Function monoPartsX

src/compute-engine/rubi/rubi-utils.ts:1521–1584

structural monomial split u = coef·x^exp (coef and exp x-free; exp may * be symbolic). No expansion — mirrors Mathematica's literal matching of * a_.*x_^n_. terms over CE canonical form (Divide/Negate/Sqrt present).

(
  u: Expression,
  x: string
)

          };
          let i = -1;
          if (rest.some(sumBaseQ))
            i = pickBy(
              (f) => sumBaseQ(f) && allNegTermQ(f),
              (f) => negSumBaseQ(f),
              (f) => sumBaseQ(f) && someNegTermQ(f),
              sumBaseQ
            );
          if (i < 0) i = pickBy(atomBaseQ);
          if (i < 0) i = 0;
          return rtAux(rest[i].neg().evaluate(), n).mul(
            rtAux(
              productOf(
                ce,
                rest.filter((_, j) => j !== i)
              ),
              n
            )
          );
        }
        // -1 · single non-power factor
        if (n % 2 === 1) return rtAux(productOf(ce, rest), n).neg();
        return nthRoot(u, n);
      }
      // c < 0, c ≠ -1: RtAux[-c]·RtAux[-rest]
      return rtAux(c.neg().evaluate(), n).mul(
        rtAux(productOf(ce, rest).neg().evaluate(), n)
      );
    }
    // 3./4. double sign-flip pairings across two sum-base factors
    const iAll = fs.findIndex((f) => sumBaseQ(f) && allNegTermQ(f));
    if (iAll >= 0 && fs.some((f, i) => i !== iAll && sumBaseQ(f))) {
      const rest = productOf(
        ce,
        fs.filter((_, i) => i !== iAll)
      );
      return rtAux(fs[iAll].neg().evaluate(), n).mul(
        rtAux(rest.neg().evaluate(), n)
      );
    }
    const iNegSum = fs.findIndex(negSumBaseQ);
    if (iNegSum >= 0 && fs.some((f, i) => i !== iNegSum && negSumBaseQ(f))) {
      const rest = productOf(
        ce,
        fs.filter((_, i) => i !== iNegSum)
      );
      return rtAux(fs[iNegSum].neg().evaluate(), n).mul(
        rtAux(rest.neg().evaluate(), n)
      );
    }
    // 5. distribute the root over every factor
    return productOf(
      ce,
      fs.map((f) => rtAux(f, n))
    );
  }

  // non-product
  const r = realNum(u);