diffalg(deprecated)/is_orthonomic - Maple Help

diffalg

 is_orthonomic
 test if a characterizable differential ideal is presented by an orthonomic system of equations

 Calling Sequence is_orthonomic (J)

Parameters

 J - characterizable differential ideal

Description

 • 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.

Examples

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

 > $\mathrm{with}\left(\mathrm{diffalg}\right):$
 > $R≔\mathrm{differential_ring}\left(\mathrm{derivations}=\left[t\right],\mathrm{ranking}=\left[u\right]\right):$
 > $J≔\mathrm{Rosenfeld_Groebner}\left(\left[{u\left[t\right]}^{2}-4u\left[\right]\right],R\right)$
 ${J}{≔}\left[{\mathrm{characterizable}}{,}{\mathrm{characterizable}}\right]$ (1)
 > $\mathrm{rewrite_rules}\left(J\right)$
 $\left[\left[{{u}}_{{t}}^{{2}}{=}{4}{}{u}\left[\right]\right]{,}\left[{u}\left[\right]{=}{0}\right]\right]$ (2)
 > $\mathrm{is_orthonomic}\left(J\right)$
 $\left[{\mathrm{false}}{,}{\mathrm{true}}\right]$ (3)