quotientRemainder(RingElement,RingElement) -- quotient and remainder

• Function: quotientRemainder

• Usage:

  (q,r) = quotientRemainder(f,g)

• Inputs:
  • f, a ring element
  • g, a ring element
• Outputs:
  • q, a ring element, the quotient for the division of f by g
  • r, a ring element, the remainder for the division of f by g

i1 : R = QQ[x,y];

i2 : (q,r) = quotientRemainder(x^10+5,x-2);

i3 : q

      9     8     7     6      5      4      3       2
o3 = x  + 2x  + 4x  + 8x  + 16x  + 32x  + 64x  + 128x  + 256x + 512

o3 : R

i4 : r

o4 = 1029

o4 : R

i5 : q*(x-2)+r

      10
o5 = x   + 5

o5 : R