CoCoA:Colon

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 <command>
   <title>Colon</title>
   <short_description>ideal or module quotient</short_description>
   <description>

This function 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. The command M : N is a shortcut for Colon(M,N). <par/> See also <ttref>HColon</ttref> for non-homogeneous input.

<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)


</example>

   </description>
   <syntax>

Colon(M:IDEAL,N:IDEAL):IDEAL Colon(M:MODULE,N:MODULE):IDEAL </syntax>

   <see>Saturation</see>
   <see>HSaturation</see>
   <see>HColon</see>
   <see>Shortcuts</see>
   <type>groebner</type>
   <type>groebner-basic</type>
   <type>ideal</type>
   <type>module</type>
   <type>polynomial</type>
   <type>vector</type>
   <type>cocoaserver</type>
   <key>colon</key>
 </command>