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pattern matching - Is there a way to simplify this replacement rule


I have a rather big expression which contains many sums of form q x + w y. I know that y is much smaller than x and i want to omit it where possible, namely if both q and w are integers. So i apply the replacement rule


q_?IntegerQ x + w_?IntegerQ y -> q x


However this rule obviously doesn't work if either q or w (or both) is equal to unity because FullForm of q x contains Times and one of x doesn't. So to get replacement done i need to use the ugly set of rules


{ q_?IntegerQ x + w_?IntegerQ y -> q x , x + w_?IntegerQ y -> x , ... }

and in place of dots there are two more rules with w and both w and q omitted.


So the question is whether it is possible (in general) to somehow simplify this ugly set to anything more simple.



Answer



You can take advantage of the OneIdentity attribute of Times as it affects pattern matching(1),(2),(3) by making q and w Optional. (As Rojo shows in a comment above.) Condition is then used to check the q and w matches.


{3 x + 7 y, 2 x + E y, x + 5 y} /.
  q_. x + w_. y /; IntegerQ[q] && IntegerQ[w] :> q x



{3 x, 2 x + E y, x}

Note that I used RuleDelayed rather than Rule to localize q.


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