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DEtools

  

rightdivision

  

perform right division of differential operators

  

leftdivision

  

perform left division of differential operators

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

rightdivision(a, b, domain)

leftdivision(a, b, domain)

Parameters

a, b

-

differential operators

domain

-

list containing two names

Description

• 

For operators a and b (as for polynomials, see quo) there exist operators q and r such that a&equals;bq&plus;r and orderr<orderb. The output rightdivision is the list q&comma;r.

• 

The procedure leftdivision does precisely the same, only the order of multiplication q b is reversed: b q.

• 

The argument domain describes the differential algebra. If this argument is the list Dt&comma;t then the differential operators are notated with the symbols Dt and t. They are viewed as elements of the differential algebra Ct Dt 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.

• 

These functions are part of the DEtools package, and so they can be used in the form rightdivision(..) and leftdivision(..) only after executing the command with(DEtools).  However, they can always be accessed through the long form of the command by using DEtools[rightdivision](..) or DEtools[leftdivision](..).

Examples

withDEtools&colon;

rightdivisionDt4&comma;Dt218t1&plus;2t&plus;3t3&comma;Dt&comma;t

Dt2&plus;18t3t3&plus;2t&plus;1&comma;366t31Dt3t3&plus;2t&plus;12&plus;3654t5&plus;12t39t223t3&plus;2t&plus;13

(1)

See Also

diffop

Ore_algebra/skew_pdiv