pseudoRemainder(RingElement,RingElement,RingElement) -- pseudo-remainder

Synopsis

• Function: pseudoRemainder

• Usage:

  pseudoRemainder(x,f,g)

• Inputs:
  • x, a ring element,
  • f, a ring element,
  • g, a ring element,
• Outputs:
  • a ring element, pseudo-remainder of f by g with respect to x

Description

i1 : R = QQ[x,y];

i2 : f = x^4

      4
o2 = x

o2 : R

i3 : g = x^2*y + 13*x^2*y^4 +x*y^2-3*x - 1

        2 4    2       2
o3 = 13x y  + x y + x*y  - 3x - 1

o3 : R

i4 : pseudoRemainder(x,f,g)

        27    6    87    4     2    3    14  4    27    2     6         6  2
o4 = - ----x*y  + ----x*y  - ----x*y  + ----y  - ----x*y  + ----x*y - ----y 
       2197       2197       2197       2197     2197       2197      2197  
     ------------------------------------------------------------------------
        27       1       9
     + ----x + ----y + ----
       2197    2197    2197

o4 : R

i5 : pseudoRemainder(y,f,g)

      4
o5 = x

o5 : R

See also

• pseudoRemainder -- compute the pseudo-remainder
• mvar -- main variable of a polynomial
• initial -- initial of a polynomial
• pseudoRemainder(RingElement,TriaSystem) -- pseudo-remainder by a triangular set