Function extractContent

src/compute-engine/boxed-expression/factor.ts:483–544

* Extract the integer content (GCD of all integer coefficients) from a * polynomial, then recursively factor the primitive part. * Returns null if content is 1 or coefficients are not all integers. * * IMPORTANT: Does not call .simplify() to avoid infinite recursion.

(expr: Expression, variable: string)

    for (let i = 1; i * i <= n; i++) {
      if (n % i === 0) {
        result.push(i);
        if (i !== n / i) result.push(n / i);
      }
    }
    return result;
  };

  // Enumerate candidate rational roots ±p/q
  const pDivisors = divisors(constantInt);
  const qDivisors = divisors(leadingInt);
  const candidates: [number, number][] = [];
  const seen = new Set<number>();
  for (const p of pDivisors) {
    for (const q of qDivisors) {
      const pos = p / q;
      const neg = -p / q;
      if (!seen.has(pos)) {
        seen.add(pos);
        candidates.push([p, q]);
      }
      if (!seen.has(neg)) {
        seen.add(neg);
        candidates.push([-p, q]);
      }
    }
  }

  if (candidates.length > 100) return null;

  const x = ce.symbol(variable);
  const factors: Expression[] = [];
  let remaining = expr;

  for (const [p, q] of candidates) {
    // Check remaining degree
    const remDeg = polynomialDegree(remaining, variable);
    if (remDeg <= 0) break;

    const root = q === 1 ? ce.number(p) : ce.number(p).div(ce.number(q));
    // Evaluate the remaining polynomial at the candidate root
    const value = remaining.subs({ [variable]: root }).N();
    if (!value.isSame(0)) continue;

    // Root found — divide out (x - root)
    const linearFactor =
      q === 1 ? x.sub(ce.number(p)) : ce.number(q).mul(x).sub(ce.number(p));

    const divResult = polynomialDivide(remaining, linearFactor, variable);
    if (!divResult) continue;

    factors.push(linearFactor);
    remaining = divResult[0];
  }

  if (factors.length === 0) return null;

  // Try quadratic factoring on any remaining degree-2 polynomial
  const remDeg = polynomialDegree(remaining, variable);