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diffalg

 denote
 convert a differential polynomial from an external form to another one

 Calling Sequence denote (q, code, R)

Parameters

 q - differential polynomial in R code - name; jet, diff, or Diff R - differential polynomial ring

Description

 • Important: The diffalg package has been deprecated. Use the superseding package DifferentialAlgebra instead.
 • The command denote converts the differential polynomial q given in the notation  defined on R to the notation code.
 • The command with(diffalg,denote) allows the use of the abbreviated form of this command.

Examples

Important: The diffalg package has been deprecated. Use the superseding package DifferentialAlgebra instead.

 > $\mathrm{with}\left(\mathrm{diffalg}\right):$
 > $R≔\mathrm{differential_ring}\left(\mathrm{derivations}=\left[t\right],\mathrm{ranking}=\left[u\right]\right)$
 ${R}{≔}{\mathrm{ODE_ring}}$ (1)
 > $p≔{u\left[t\right]}^{2}-4u\left[\right]$
 ${p}{≔}{{u}}_{{t}}^{{2}}{-}{4}{}{u}\left[\right]$ (2)
 > $\mathrm{denote}\left(p,\mathrm{diff},R\right)$
 ${\left(\frac{{ⅆ}}{{ⅆ}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{u}{}\left({t}\right)\right)}^{{2}}{-}{4}{}{u}{}\left({t}\right)$ (3)
 > $Q≔\mathrm{differential_ring}\left(\mathrm{derivations}=\left[t\right],\mathrm{ranking}=\left[u\right],\mathrm{notation}=\mathrm{diff}\right)$
 ${Q}{≔}{\mathrm{ODE_ring}}$ (4)
 > $q≔\mathrm{diff}\left(u\left(t\right),t,t\right)-tu\left(t\right)+{\mathrm{diff}\left(u\left(t\right),t\right)}^{2}$
 ${q}{≔}\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{t}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{u}{}\left({t}\right){-}{t}{}{u}{}\left({t}\right){+}{\left(\frac{{ⅆ}}{{ⅆ}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{u}{}\left({t}\right)\right)}^{{2}}$ (5)
 > $\mathrm{denote}\left(q,\mathrm{jet},Q\right)$
 ${-}{t}{}{u}\left[\right]{+}{{u}}_{{t}}^{{2}}{+}{{u}}_{{t}{,}{t}}$ (6)

 See Also