CoCoA:HColon

HColon

ideal or module quotient

Description

The function <ttref>Colon</ttref> returns the quotient of M by N:

the ideal of all polynomials F such that F*G is in M for all G in N.

This function computes the same ideal using a Hilbert-driven

algorithm. It differs from <ttref>Colon</ttref> only when the input

is non-homogeneous, in which case, HColon may be faster.

Example

  Use R ::= Q[x,y];
  Ideal(xy,x^2) : Ideal(x);
Ideal(y, x)
-------------------------------
  Colon(Ideal(x^2,xy), Ideal(x,x-y^2));
Ideal(x)
-------------------------------
  HColon(Ideal(x^2,xy), Ideal(x,x-y^2));
Ideal(x)
-------------------------------

Syntax

HColon(M:IDEAL,N:IDEAL):IDEAL

HSaturation

Saturation

HColon

Colon

   <type>groebner</type>
   <type>groebner-basic</type>
   <type>ideal</type>
   <type>module</type>
   <type>polynomial</type>
   <type>vector</type>