isUnit -- whether a ring element is a unit

• Usage:

  isUnit r

• Inputs:
  • r, a ring element
• Outputs:
  • a Boolean value, true if the ring element r generates an ideal containing the multiplicative identity 1 and false otherwise

i1 : R = QQ[z]/(z^2+1);

i2 : isUnit z

o2 = true

i3 : S = QQ[x,y]/(1-(x-1)*(y-1));

i4 : isUnit (x^2 - 2*x + 1)

o4 = true

i5 : isUnit x

o5 = false