LREtools[HypergeometricTerm] - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Factorization and Solving Equations : LREtools : HypergeometricTerm : LREtools/HypergeometricTerm/HGDispersion

LREtools[HypergeometricTerm]

  

HGDispersion

  

return the hypergeometric dispersion of two polynomials depending on a hypergeometric term

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

HGDispersion(p, q, x, r)

Parameters

p

-

first polynomial

q

-

second polynomial

x

-

independent variable, for example, x

r

-

list of equations that specifies the tower of hypergeometric extensions

Description

• 

The HGDispersion(p, q, x, r) command returns the hypergeometric dispersion of p and q, that is,

D=max{n0:deggcdp,Enq>0}

where E: Ex=x+1 is the shift operator and px and qx are polynomials in K(r), where K is the ground field and r is the tower of hypergeometric extensions. Each ri is specified by a hypergeometric term, that is, Eriri is a rational function over K. The HGDispersion function returns 1 if the hypergeometric dispersion is not defined.

• 

The polynomials can contain hypergeometric terms in their coefficients. These terms are defined in the formal parameter r. Each hypergeometric term in the list is specified by a name, for example, t. It can be specified directly in the form of an equation, for example, t=n!, or specified as a list consisting of the name of the term variable and the consecutive term ratio, for example, t,n+1.

• 

The computation of hypergeometric dispersions is reduced to solving the σ-orbit problem (see OrbitProblemSolution) in the shortened tower of hypergeometric extensions.

Examples

withLREtoolsHypergeometricTerm:

aliasφ=3+4RootOfx2+15:

pφ4s2+φ2s+1

p:=3+45RootOf_Z2+14s2+3+45RootOf_Z2+12s+1

(1)

qs2+s+1

q:=s2+s+1

(2)

exts=φx

ext:=s=3+45RootOf_Z2+1x

(3)

HGDispersionp,q,x,ext

2

(4)

aliasφ=RootOfx35:

pφ4s2+φ2s+1

p:=RootOf_Z354s2+RootOf_Z352s+1

(5)

qs2+s+1

q:=s2+s+1

(6)

exts=φx

ext:=s=RootOf_Z35x

(7)

HGDispersionp,q,x,ext

1

(8)

p24s2+22s+1+v

p:=16s2+4s+v+1

(9)

q16x+32x+22x+12s2+4x+3x+2x+1s+1+8v

q:=16x+32x+22x+12s2+4x+3x+2x+1s+1+8v

(10)

extv=2x,s=x!

ext:=v=2x,s=x!

(11)

HGDispersionsq,pv+s,x,ext

3

(12)

References

  

Abramov, S.A., and Bronstein, M. "Hypergeometric dispersion and the orbit problem." Proc. ISSAC 2000.

See Also

alias

LREtools[HypergeometricTerm]

LREtools[HypergeometricTerm][OrbitProblemSolution]

LREtools[HypergeometricTerm][RationalSolution]

LREtools[HypergeometricTerm][UniversalDenominator]

 


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