The function defform is used to define the basic variables used in a computation, or to define the exterior derivative of an expression.

The function defform clears the remember tables of all functions in the forms package, as changing the definition of a form can make the remembered results invalid. However, definitions made through defform are not cleared; they are remembered permanently.

The function defform takes an arbitrary number of equations, where each equation is name = expr. There are certain expressions - const, scalar, form, odd, even, -1, and 0 that have special meanings.  Except for these, name = expr means name is a form and wdegree(name) = expr.

The expression const or -1 means type(name,const) is true.  The name even or odd means type(name,const) is true, but also that parity(name) is 0 or 1, as appropriate.  The names even and odd are useful for specifying a form with even or odd, but otherwise unknown wdegree.

The expression scalar or 0 means type(name,scalar) is true.  The name form means that type(name,form) is true, but does not give a value to wdegree(name).

The function defform can be used to define the exterior derivative of an expression, and these derivatives are remembered permanently.

The wdegree of an indexed name is by default the wdegree of the non-indexed name. Values of wdegree for a particular index can be explicitly stated.

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

$\mathrm{with}\left(\mathrm{difforms}\right)\:$

$\mathrm{defform}\left(a=\mathrm{const}\,b=\mathrm{scalar}\,e=\mathrm{nonhmg}\,j=3\,f=\mathrm{odd}\,l=f^3\,d\left(l\right)=e\,t=2\,t\left[3\right]=4\right)$

$\mathrm{type}\left(a\,\mathrm{const}\right)$

$\mathrm{true}$

$\mathrm{type}\left(b\,\mathrm{scalar}\right)$

$\mathrm{true}$

$\mathrm{type}\left(e\,\mathrm{form}\right),\mathrm{wdegree}\left(e\right)$

$\mathrm{true},\mathrm{nonhmg}$

$\mathrm{type}\left(j\,\mathrm{form}\right),\mathrm{wdegree}\left(j\right)$

$\mathrm{true},3$

$\mathrm{type}\left(f\,\mathrm{const}\right),\mathrm{parity}\left(f\right)$

$\mathrm{true},1$

$d\left(l\right)$

$e$

$\mathrm{wdegree}\left(t\right)$

$2$

$\mathrm{wdegree}\left(t\left[1\right]\right)$

$2$

$\mathrm{wdegree}\left(t\left[3\right]\right)$

$4$

$\mathrm{wdegree}\left(u\left[3\right]\right)=\mathrm{wdegree}\left(u\right)$

$\mathrm{wdegree}\left(u\right)=\mathrm{wdegree}\left(u\right)$