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genfunc

  

rgf_charseq

  

find characteristic sequence of a rational generating function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

rgf_charseq(Fz, z, Fn, n)

Parameters

Fz

-

rational generating function

z

-

name, generating function variable

Fn

-

expression for nth term of the sequence encoded by Fz

n

-

name, index variable for Fn

Description

• 

This command returns the characteristic sequence of Fz as a function of Fn.

• 

The characteristic generating function Cz of Fz is defined as:

dzdenomFz

Cztcoeffdz,zzldegreedz,zdz

  

The sequence encoded by Cz is the characteristic sequence of Fz.

• 

The value FAIL is returned if Fz is a trivial rational generating function.

• 

The command with(genfunc,rgf_charseq) allows the use of the abbreviated form of this command.

Examples

withgenfunc:

rgf_charseqz1zz2,z,Fn,n

Fn+1

(1)

rgf_charseq1+2z13z4z2,z,tn,n

13tn+43tn1

(2)

Gy1+y+y21y3:

rgf_expandGy,y,j

3j2+3j+112j+1

(3)

rgf_charseqGy,y,,j

j53+83j+112j+1+13j1j73j12j+12

(4)

factor

12j+2j+1

(5)

rgf_encode,j,z

11z+32z1z2+12z11z2+2z1z3

(6)

normal

1z13

(7)

See Also

denom

genfunc

genfunc/rgf_encode

genfunc/rgf_expand

genfunc[termscale]

ldegree

tcoeff

 


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