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Groebner

  

UnivariatePolynomial

  

compute a univariate polynomial

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

UnivariatePolynomial(v, J, X, characteristic=p)

Parameters

v

-

variable

J

-

a list or set of polynomials or a PolynomialIdeal

X

-

(optional) list or set of variables of the system

p

-

(optional) characteristic

Description

• 

The UnivariatePolynomial command returns a univariate polynomial in v of least degree in the ideal generated by J.  If no such polynomial exists then zero is returned. A zero-dimensional ideal contains a univariate polynomial for every variable.

• 

An optional third argument X specifies the variables of the system. By default every indeterminate not appearing in a RootOf or radical is considered a variable when J is a list or a set. If J is a PolynomialIdeal a default set of variables is stored as part of the data structure.  See PolynomialIdeals[IdealInfo].

• 

The optional argument characteristic=p specifies the ring characteristic when J is a list or a set. This option has no effect when J is a PolynomialIdeal, however you can specify J mod p as the first argument to obtain the desired result.

• 

Note that the univpoly command is deprecated.  It may not be supported in a future Maple release.

Examples

withGroebner:

Fx33xy,x2y2y2+x

F:=x33xy,x2y2y2+x

(1)

UnivariatePolynomialx,F

x5+9x2

(2)

UnivariatePolynomialy,F

y63y3

(3)

UnivariatePolynomialy,F,characteristic=3

y6

(4)

The ideal below has infinitely many solutions, yet a univariate polynomial in x exists.

withPolynomialIdeals:

Jx4+zy3,xzy3+1,z2y6x3

J:=x4+y3z,xy3z+1,y6z2x3

(5)

IsZeroDimensionalJ

false

(6)

NumberOfSolutionsJ

∞

(7)

UnivariatePolynomialx,J

x51

(8)

A univariate polynomial in y does not exist, however we can treat z as a parameter to obtain a univariate polynomial in y with coefficients in Q(z).

UnivariatePolynomialy,J

0

(9)

UnivariatePolynomialy,J,x,y

y15z5+1

(10)

See Also

Basis

FGLM

IsZeroDimensional

PolynomialIdeals[UnivariatePolynomial]

Walk

 


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