 Builtins - Maple Help

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...

 > $X≔\mathrm{VectorField}\left(\mathrm{ξ}\left(x,y\right){\mathrm{D}}_{x}+\mathrm{η}\left(x,y\right){\mathrm{D}}_{y},\mathrm{space}=\left[x,y\right]\right)$
 ${X}{≔}{\mathrm{\xi }}{}\left({x}{,}{y}\right){}\left(\frac{{ⅆ}}{{ⅆ}{x}}\right){+}{\mathrm{\eta }}{}\left({x}{,}{y}\right){}\left(\frac{{ⅆ}}{{ⅆ}{y}}\right)$ (1)
 > $\mathrm{Δ}≔\mathrm{VFPDO}\left(\left[{a}_{1}\left(\frac{\partial }{\partial x}\mathrm{ξ}\left(x,y\right)\right)-{a}_{2}\mathrm{ξ}\left(x,y\right),\frac{{\partial }^{2}}{\partial {x}^{2}}\mathrm{η}\left(x,y\right)-\left({a}_{1}^{2}+{a}_{2}^{2}\right)\mathrm{η}\left(x,y\right)\right],X\right)$
 ${\mathrm{\Delta }}{≔}{X}{→}\left[{{a}}_{{1}}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}{}{X}{}\left({x}\right)\right){-}{{a}}_{{2}}{}{X}{}\left({x}\right){,}\frac{{\partial }}{{\partial }{x}}{}\left(\frac{{\partial }}{{\partial }{x}}{}{X}{}\left({y}\right)\right){+}\left({-}{{a}}_{{1}}^{{2}}{-}{{a}}_{{2}}^{{2}}\right){}{X}{}\left({y}\right)\right]$ (2) type

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

The VFPDO object contains x

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

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

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