PolynomialNormalForm - Maple Help
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RationalNormalForms

  

PolynomialNormalForm

  

construct the polynomial normal form of a rational function

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

PolynomialNormalForm(F, x)

Parameters

F

-

rational function in x

x

-

variable

Description

• 

The PolynomialNormalForm(F,x) function constructs the polynomial normal form for F, where F is a rational function in x over a field of characteristic 0.

• 

A sequence of four elements z,a,b,c, where z is an element in K and a,b,c are monic polynomials over K such that the following three conditions are satisfied, is returned: F=zaEcbc.  gcda,Ekb=1for allnonnegative integersk. gcda,c=1,gcdb,Ec=1.

  

Note: E is the automorphism of K(x) defined by {E(f(x)) = f(x+1)}.

• 

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

Examples

withRationalNormalForms:

F32nn+23n+23n+4n12n+9n+42

F3nn+23n+23n+42n12n+9n+42

(1)

z,a,b,cPolynomialNormalFormF,n

z,a,b,c274,n+2n+23n+43,n+92n+42,n1

(2)

Check the results.

Condition 1:

evalbF=normalzabsubsn=n+1,cc

true

(3)

Condition 2:

LREtoolsdispersionb,a,n

FAIL

(4)

Condition 3:

gcda,c,gcdb,subsn=n+1,c

1,1

(5)

References

  

Petkovsek, M.; Wilf, H.; and Zeilberger, D. A=B. Wellesley, Massachusetts: A. K. Peters Ltd., 1996.

See Also

evalb

gcd

LREtools

RationalNormalForms[RationalCanonicalForm]