check for an even function
check for an odd function
expression, regarded as a function of x
These procedures test the parity of the expression f, that is, whether it is even or odd, with respect to x.
More precisely, type⁡f⁡x,evenfunc⁡x returns true if Maple can determine that f⁡x−f⁡−x is zero and false otherwise. Maple performs this test by calling Testzero on this difference. If false is returned, that is not a guarantee that f is not even: it may be zero, but if so, Testzero is not strong enough to recognize that the result is zero. Type oddfunc⁡x is determined in a similar way but using the expression f⁡x+f⁡−x.
In the following case, f is even, but the default zero testing algorithm does not recognize this.
By changing the zero testing algorithm, we can make this return true. By default, Testzero calls Normalizer. In this case, we strengthen Normalizer.
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