Hardy-Weinberg with exact fractions

You will write the three calculations of the Hardy-Weinberg principle as functions. They use exact fractions, so an answer is never rounded.

The idea. Count the gene copies to find $p$. Square and multiply to find the genotype frequencies. Compare them with the observed genotypes to see whether a sample is in equilibrium.

Your tasks.

1. Finish allele_frequencies. It gives $(p, q)$ as fractions from the counts of $AA$, $Aa$ and $aa$.
2. Finish genotype_frequencies. It gives the frequencies of $AA$, $Aa$ and $aa$ for a given $p$.
3. Finish in_equilibrium. It says whether the counts of a sample have the Hardy-Weinberg proportions.