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Overview of the LinearOperators Package

 Calling Sequence LinearOperators:-command(arguments) command(arguments)

Description

 • The main functionalities of the LinearOperators package are the following.
 - Given a linear equation with a d'Alembertian right-hand side, find a d'Alembertian solution if it exists.
 - Given a d'Alembertian term, find a completely factorable annihilator of the term.
 - Given a d'Alembertian term, find the minimal annihilator of the term.
 - Given a d'Alembertian term, find the minimal completely factorable annihilator of the term.
 - Given two operators, find their greatest common right divisor in factored form.
 - Given an operator L, find the annihilator of the term g that is primitive for the solution f of Ly=0, and the operator K that converts f to g such that K(y)=g (if they exist). This is called accurate integration.
 • There are commands that convert between Ore operators and the corresponding Maple expressions. See LinearOperators[converters].
 • Each command in the LinearOperators package can be accessed by using either the long form or the short form of the command name in the command calling sequence.
 • The long form, LinearOperators:-command, is always available. The short form can be used after loading the package.

List of LinearOperators Package Commands

 The following is a list of available commands.

 To display the help page for a particular LinearOperators command, see Getting Help with a Command in a Package.

Examples

 > $\mathrm{with}\left(\mathrm{LinearOperators}\right)$
 $\left[{\mathrm{Apply}}{,}{\mathrm{DEToOrePoly}}{,}{\mathrm{FactoredAnnihilator}}{,}{\mathrm{FactoredGCRD}}{,}{\mathrm{FactoredMinimalAnnihilator}}{,}{\mathrm{FactoredOrePolyToDE}}{,}{\mathrm{FactoredOrePolyToOrePoly}}{,}{\mathrm{FactoredOrePolyToRE}}{,}{\mathrm{IntegrateSols}}{,}{\mathrm{MinimalAnnihilator}}{,}{\mathrm{OrePolyToDE}}{,}{\mathrm{OrePolyToRE}}{,}{\mathrm{REToOrePoly}}{,}{\mathrm{dAlembertianSolver}}\right]$ (1)
 > $L≔\mathrm{OrePoly}\left(-x,0,1\right)$
 ${L}{≔}{\mathrm{OrePoly}}{}\left({-}{x}{,}{0}{,}{1}\right)$ (2)
 > $b≔\frac{\left(4{x}^{3}+1\right)\mathrm{ln}\left(x\right)}{x\sqrt{x}}$
 ${b}{≔}\frac{\left({4}{}{{x}}^{{3}}{+}{1}\right){}{\mathrm{ln}}{}\left({x}\right)}{{{x}}^{{3}}{{2}}}}$ (3)
 > $\mathrm{dAlembertianSolver}\left(L,b,x,'\mathrm{differential}'\right)$
 ${-}{4}{}\sqrt{{x}}{}{\mathrm{ln}}{}\left({x}\right)$ (4)

 See Also