The greatest term, tried and ruled

The ratio rule is quick, but a computer can check it against every term. In this lab you find the greatest terms of $(a + b)^n$ by trying every term, then by the rule, and then you test for a tie.

Your tasks.

1. In by_trying, return the list of the numbers of the greatest terms of $(a + b)^n$. Work out every term, find the greatest, and list every place that equals it. Count the first term as 1.
2. In by_rule, return the same list, using $m = \dfrac{(n + 1)\,b}{a + b}$. Use a Fraction so that a whole number $m$ is recognised exactly.
3. In ties, return True when two terms are equal and greatest, and False otherwise.