 difforms - Maple Programming Help

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difforms

 defform
 define a constant, scalar, or form

 Calling Sequence defform(n1 = e1, n2 = e2, . . . )

Parameters

 n1, n2, ... - names or calls to difforms[d] e1, e2, ... - Maple expressions

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{difforms}\right):$
 > $\mathrm{defform}\left(a=\mathrm{const},b=\mathrm{scalar},e=\mathrm{nonhmg},j=3,f=\mathrm{odd},l={f}^{3},d\left(l\right)=e,t=2,t\left[3\right]=4\right)$
 > $\mathrm{type}\left(a,\mathrm{const}\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{type}\left(b,\mathrm{scalar}\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{type}\left(e,\mathrm{form}\right),\mathrm{wdegree}\left(e\right)$
 ${\mathrm{true}}{,}{\mathrm{nonhmg}}$ (3)
 > $\mathrm{type}\left(j,\mathrm{form}\right),\mathrm{wdegree}\left(j\right)$
 ${\mathrm{true}}{,}{3}$ (4)
 > $\mathrm{type}\left(f,\mathrm{const}\right),\mathrm{parity}\left(f\right)$
 ${\mathrm{true}}{,}{1}$ (5)
 > $d\left(l\right)$
 ${e}$ (6)
 > $\mathrm{wdegree}\left(t\right)$
 ${2}$ (7)
 > $\mathrm{wdegree}\left(t\left[1\right]\right)$
 ${2}$ (8)
 > $\mathrm{wdegree}\left(t\left[3\right]\right)$
 ${4}$ (9)
 > $\mathrm{wdegree}\left(u\left[3\right]\right)=\mathrm{wdegree}\left(u\right)$
 ${\mathrm{wdegree}}{}\left({u}\right){=}{\mathrm{wdegree}}{}\left({u}\right)$ (10)