Function posAux

src/compute-engine/rubi/rubi-utils.ts:1079–1116

(u: Expression)

  // raw relational heads (older Rubi guards; symbolic operands ⇒ false)
  Less: (args, ctx) => cmpChain(args, ctx, (a, b) => a < b),
  Greater: (args, ctx) => cmpChain(args, ctx, (a, b) => a > b),
  LessEqual: (args, ctx) => cmpChain(args, ctx, (a, b) => a <= b),
  GreaterEqual: (args, ctx) => cmpChain(args, ctx, (a, b) => a >= b),
  Equal: (args, ctx) => cmpChain(args, ctx, (a, b) => a === b),
  Unequal: (args, ctx) => cmpChain(args, ctx, (a, b) => a !== b),
};

// IntegerQ-style helpers over built expressions (IntBinomialQ/IntQuadraticQ)
function intQE(e: Expression): boolean {
  return isLiteralInteger(e.evaluate());
}
function intsQE(...es: Expression[]): boolean {
  return es.every(intQE);
}
function igtQE(e: Expression, k: number): boolean {
  const ev = e.evaluate();
  return isLiteralInteger(ev) && (realNum(ev) ?? -Infinity) > k;
}
function eqNum(e: Expression, k: number): boolean {
  const r = realNum(e.evaluate());
  return r !== null ? r === k : zeroQ(e.sub(e.engine.number(k)));
}

/** Rubi QuadraticQ (scalar case): PolyQ[u,x,2] and not a pure c·x² */
function quadraticQX(u: Expression, x: string): boolean {
  const c = polyCoeffsX(u, x);
  if (c === null) return false;
  const t = trimZeros(c);
  if (t.length !== 3) return false;
  return !(t[0].isSame(0) && t[1].isSame(0));
}

function cmpChain(
  args: Json[],
  ctx: Ctx,
  cmp: (a: number, b: number) => boolean
): boolean {
  // numeric first; fall back to simplification (symbolic ratios like
  // b/(b·c−a·d) after a normalization step can simplify to a number —
  // several Rubi guards rely on this to stop rule refiring), then to
  // multivariate rational collapse (nested-rational identities that