construct the differential polynomial normal form of a rational function - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Differential Equations : DEtools : Differential Rational Normal Forms : DEtools/PolynomialNormalForm

DEtools[PolynomialNormalForm] - construct the differential polynomial normal form of a rational function

Calling Sequence

PolynomialNormalForm(F, x)

Parameters

F

-

rational function of x

x

-

variable

Description

• 

Let F be a rational function of x over a field K of characteristic 0. The PolynomialNormalForm(F,x) command constructs the differential polynomial normal form for F.

• 

The output is a sequence of 3 elements a,b,c where a,b,c are polynomials over K such that:

1. 

 F=ab+ⅆⅆxcc. 

2. 

gcdb,aixb=1 for all non-negative integers i.

3. 

gcdb,c=1.

Examples

withDEtools:

F:=4x2+4x+13x+129x129x2+12x3+4x2+1x3+4x22

F:=4x2+4x+13x+129x129x2+12x3+4x2+1x3+4x22

(1)

a,b,c:=PolynomialNormalFormF,x

a,b,c:=5x916x814x7134x6+39x5331x4+96x3+32x2+16x7,x+12x12x3+4x22,x24

(2)

Check the result:

nF:=ab+xcc:

TestzeronormalFnF

true

(3)

res:=resultantb,ajxb,x:

H:=selecttype,solveres,j,'nonnegint':

evalbH=andgcdb,c=1

true

(4)

See Also

DEtools[Gosper], DEtools[RationalCanonicalForm], SumTools[Hypergeometric][PolynomialNormalForm]

References

  

Almkvist, G, and Zeilberger, D. "The method of differentiating under the integral sign." Journal of Symbolic Computation. Vol. 10. (1990): 571-591.


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam