I run into this type of issue frequently when trying to apply known identities to complicated expressions: some of my expressions will have their forms simplified by mathematica in such a way that mathematica will not be capable of easily pattern-matching uniformly all the expressions. What are good ways of preventing premature reductions of complex expressions so that I can pattern match everything nicely?
Here's a simple example.
Say we have a table involving numbers $a,b$ generated as follows:
arr = Table[i*j a^i b^j, {i, 1, 5}, {j, 1, 5}]
$$\left( \begin{array}{ccccc} a b & 2 a b^2 & 3 a b^3 & 4 a b^4 & 5 a b^5 \\ 2 a^2 b & 4 a^2 b^2 & 6 a^2 b^3 & 8 a^2 b^4 & 10 a^2 b^5 \\ 3 a^3 b & 6 a^3 b^2 & 9 a^3 b^3 & 12 a^3 b^4 & 15 a^3 b^5 \\ 4 a^4 b & 8 a^4 b^2 & 12 a^4 b^3 & 16 a^4 b^4 & 20 a^4 b^5 \\ 5 a^5 b & 10 a^5 b^2 & 15 a^5 b^3 & 20 a^5 b^4 & 25 a^5 b^5 \\ \end{array} \right)$$
and furthermore let's say that we're working in regime for which $a,b$ are each so small that if the total power on both of them is larger than $5$ the term can be neglected. Then we might try to implement this via
arr /. a^i_ b^j_ :> RuleCondition[0, i + j > 5]
but the output is actually
$$\left( \begin{array}{ccccc} a b & 2 a b^2 & 3 a b^3 & 4 a b^4 & 5 a b^5 \\ 2 a^2 b & 4 a^2 b^2 & 6 a^2 b^3 & 0 & 0 \\ 3 a^3 b & 6 a^3 b^2 & 0 & 0 & 0 \\ 4 a^4 b & 0 & 0 & 0 & 0 \\ 5 a^5 b & 0 & 0 & 0 & 0 \\ \end{array} \right)$$
because even though the terms in the corners are order $6$ they are not of the form given by the pattern since $5ab^5$ is represented as Times[5,Power[a,5],b]. Since there is no Power on the b it isn't matched by the pattern. Are there any ways to handle the corner cases without hardcoding new patterns especially for them?
