VFPDO Object Overloaded Builtins - Maple Programming Help

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overview of overloaded builtins for VFPDO object.

Description

 • The functionalities of some Maple builtin commands are extended for use on VFPDO object.
 • The following builtins have been overloaded for this purpose: indets, has, type, hastype
 • Let Delta be a VFPDO object.
 • (i) The call type(Delta, t) returns true if t is any of the following types: module, object, anything, appliable and VFPDO. See examples below.
 • (ii) The calls type(Delta, dependent(x)) and type(Delta, freeof(x)) respectively return true if the differential operator or the independent variables of Delta contain (respectively don't contain) x. See example below.
 • The indets, has, hastype builtin commands accept a VFPDO object and apply their methods onto the differential operator and the independent variables of the object.
 • These overloaded builtins are associated with the VFPDO object. For more detail, see Overview of the VFPDO object.

Examples

 > $\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right):$

Construct an VFPDO object from some differential expressions...

 > $X≔\mathrm{VectorField}\left(\mathrm{\xi }\left(x,y\right)\mathrm{D}\left[x\right]+\mathrm{\eta }\left(x,y\right)\mathrm{D}\left[y\right],\mathrm{space}=\left[x,y\right]\right)$
 ${X}{≔}{\mathrm{\xi }}{}\left({x}{,}{y}\right){}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{+}{\mathrm{\eta }}{}\left({x}{,}{y}\right){}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}$ (1)
 > $\mathrm{\Delta }≔\mathrm{VFPDO}\left(\left[a\left[1\right]\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),x\right)-a\left[2\right]\mathrm{\xi }\left(x,y\right),\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),x,x\right)-\left({a\left[1\right]}^{2}+{a\left[2\right]}^{2}\right)\mathrm{\eta }\left(x,y\right)\right],X\right)$
 ${\mathrm{\Delta }}{≔}{X}{→}\left[{{a}}_{{1}}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}{}{X}{}\left({x}\right)\right){-}{{a}}_{{2}}{}{X}{}\left({x}\right){,}\frac{{\partial }}{{\partial }{x}}{}\left(\frac{{\partial }}{{\partial }{x}}{}{X}{}\left({y}\right)\right){+}\left({-}{{a}}_{{1}}^{{2}}{-}{{a}}_{{2}}^{{2}}\right){}{X}{}\left({y}\right)\right]$ (2)

type

 > $\left[\mathrm{type}\left(\mathrm{\Delta },'\mathrm{VFPDO}'\right),\mathrm{type}\left(\mathrm{\Delta },'\mathrm{object}'\right),\mathrm{type}\left(\mathrm{\Delta },'\mathrm{module}'\right),\mathrm{type}\left(\mathrm{\Delta },'\mathrm{appliable}'\right)\right]$
 $\left[{\mathrm{true}}{,}{\mathrm{true}}{,}{\mathrm{true}}{,}{\mathrm{true}}\right]$ (3)

The VFPDO object contains x

 > $\mathrm{type}\left(\mathrm{\Delta },\mathrm{dependent}\left(x\right)\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{type}\left(\mathrm{\Delta },\mathrm{freeof}\left(a\left[1\right]\right)\right)$
 ${\mathrm{false}}$ (5)
 > $\mathrm{type}\left(\mathrm{\Delta },\mathrm{dependent}\left(\left[x,y\right]\right)\right)$
 ${\mathrm{true}}$ (6)

indets, has, hastype

 > $\mathrm{indets}\left(\mathrm{\Delta }\right)$
 $\left\{{x}{,}{y}{,}{{a}}_{{1}}{,}{{a}}_{{2}}\right\}$ (7)
 > $\mathrm{has}\left(\mathrm{\Delta },a\left[1\right]\right)$
 ${\mathrm{true}}$ (8)
 > $\mathrm{hastype}\left(\mathrm{\Delta },'\mathrm{name}'\right)$
 ${\mathrm{true}}$ (9)
 > $\mathrm{hastype}\left(\mathrm{\Delta },'\mathrm{list}'\right)$
 ${\mathrm{true}}$ (10)

Compatibility

 • The VFPDO Object Overloaded Builtins command was introduced in Maple 2020.