isMember(RingElement,Ideal) -- test membership in an ideal

Synopsis

• Function: isMember

• Usage:

  isMember(r,I)

• Inputs:
  • r, a ring element, a ring element or a number,
  • I, an ideal,
• Outputs:
  • a Boolean value, whether r is in the ideal I;

Description

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : I = ideal(-x^3 + y, x^2*y - z)

               3       2
o2 = ideal (- x  + y, x y - z)

o2 : Ideal of R

i3 : isMember(x*y^3 - z^2 + y^5 - z^3, I)

o3 = true

i4 : J = ideal(x*z - y, x*y + 2*z^2, y - z)

                             2
o4 = ideal (x*z - y, x*y + 2z , y - z)

o4 : Ideal of R

i5 : isMember(x^3*z - 2*y^2, J)

o5 = false