the stationary points are read by Vars, not FreeVariables, because FreeVariables counts the constants pi, e and i — which appear in the roots the solver writes (ln(...)/i for a trig zero) — and miscounting them as parameters of a periodic family sent every interval case down the wrong branch.

The cost

Measured on 27ed5b53: max(f(t), t in S) was the two-value max of f(t) and the boolean t in S, unevaluated; argmax(f, t in S) was a parse error. A Loud row in BREAKING-CHANGES.md, with the table on both builds.

Not in this PR

The two-argument functions still have their old behaviour for every shape but variable in set, so nothing that parsed before changes except that one shape. The ~/E/P distribution nodes and Sequence are the remaining agreed nodes.

Checks

ExtremumTest: the sheet's I.6, fourteen answered extrema over finite sets and intervals, seven point-sets, twelve left-as-written shapes, three round trips, LaTeX, the four code spellings, JSON, the bound variable, and the two-value max unchanged. The reflection-driven node tests pass with the four new nodes. Full suite in two chunks: 8395 and 1458 pass.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura