Function buildMono

src/compute-engine/rubi/rubi-utils.ts:2840–2850

Build `(coef·head[arg])^exp` (dropping a unit coefficient / exponent).

(
  ce: ComputeEngine,
  coef: Expression,
  head: string,
  arg: Expression,
  exp: Expression
)

  const shifted = cofunctionShiftRec(ce, e, x);
  if (hasDesyncedTargetArgs(shifted)) return e; // within-pair arg desync: revert
  return shifted;
}

// Reciprocal inert heads → negative power of their base cofunction: `csc→1/sin`,
// `sec→1/cos`. Unlike Mathematica Rubi — which keeps `csc`/`sec` as distinct
// inert heads and carries a full parallel family of `(b·csc)^n`/`(b·sec)^n`
// rules — this port routes reciprocal-head integrands through the sine/cosine
// POWER rules, which already handle negative exponents (`∫sin·cos^-5` closes
// but `∫sin·sec^5` did not, because `sec` is an opaque head no `(d·cos)^n`
// pattern matches). Rewriting the reciprocal to a negative power collapses
// products like `sin·csc^5 → sin^-4` and exposes `cos·csc^5 → cos·sin^-5` to
// the odd-power substitution, so the whole `(g cos)^p (a+b sin)^m (c+d sin)^n`
// (§4.1.2.2) and bare `∫csc^n`/`∫sec^n` families close. Value-preserving.
const RECIP_BASE: Record<string, string> = { csc: 'sin', sec: 'cos' };