By Roger Godement
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Additional info for Algebra (Translation of Cours d'algèbre)
This is because both the left-hand side and right-hand side of a SetDelayed function are placed in the rule base without being evaluated. In view of this difference between the SetDelayed and Set functions, the question is when should you use one or the other function to create a rewrite rule? When you define a function, you usually do not want either the left-hand side or the right-hand side to be evaluated; you just want to make it available for use when the appropriate function call is made.
More… Clicking the More… hyperlink would take you directly to the Help Browser where a much more detailed explanation of this function can be found. You can also get help by highlighting any Mathematica function and pressing the F1 key on your keyboard. This will take you directly into the documentation for that function in the Help Browser. The Help Browser Mathematica contains a very useful addition to the help system called the Help Browser. The Help Browser allows you to search for functions easily and it provides extensive documentation and examples.
Some of the most useful such constructs are called predicates. A predicate is a function that returns a value of true or false depending upon whether its argument passes a test. For example, the predicate PrimeQ tests for the primality of its argument. In:= Out= PrimeQ 144 False Other predicates are available for testing numbers to see whether they are even, odd, integral, and so on. In:= Out= In:= Out= In:= Out= OddQ True EvenQ False IntegerQ[5/9] False The NumericQ predicate tests whether its argument is a numeric quantity.