Function ratConstant

src/compute-engine/rubi/rubi-utils.ts:203–234

If e is identically a rational constant p/q (a multivariate rational * identity, e.g. b/(b·(bc/(bc−ad)) − a·(bd/(bc−ad))) = 1), return that * constant; else null. Sample-then-verify: a numeric sample guesses the * constant, polynomial expansion verifies the identity exactly.

(e: Expression)

        let t = rs[i].num;
        for (let j = 0; j < rs.length; j++) if (j !== i) t = t.mul(rs[j].den);
        num = num.add(t);
      }
      return { num, den };
    }
    case 'Subtract': {
      const u = asNumDen(ops![0]);
      const v = asNumDen(ops![1]);
      return {
        num: u.num.mul(v.den).sub(v.num.mul(u.den)),
        den: u.den.mul(v.den),
      };
    }
    case 'Power': {
      const k = ops![1].re;
      if (
        ops![1].isInteger &&
        typeof k === 'number' &&
        Number.isInteger(k) &&
        k !== 0 &&
        Math.abs(k) <= 6
      ) {
        const r = asNumDen(ops![0]);
        if (k > 0) return { num: r.num.pow(k), den: r.den.pow(k) };
        return { num: r.den.pow(-k), den: r.num.pow(-k) };
      }
      return { num: e, den: ce.One };
    }
    default:
      return { num: e, den: ce.One };
  }
}

/** If e is identically a rational constant p/q (a multivariate rational
 * identity, e.g. b/(b·(bc/(bc−ad)) − a·(bd/(bc−ad))) = 1), return that
 * constant; else null. Sample-then-verify: a numeric sample guesses the