Tricks_L-O_10.html

MatchQ

In order for a pattern to match an expression, the pattern and the expression
it is compared with must have the same FullForm after evaluation.  For
example the expression a/b has the FullForm Times[a,Power[b,-1]], so it
doesn't match the pattern (_Rational).  MatchQ is a very good tool to use
when testing a pattern to see if it matches the intended expressions.  Some
interesting examples of MatchQ are given below.

${MatchQ[3/2, p_/q_], MatchQ[3/2, _Rational]}$

The head HoldPattern used in next cell is explained in another section.

$Clear[a, b] ; {MatchQ[a/b, _Rational], MatchQ[a/b, _/_], MatchQ[a/b, HoldPattern[_/_]], MatchQ[a/b, p_/q_]}$

${MatchQ[a/2, p_/q_], MatchQ[a/2, _Rational], MatchQ[a/2, _ * _Rational]}$

${MatchQ[1/Sqrt[b], _/Sqrt[_]], MatchQ[1/Sqrt[b], HoldPattern[_/Sqrt[_]]], MatchQ[1/Sqrt[b], 1/Sqrt[_]]}$

${MatchQ[a/Sqrt[b], _/Sqrt[_]], MatchQ[a/Sqrt[b], HoldPattern[_/Sqrt[_]]], MatchQ[a ... tern[x_/Sqrt[y_]]], MatchQ[a/Sqrt[b], x_ * y_^(-1/2)], <br />MatchQ[a/Sqrt[b], x_/Sqrt[y_]]}$

${MatchQ[2 + 3I, a_ + b_ * I], MatchQ[2 + 3I, _Complex]}$

${MatchQ[a + b I, _Complex], MatchQ[a + b I, _ + _Complex], MatchQ[a + b I, _ + _ * ... _ * Complex[0, 1]]], MatchQ[a + b I, _ + _ * _Complex ], MatchQ[a + b I, x_ + y_ * I]}$

$data = {{2, 3}, {1, 4}, {6, 7}, {8, 6}, {2, 1}} ; MatchQ[data, {{_, _} ..}]$

I don't provide further examples, but any combination of pattern matching constructs can be used with MatchQ. Nuances of pattern matching are discussed in another section.

Created by Mathematica (May 16, 2004)

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