Function eToTheI

test/compute-engine/power-combination.test.ts:229–233

(theta: Expression)

  test('e^{iπ/3} evaluates to an EXACT expression, not a float (Euler form)', () => {
    // Regression: the Euler branch assembled the result with the `.add()`/
    // `.mul()` methods, which fold the exact cos/sin literals (1/2, √3/2) to
    // machine floats — violating the evaluate-vs-N exactness contract.
    const e = engine.parse('e^{i\\pi/3}').evaluate();
    // No decimal float appears in the serialization (exact radical/rational).
    expect(e.toString()).toBe('1/2 + sqrt(3)/2i');
    expect(e.isSame(engine.parse('\\frac12 + \\frac{\\sqrt3}{2}i'))).toBe(true);
    // .N() still numericizes.
    const n = e.N();