Read factorial(x) as the factorial rather than as a product (#733)

[Rafael-SOWNet]

Part of #733 -- the last of its defect half.

factorial is the name the function has in sympy, MATLAB, Mathematica and Python's math module, and the grammar did not have it -- while having the function already, as the postfix x! and as MathS.Factorial. Nothing was missing but the spelling.

A one-argument call under a name the grammar does not know never errors: it falls through to the implicit multiplication that lets a(b + c) mean a * (b + c). So

"factorial(5)".ToEntity()      // factorial * 5   -- an undeclared variable times 5

came back as a product, silently, where the answer is 120.

Fix

One rule, mapping to MathS.Factorial(arg), placed next to gamma( -- the same fact one shift along, which the grammar already had -- so that factorial(x) and x! parse to one tree rather than each being separately defined.

Only the exact name followed by a bracket is the function, as for every other function in the grammar:

written	parses as
factorial(x)	x!	the function
factorial	factorial	an ordinary variable, as before
factorial2	factorial ^ 2	the implicit power x2 means, as before
factoriall(x)	factoriall * x	the implicit product a(b + c) means, as before
factorial3(x)	factorial ^ 3 * x	likewise, as before

Tests pin all of them, and the postfix x! is untouched.

How it was found

By sweeping the rest of MathS's public surface past the parser, rather than the CAS spellings that #733 came from. That sweep is otherwise clean: every hyperbolic spelling, signum, abs and gamma are read correctly, and taylor, sinc and conjugate name nothing the library has as a node.

#733 stays open for the names the library genuinely does not have -- floor, ceil, round, min, max, gcd, lcm -- since each wants its own judgement about whether the library should have the function at all.

Measured

factorial(5) from factorial * 5 to 120; factorial(0) 1; factorial(1) 1; factorial(6) 720; factorial(x) now the same tree as x!; factorial(5) agrees with gamma(6).

Parser regenerated with antlr-4.13.1 and the post-processor, as in #734. Full suite 4920 passed / 0 failed, F# 130/130, corpus 112/117 with 0 wrong, 0 error, 0 timeout.

🤖 Generated with Claude Code