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liesymm

 translate
 the total derivative

 Calling Sequence translate(w1)

Parameters

 w1 - (optional) named partial derivative

Description

 • Various routines in the liesymm package generate names on an as needed basis to represent partial derivatives of the underlying dependent variables with respect to one or more of the independent variables.  This routine can be used to discover which partial is represented by a given name.
 • If no argument is given then a name translation table is returned. The entries of the table are the arguments that would have been used in the corresponding Diff() command.
 • If translate is called with a name then the entry for that name is retrieved from the table. If no entry is present then the name is returned.
 • This routine is part of the liesymm package and is ordinarily loaded via with(liesymm). It can also be called via the package style'' name liesymm[translate].

Examples

 > $\mathrm{with}\left(\mathrm{liesymm}\right):$
 > $\mathrm{eq}≔\frac{{{\partial }}^{3}}{{\partial }{x}^{3}}h\left(t,x\right)=\frac{{{\partial }}^{2}}{{\partial }x{\partial }t}h\left(t,x\right)$
 ${\mathrm{eq}}{≔}\frac{{{\partial }}^{{3}}}{{\partial }{{x}}^{{3}}}{}{h}{}\left({t}{,}{x}\right){=}\frac{{{\partial }}^{{2}}}{{\partial }{x}{}{\partial }{t}}{}{h}{}\left({t}{,}{x}\right)$ (1)
 > $\mathrm{makeforms}\left(\mathrm{eq},h\left(t,x\right),k\right)$
 $\left[{d}{}\left({h}\right){-}{\mathrm{k1}}{}{d}{}\left({t}\right){-}{\mathrm{k2}}{}{d}{}\left({x}\right){,}{d}{}\left({\mathrm{k2}}\right){-}{\mathrm{k3}}{}{d}{}\left({t}\right){-}{\mathrm{k4}}{}{d}{}\left({x}\right){,}\left({d}{}\left({t}\right)\right){&^}\left({d}{}\left({\mathrm{k4}}\right)\right){-}\left({d}{}\left({t}\right)\right){&^}\left({d}{}\left({\mathrm{k1}}\right)\right)\right]$ (2)
 > $\mathrm{translate}\left(\mathrm{k4}\right)$
 ${h}{,}{x}{,}{x}$ (3)
 > $\mathrm{translate}\left(\right)$
 ${\mathrm{table}}\left(\left[{\mathrm{k1}}{=}\left({h}{,}{t}\right){,}{\mathrm{k3}}{=}\left({h}{,}{x}{,}{t}\right){,}{h}{=}{h}{,}{t}{=}{t}{,}{\mathrm{k4}}{=}\left({h}{,}{x}{,}{x}\right){,}{x}{=}{x}{,}{\mathrm{k2}}{=}\left({h}{,}{x}\right)\right]\right)$ (4)

 See Also