The function parity computes the parity of an expression, by assuming that unspecified exponents are integers. Given n is an integer, $p^n\mathbf{mod}2=p$. For unassigned names, the function parity returns the name.

It is with the parity function that defform recognizes certain names as even or odd.

The command with(difforms,parity) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{difforms}\right)\:$$\mathrm{defform}\left(w=p\,p=\mathrm{even}\right)$

$\mathrm{parity}\left(3p\right)$

$0$

$\mathrm{parity}\left(p^m+k\right)$

$k$