Function monomialsX

src/compute-engine/rubi/rubi-utils.ts:290–348

monomial decomposition: u = Σ coeff·x^deg, coefficients x-free. * Returns null when u is not a polynomial in x.

(u: Expression, x: string)

      let m = 0;
      for (const t of ops) {
        const d = polyDegreeX(t, x);
        if (d < 0) return -1;
        m = Math.max(m, d);
      }
      return m;
    }
    case 'Multiply': {
      let s = 0;
      for (const t of ops) {
        const d = polyDegreeX(t, x);
        if (d < 0) return -1;
        s += d;
      }
      return s;
    }
    case 'Negate':
      return polyDegreeX(ops[0], x);
    case 'Subtract': {
      const d0 = polyDegreeX(ops[0], x);
      const d1 = polyDegreeX(ops[1], x);
      return d0 < 0 || d1 < 0 ? -1 : Math.max(d0, d1);
    }
    case 'Power': {
      const e = realNum(ops[1]);
      if (e === null || !Number.isInteger(e) || e < 0) return -1;
      const d = polyDegreeX(ops[0], x);
      return d < 0 ? -1 : d * e;
    }
    case 'Divide':
      return ops[1].has(x) ? -1 : polyDegreeX(ops[0], x);
  }
  return -1;
}

/** monomial decomposition: u = Σ coeff·x^deg, coefficients x-free.
 * Returns null when u is not a polynomial in x. */
function monomialsX(u: Expression, x: string): [Expression, number][] | null {
  const ce = u.engine;
  if (!u.has(x)) return [[u, 0]];
  if (u.symbol === x) return [[ce.One, 1]];
  const ops = u.ops;
  if (!ops) return null;
  switch (u.operator) {
    case 'Add': {
      const out: [Expression, number][] = [];
      for (const t of ops) {
        const m = monomialsX(t, x);
        if (m === null) return null;
        out.push(...m);
      }
      return out;
    }
    case 'Negate': {
      const m = monomialsX(ops[0], x);
      return m === null ? null : m.map(([c, d]) => [c.neg(), d]);
    }
    case 'Subtract': {
      const m0 = monomialsX(ops[0], x);