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

The command is_orthonomic determines if the characteristic set defining J  is orthonomic.

Characterizable differential ideal are constructed by using the Rosenfeld_Groebner command.

A characteristic set is orthonomic when its initials and separants  belong to the ground field. It is the case if inequations(J) is empty.

Characterizable differential ideals given by orthonomic characteristic sets are prime differential ideal. The function Rosenfeld_Groebner recognizes and can take advantage of this fact.

If J is a radical differential ideal represented by a list of characterizable differential ideals, then the function is mapped on all its components.

$\mathrm{with}\left(\mathrm{diffalg}\right)\:$

$R≔\mathrm{differential\_ring}\left(\mathrm{derivations}=\left[t\right]\,\mathrm{ranking}=\left[u\right]\right)\:$

$J≔\mathrm{Rosenfeld\_Groebner}\left(\left[{u\left[t\right]}^2-4u\left[\right]\right]\,R\right)$

$J≔\left[\mathrm{characterizable}\,\mathrm{characterizable}\right]$

$\mathrm{rewrite\_rules}\left(J\right)$

$\left[\left[u_t^2=4u\left[\right]\right]\,\left[u\left[\right]=0\right]\right]$

$\mathrm{is\_orthonomic}\left(J\right)$

$\left[\mathrm{false}\,\mathrm{true}\right]$