PolynomialTools - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Algebra : Polynomials : PolynomialTools : PolynomialTools/ShiftEquivalent

PolynomialTools

  

ShiftEquivalent

  

test whether two polynomials are shift equivalent

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ShiftEquivalent(f,g,x)

ShiftEquivalent(f,g,x,T)

Parameters

f, g

-

polynomials in x

x

-

indeterminate

T

-

(optional) type

Description

• 

The ShiftEquivalent command determines whether the two polynomials f,g are shift equivalent w.r.t. the variable x, that is, whether there is an h independent of x satisfying lcgfx+h=lcfgx, where lc denotes the leading coefficient with respect to x. It returns h, if it exists, and otherwise FAIL.

• 

If the optional argument T is specified, then ShiftEquivalent returns FAIL even if h exists but is not of type T. This is more efficient than first calling ShiftEquivalent without the optional argument and then checking whether the return value is of type T.

• 

It is assumed that both input polynomials are collected w.r.t. the variable x.

• 

If f,g are nonconstant w.r.t. x, then h is uniquely determined. If both are nonzero and constant w.r.t. x, or if both are zero, then the return value is 0.

Examples

withPolynomialTools:

ShiftEquivalentx2+x+1,x2x+1,x

1

(1)

Translatex2+x+1,x,

x2x+1

(2)

ShiftEquivalentx2+1,x2x+1,x

FAIL

(3)

Leading coefficients do not matter.

ShiftEquivalent2x1,x+12,x

1

(4)

Translate2x1,x,

1+2x

(5)

ShiftEquivalent2x1,x,x

12

(6)

ShiftEquivalent2x1,x,x,'integer'

FAIL

(7)

ShiftEquivalentx,x+n,x

n

(8)

See Also

LREtools[dispersion]

PolynomialTools

PolynomialTools[ShiftlessDecomposition]

PolynomialTools[Translate]

 


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