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DFactor

  

factor a linear differential operator

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

DFactor(L, domain, opt)

Parameters

L

-

differential operator

domain

-

list containing two names

opt

-

(optional) sequence of options

Description

• 

The input is a differential operator L with rational function coefficients.

• 

The output is a list of irreducible factors L1,...,Lr such that L=multL1,...,Lr.

• 

The optional argument one step causes the computation to stop whenever a factorization is found. In this case the output is L if L is irreducible, but it contains two (not necessarily irreducible) factors if L is reducible.

• 

The argument domain describes the differential algebra. If this argument is the list Dx,x then the differential operators are notated with the symbols Dx and x. They are viewed as elements of the differential algebra Cx[Dx] where C is the field of constants.

• 

If the argument domain is omitted then the differential specified by the environment variable _Envdiffopdomain will be used. If this environment variable is not set then the argument domain may not be omitted.

• 

This function is part of the DEtools package, and so it can be used in the form DFactor(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[DFactor](..).

Examples

withDEtools:

aRootOfx210

aRootOf_Z210

(1)

R3545a2x2552+11a2

R35452RootOf_Z210x2552+112RootOf_Z210

(2)

LDF2R

LDF235452RootOf_Z210x2+552112RootOf_Z210

(3)

NDFactorL,DF,x

NDF+130RootOf_Z210545x660x4RootOf_Z210300x4+525x2+150x2RootOf_Z21011034RootOf_Z210x3x42x2RootOf_Z21010x2+2RootOf_Z210+7,DF130RootOf_Z210545x660x4RootOf_Z210300x4+525x2+150x2RootOf_Z21011034RootOf_Z210x3x42x2RootOf_Z21010x2+2RootOf_Z210+7

(4)

multopN,DF,x

DF2+1127+2RootOf_Z21015x222RootOf_Z210110

(5)

LmultDF2+x3+1x3,DF2+x21x3,DF,x

LDF4+x2x+1DF2+22x5+3DFx4+x11+x6+x512x1x6

(6)

DFactorL,DF,x,`one step`

DF2+x6+1x3,DF2+x51x3

(7)

References

  

van der Put, M., and Singer, M. F. Galois Theory of Linear Differential Equations, Vol. 328. Springer: 2003. An electronic version of this book is available at http://www4.ncsu.edu/~singer/ms_papers.html.

  

van Hoeij, M. "Factorization of Differential Operators with Rational Functions Coefficients." J. Symb. Comput. Vol. 24. (1997): 537-561.

See Also

DEtools[DFactorLCLM]

DEtools[expsols]

DEtools[mult]

diffop