diffalg(deprecated)/denote - Help

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)
 > $p≔{u}_{t}^{2}-4{u}_{[]}$
 ${p}{≔}{{u}}_{{t}}^{{2}}{-}{4}{}{{u}}_{{[}{]}}$ (2)
 > $\mathrm{denote}\left(p,\mathrm{diff},R\right)$
 ${\left(\frac{{ⅆ}}{{ⅆ}{t}}{}{u}{}\left({t}\right)\right)}^{{2}}{-}{4}{}{u}{}\left({t}\right)$ (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)
 > $q≔\frac{{ⅆ}^{2}}{ⅆ{t}^{2}}u\left(t\right)-tu\left(t\right)+{\left(\frac{ⅆ}{ⅆt}u\left(t\right)\right)}^{2}$
 ${q}{≔}\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{t}}^{{2}}}{}{u}{}\left({t}\right){-}{t}{}{u}{}\left({t}\right){+}{\left(\frac{{ⅆ}}{{ⅆ}{t}}{}{u}{}\left({t}\right)\right)}^{{2}}$ (5)
 > $\mathrm{denote}\left(q,\mathrm{jet},Q\right)$
 ${-}{t}{}{{u}}_{{[}{]}}{+}{{u}}_{{t}}^{{2}}{+}{{u}}_{{t}{,}{t}}$ (6)