prolong - Maple Help
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liesymm

 prolong
 make substitutions for components of the extended isovector in terms of partials of the original isovector

 Calling Sequence prolong(Vn) prolong[1](Vn) prolong[2](Vn) prolong[3](Vn)

Parameters

 V - isovector as a list or name

Description

 • This routine construct equations that can be used to rewrite the components of isovector corresponding to the extended variables in terms of partials of isovector components corresponding to the independent and dependent variables.
 • The resulting set of equations can be used in subs().
 • This routine is used by reduce() to help simplify the determining equations of the contact symmetries.
 • 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[Eta].

Examples

 > $\mathrm{with}\left(\mathrm{liesymm}\right):$
 > $\mathrm{indepvars}\left(x,y\right)$
 $\left[{x}{,}{y}\right]$ (1)
 > $\mathrm{depvars}\left(f,g\right)$
 $\left[{f}{,}{g}\right]$ (2)
 > $\mathrm{prolong}\left(V\right)$
 $\left\{{\mathrm{V5}}{=}\frac{{ⅆ}{\mathrm{V3}}}{{ⅆ}{x}}{+}{\mathrm{w1}}{}\left(\frac{{ⅆ}{\mathrm{V3}}}{{ⅆ}{f}}\right){+}{\mathrm{w3}}{}\left(\frac{{ⅆ}{\mathrm{V3}}}{{ⅆ}{g}}\right){-}{\mathrm{w1}}{}\left(\frac{{ⅆ}{\mathrm{V1}}}{{ⅆ}{x}}{+}{\mathrm{w1}}{}\left(\frac{{ⅆ}{\mathrm{V1}}}{{ⅆ}{f}}\right){+}{\mathrm{w3}}{}\left(\frac{{ⅆ}{\mathrm{V1}}}{{ⅆ}{g}}\right)\right){-}{\mathrm{w2}}{}\left(\frac{{ⅆ}{\mathrm{V2}}}{{ⅆ}{x}}{+}{\mathrm{w1}}{}\left(\frac{{ⅆ}{\mathrm{V2}}}{{ⅆ}{f}}\right){+}{\mathrm{w3}}{}\left(\frac{{ⅆ}{\mathrm{V2}}}{{ⅆ}{g}}\right)\right){,}{\mathrm{V6}}{=}\frac{{ⅆ}{\mathrm{V3}}}{{ⅆ}{y}}{+}{\mathrm{w2}}{}\left(\frac{{ⅆ}{\mathrm{V3}}}{{ⅆ}{f}}\right){+}{\mathrm{w4}}{}\left(\frac{{ⅆ}{\mathrm{V3}}}{{ⅆ}{g}}\right){-}{\mathrm{w1}}{}\left(\frac{{ⅆ}{\mathrm{V1}}}{{ⅆ}{y}}{+}{\mathrm{w2}}{}\left(\frac{{ⅆ}{\mathrm{V1}}}{{ⅆ}{f}}\right){+}{\mathrm{w4}}{}\left(\frac{{ⅆ}{\mathrm{V1}}}{{ⅆ}{g}}\right)\right){-}{\mathrm{w2}}{}\left(\frac{{ⅆ}{\mathrm{V2}}}{{ⅆ}{y}}{+}{\mathrm{w2}}{}\left(\frac{{ⅆ}{\mathrm{V2}}}{{ⅆ}{f}}\right){+}{\mathrm{w4}}{}\left(\frac{{ⅆ}{\mathrm{V2}}}{{ⅆ}{g}}\right)\right){,}{\mathrm{V7}}{=}\frac{{ⅆ}{\mathrm{V4}}}{{ⅆ}{x}}{+}{\mathrm{w1}}{}\left(\frac{{ⅆ}{\mathrm{V4}}}{{ⅆ}{f}}\right){+}{\mathrm{w3}}{}\left(\frac{{ⅆ}{\mathrm{V4}}}{{ⅆ}{g}}\right){-}{\mathrm{w3}}{}\left(\frac{{ⅆ}{\mathrm{V1}}}{{ⅆ}{x}}{+}{\mathrm{w1}}{}\left(\frac{{ⅆ}{\mathrm{V1}}}{{ⅆ}{f}}\right){+}{\mathrm{w3}}{}\left(\frac{{ⅆ}{\mathrm{V1}}}{{ⅆ}{g}}\right)\right){-}{\mathrm{w4}}{}\left(\frac{{ⅆ}{\mathrm{V2}}}{{ⅆ}{x}}{+}{\mathrm{w1}}{}\left(\frac{{ⅆ}{\mathrm{V2}}}{{ⅆ}{f}}\right){+}{\mathrm{w3}}{}\left(\frac{{ⅆ}{\mathrm{V2}}}{{ⅆ}{g}}\right)\right){,}{\mathrm{V8}}{=}\frac{{ⅆ}{\mathrm{V4}}}{{ⅆ}{y}}{+}{\mathrm{w2}}{}\left(\frac{{ⅆ}{\mathrm{V4}}}{{ⅆ}{f}}\right){+}{\mathrm{w4}}{}\left(\frac{{ⅆ}{\mathrm{V4}}}{{ⅆ}{g}}\right){-}{\mathrm{w3}}{}\left(\frac{{ⅆ}{\mathrm{V1}}}{{ⅆ}{y}}{+}{\mathrm{w2}}{}\left(\frac{{ⅆ}{\mathrm{V1}}}{{ⅆ}{f}}\right){+}{\mathrm{w4}}{}\left(\frac{{ⅆ}{\mathrm{V1}}}{{ⅆ}{g}}\right)\right){-}{\mathrm{w4}}{}\left(\frac{{ⅆ}{\mathrm{V2}}}{{ⅆ}{y}}{+}{\mathrm{w2}}{}\left(\frac{{ⅆ}{\mathrm{V2}}}{{ⅆ}{f}}\right){+}{\mathrm{w4}}{}\left(\frac{{ⅆ}{\mathrm{V2}}}{{ⅆ}{g}}\right)\right)\right\}$ (3)

 See Also