diffalg(deprecated)/derivatives - Maple Help

diffalg

 derivatives
 return the derivatives occurring in a differential polynomial

 Calling Sequence derivatives (p, R, code)

Parameters

 p - differential polynomial in R R - differential polynomial ring code - (optional) name; 'increasingly' or 'decreasingly'

Description

 • Important: The diffalg package has been deprecated. Use the superseding package DifferentialAlgebra instead.
 • The function derivatives returns the set of the derivatives occurring in the differential polynomial p.
 • If the third parameter is present, the function returns the list of the derivatives, sorted increasingly or decreasingly, with respect to the ranking of R.
 • The command with(diffalg,derivatives) allows the use of the abbreviated form of this command.

Examples

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

 > $\mathrm{with}\left(\mathrm{diffalg}\right):$
 > $K≔\mathrm{field_extension}\left(\mathrm{transcendental_elements}=\left[u\left[t\right]\right]\right):$
 > $R≔\mathrm{differential_ring}\left(\mathrm{field_of_constants}=K,\mathrm{derivations}=\left[x,y\right],\mathrm{ranking}=\left[\mathrm{lex}\left[u\right]\right]\right)$
 ${R}{≔}{\mathrm{PDE_ring}}$ (1)
 > $p≔u\left[x\right]u\left[t\right]+u\left[x,x\right]+{u\left[x,x\right]}^{2}+x{u\left[x,y,y\right]}^{2}+1$
 ${p}{≔}{x}{}{{u}}_{{x}{,}{y}{,}{y}}^{{2}}{+}{{u}}_{{x}}{}{{u}}_{{t}}{+}{{u}}_{{x}{,}{x}}^{{2}}{+}{{u}}_{{x}{,}{x}}{+}{1}$ (2)
 > $\mathrm{derivatives}\left(p,R,'\mathrm{increasingly}'\right)$
 $\left[{{u}}_{{x}}{,}{{u}}_{{x}{,}{y}{,}{y}}{,}{{u}}_{{x}{,}{x}}\right]$ (3)