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

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

Returns the pseudo-remainder of $f$ by $g$, viewed as univariate polynomials in x.

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

Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/TriangularSets/TriangularSetsDoc.m2:552:0.

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

Description

See also

Ways to use this method: