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numtheory

  

cfracpol

  

compute simple continued fraction expansions for all real roots of a rational polynomial

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

cfracpol(pol, n)

cfracpol(pol)

Parameters

pol

-

rational polynomial

n

-

integer (n + 1 is the number of partial quotients)

Description

• 

Important: The numtheory[cfracpol] command has been deprecated.  Use the superseding command NumberTheory[ContinuedFractionPolynomial] instead.

• 

The cfracpol function returns simple continued fraction expansions of all real roots of a rational polynomial pol. Each expansion is given in list form with at most n+1 quotients. If the second argument n is not present, it defaults to 10.

• 

The command with(numtheory,cfracpol) allows the use of the abbreviated form of this command.

Examples

withnumtheory:

cfracpolx4x34x2+4x+1,20

2,22,1,7,2,1,1,2,1,2,1,17,4,4,1,1,4,2,18,1,10,...,1,1,3,1,3,1,1,1,1,1,1,4,1,1,1,4,1,2,4,5,18,...,1,2,1,21,1,7,2,1,1,2,1,2,1,17,4,4,1,1,4,2,18,...,1,1,4,1,3,1,1,1,1,1,1,4,1,1,1,4,1,2,4,5,18,...

(1)

cfracpolx6x56x4+6x3+8x28x+1

2,44,1,3,3,1,1,1,3,2,3,...,2,1,1,6,1,7,34,1,12,1,5,...,0,6,1,2,4,3,1,1,3,1,63,...,0,1,2,1,2,2,16,1,1,5,11,...,1,1,1,1,7,6,10,2,29,20,1,...,1,1,10,3,1,13,1,1,3,1,4,...

(2)

a117260219x6+139540883x5+17033080x4+800302x3+18628x2+216x+1:

cfracpola

1,1,41,7,1,7,34,1,12,1,5,...,1,1,42,1,1,6,1,2,4,3,1,...,1,1,42,1,1,1,2,1,2,2,16,...,1,1,42,1,2,1,1,1,7,6,10,...,1,1,42,1,2,1,10,3,1,13,1,...,1,3,3,1,1,1,3,2,3,4,1,...

(3)

cfracpol232x+543x6x56x4+6x3+8x28x+1,10

3,1,1,1,14,1,4,2,44,1,3,3,1,1,1,3,2,3,...,2,1,1,6,1,7,34,1,12,1,5,...,0,6,1,2,4,3,1,1,3,1,63,...,0,1,2,1,2,2,16,1,1,5,11,...,1,1,1,1,7,6,10,2,29,20,1,...,1,1,10,3,1,13,1,1,3,1,4,...

(4)

cfracpolx63x5+5x33x+1

See Also

convert/confrac

numtheory[cfrac]

numtheory[nthconver]

 


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