Function splitNumericFactor

src/compute-engine/rubi/rubi-utils.ts:482–512

Rubi NumericFactor/NonnumericFactors split of a term: the leading * rational coefficient and the remaining (non-numeric) factors.

(u: Expression)

}

/** Rubi PossibleZeroQ: canonical zero, simplified zero, or numerically ~0
 *
 * The `.N()` below must stay UNGATED — do not funnel it through
 * `numericValueOf`/`numberLiteralOf` (`boxed-expression/numerics.ts`), whose
 * `.unknowns` gate declines anything carrying a free variable. Deciding a
 * *symbolic* zero is this predicate's entire job, and `.N()` does it by
 * floating the exponents: `(⁴√b/⁴√a)² − √b/√a` numericizes to `0` (both terms
 * become `b^0.5·a^-0.5`) where `simplify()` sees nothing. Gating it made this
 * return `false` for a true zero and cost the R28a mixed-parity split its
 * closed form (integration-rules #544). Same reasoning for `posAux` below. */
export function zeroQ(d: Expression): boolean {
  if (d.isSame(0)) return true;
  const key = activeCaches ? d.toString() : '';
  const cached = activeCaches?.zeroQ.get(key);
  if (cached !== undefined) return cached;
  let result = false;
  const s = safeSimplify(d);
  if (s.isSame(0)) result = true;
  else {
    const n = s.N();
    if (isNumber(n) && typeof n.re === 'number' && typeof n.im === 'number')
      result = Math.abs(n.re) < 1e-12 && Math.abs(n.im) < 1e-12;
  }
  activeCaches?.zeroQ.set(key, result);
  return result;
}

function isLiteralInteger(e: Expression): boolean {
  return isNumber(e) && e.isInteger === true;
}
function isLiteralRational(e: Expression): boolean {
  return isNumber(e) && e.isRational === true;
}