Hardy-Weinberg identity: p²+2pq+q² = (p+q)²; at p=q=1/2 → {1/4, 1/2, 1/4}

Sympy-exact witness of the Hardy-Weinberg binomial identity and its evaluation at the symmetric-allele anchor p = q = 1/2. Setup: frequencies (p², 2pq, q²) for (AA, Aa, aa) genotypes under random mating. Sum: p² + 2pq + q² = (p+q)² as a…