Function pellFamilyMembersInBox

test/compute-engine/diophantine.test.ts:406–432

* Applies the family-generation rule documented on `PellResult`: every class * rep times unit^t for `t` in `[-tRange, tRange]`, plus the global negation, * filtered down to the `|x|,|y| ≤ bound` box (to match a bounded * `bruteForcePell` oracle).

(
  classes: [bigint, bigint][],
  unit: [bigint, bigint],
  D: bigint,
  tRange: bigint,
  bound: bigint
)

 * `bruteForcePell` oracle).
 */
function pellFamilyMembersInBox(
  classes: [bigint, bigint][],
  unit: [bigint, bigint],
  D: bigint,
  tRange: bigint,
  bound: bigint
): [bigint, bigint][] {
  const invUnit: [bigint, bigint] = [unit[0], -unit[1]];
  const all: [bigint, bigint][] = [];
  for (const cls of classes) {
    all.push(cls);
    let pos = cls;
    for (let t = 1n; t <= tRange; t++) {
      pos = pellMul(pos, unit, D);
      all.push(pos);
    }
    let neg = cls;
    for (let t = 1n; t <= tRange; t++) {
      neg = pellMul(neg, invUnit, D);
      all.push(neg);
    }
  }
  const withNegation = all.concat(all.map(([x, y]) => [-x, -y] as [bigint, bigint]));
  return dedupePairsLocal(withNegation).filter(
    ([x, y]) => x <= bound && x >= -bound && y <= bound && y >= -bound
  );
}

/**
 * Cross-checks a `'family'` `solvePell` result against the independent