Function functionOfQ

src/compute-engine/rubi/rubi-utils.ts:3479–3498

FunctionOfQ[v, u, x, pure] — restricted to the pure trig-substitution * targets this slice handles; false (decline) otherwise.

(
  ce: ComputeEngine,
  v: Expression,
  u: Expression,
  x: string,
  pure: boolean
)

  const FALSE = ce.symbol('False');
  // Rubi: MatchQ[y, a_.*x /; FreeQ[a,x]] → False (degree-1 monomial, no
  // constant term: the trivial linear case handled by polynomial rules).
  const ydeg = polyDegreeX(y, x);
  if (ydeg === 1) {
    const yc = polyCoeffsX(y, x);
    if (yc !== null && yc.length === 2 && zeroQ(yc[0])) return FALSE;
  }
  // Rubi: If[PolynomialQ[y], PolynomialQ[u] && Exponent[u]==Exponent[y]-1,
  // EasyDQ[y]] — a hard gate before any differentiation.
  if (ydeg >= 0) {
    const udeg = polyDegreeX(u, x);
    if (!(udeg >= 0 && udeg === ydeg - 1)) return FALSE;
  } else if (!easyDQ(y, x)) {
    return FALSE;
  }
  const v = ce.function('D', [y, ce.symbol(x)]).evaluate();
  if (zeroQ(v)) return FALSE;
  let q = u.div(v); // canonical quotient: cos/cos → 1, sin⁴/(−sin) → −sin³
  if (!q.has(x)) return q;
  q = safeSimplify(q);
  if (!q.has(x)) return q;
  return FALSE;
}