Function substFor3

src/compute-engine/rubi/rubi-utils.ts:3537–3559

SubstFor[v, u, x] — u with the trig subexpression `v` replaced by `x` * (u is a function of v). Returns null when v isn't a handled trig target.

(v: Expression, u: Expression, ctx: Ctx)

    const a = vc[0] ?? u.engine.Zero;
    const b = vc[1] ?? u.engine.Zero;
    const c = ac[0] ?? u.engine.Zero;
    const d = ac[1] ?? u.engine.Zero;
    if (!zeroQ(a.mul(d).sub(b.mul(c)))) return false;
    const bd = safeSimplify(b.div(d));
    if (!(bd.isNumberLiteral && bd.isRational === true)) return false;
    const num = bd.numerator;
    return a.div(num).add(b.div(num).mul(u.engine.symbol(x)));
  }
  if (CALCULUS_FNS.has(u.operator)) return false;
  // recurse over operands, threading the argument state
  let w: FotState = v;
  for (const op of u.ops) {
    w = fotAux(op, w, x);
    if (w === false) return false;
  }
  return w;
}

/** FunctionOfTrig[u, x]: the common linear trig argument, or the False symbol. */
function functionOfTrig(
  ce: ComputeEngine,
  u: Expression,
  x: string
): Expression {
  const r = fotAux(activateTrig(ce, u), null, x);
  return r === null || r === false ? ce.symbol('False') : r;