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2.3.6 Patterns Involving Alternatives

Specifying patterns that involve alternatives.

  • This defines h to give p when its argument is either a or b.
  • In[1]:= h[a | b] := p

  • The first two cases give p.
  • In[2]:= {h[a], h[b], h[c], h[d]}


  • You can also use alternatives in transformation rules.
  • In[3]:= {a, b, c, d} /. (a | b) -> p


  • Here is another example, in which one of the alternatives is itself a pattern.
  • In[4]:= {1, x, x^2, x^3, y^2} /. (x | x^_) -> q


    When you use alternatives in patterns, you should make sure that the same set of names appear in each alternative. When a pattern like (a[x_]|b[x_]) matches an expression, there will always be a definite expression that corresponds to the object x. On the other hand, if you try to match a pattern like (a[x_]|b[y_]), then there will be a definite expression corresponding either to x, or to y, but not to both. As a result, you cannot use x and y to refer to definite expressions, for example on the right-hand side of a transformation rule.

  • Here f is used to name the head, which can be either a or b.
  • In[5]:= {a[2], b[3], c[4], a[5]} /. (f:(a|b))[x_] -> r[f, x]