compute the smallest univariate polynomial in an ideal - Maple Help

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PolynomialIdeals[UnivariatePolynomial] - compute the smallest univariate polynomial in an ideal

Calling Sequence

UnivariatePolynomial(v, J, X)

Parameters

v

-

variable name

J

-

polynomial ideal or a list or set of generator polynomials

X

-

(optional) set of variable names

Description

• 

The UnivariatePolynomial command computes a univariate polynomial in v of least degree that is contained in the ideal J. If no such polynomial exists, then zero is returned. A zero-dimensional ideal contains a univariate polynomial in every variable.

• 

The first argument must be the variable in which a univariate polynomial is to be computed.  The second argument must be a polynomial ideal. An optional third argument overrides the default ring variables.

Examples

withPolynomialIdeals:

J:=x3y2,yx

J:=yx,x3y2

(1)

UnivariatePolynomialx,J

x3x2

(2)

K:=x3y3+1,y2+2,12zt22t3+1

K:=y2+2,2t3+12t2z+1,x3y3+1

(3)

UnivariatePolynomialx,K

x6+2x3+9

(4)

UnivariatePolynomialt,K

0

(5)

UnivariatePolynomialt,K,x,y,t

2t312t2z1

(6)

IsZeroDimensionalK,x,y,t

true

(7)

aliasα=RootOfZ3+Z+1,β=RootOfZ5+Z4+2Z+3

α,β

(8)

L:=6x2β+7y2α+3x4,4y2+4x2y26yα3

L:=3x4+7y2α+6x2β,3yα3+2x2y22y2

(9)

UnivariatePolynomialx,L

4x12+16x10β+16x8β28x1032x8β32x6β2+4x8+16x6β+42x4α2+16x4β2+84x2α2β21x442x2β

(10)

UnivariatePolynomialy,L

24α2βy3+36y2α2β12y3α2+28y5+36y2α224βy327yα212y3+27yα+27y

(11)

See Also

alias, Groebner[UnivariatePolynomial], PolynomialIdeals, PolynomialIdeals[IsZeroDimensional]


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