PolynomialIdeals - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Algebra : Polynomials : PolynomialIdeals : PolynomialIdeals/Saturate

PolynomialIdeals

  

Saturate

  

saturate an ideal

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

Saturate(J, f, s)

Parameters

J

-

polynomial ideal

f

-

polynomial, or list or set of polynomials

s

-

(optional) name

Description

• 

The Saturate command computes the saturation of an ideal J with respect to a polynomial f, denoted J:f.  Saturation removes all the solutions of f from J, and is equivalent to a repeated application of Quotient. This functionality is also available through the Simplify command.

• 

If the second argument is a list or set of polynomials, then the Saturate command removes the solutions of each polynomial, or equivalently their product.

• 

If the optional third argument s is given, it is assigned a positive integer exponent with the property that J:f^infinity = J:f^s. This value is not guaranteed to be minimal.

Examples

withPolynomialIdeals:

Jx2,y12y+1

J:=x2,y12y+1

(1)

SaturateJ,y1

x2,y+1

(2)

Kx3y2+xy2,x3y+x3y3

K:=x3y2+xy2,x3y3+x3y

(3)

SaturateK,x

y3+y,x2y+y

(4)

q1QuotientK,x

q1:=x2y+y3,x2y2+y2,x4y+x2y

(5)

q2Quotientq1,x

q2:=x2y+y3,x2y2+y2,x3y+xy

(6)

q3Quotientq2,x

q3:=y3+y,x2y+y

(7)

Saturateq3,y

x2+1,y2+1

(8)

SaturateK,x,y,'s'

x2+1,y2+1

(9)

s

3

(10)

References

  

Becker, T., and Weispfenning, V. Groebner Bases. New York: Springer-Verlag, 1993.

See Also

PolynomialIdeals

PolynomialIdeals[Quotient]

PolynomialIdeals[Simplify]

 


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