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5.1.123 quotient

Syntax:
quotient ( ideal_expression, ideal_expression )
quotient ( module_expression, module_expression )
Type:
ideal
Syntax:
quotient ( module_expression, ideal_expression )
Type:
module
Purpose:
computes the ideal quotient, resp. module quotient. Let R be the basering, I,J ideals and M a module in ${\tt R}^n$.Then
  • quotient(I,J)= $\{a \in R \mid aJ \subset I\}$,
  • quotient(M,J)= $\{b \in R^n \mid bJ \subset M\}$.
Example:
 
ring r=181,(x,y,z),(c,ls);
ideal id1=maxideal(3);
ideal id2=x2+xyz,y2-z3y,z3+y5xz;
ideal id6=quotient(id1,id2);
id6;
==> id6[1]=z
==> id6[2]=y
==> id6[3]=x
quotient(id2,id1);
==> _[1]=z2
==> _[2]=yz
==> _[3]=y2
==> _[4]=xz
==> _[5]=xy
==> _[6]=x2
module m=x*freemodule(3),y*freemodule(2);
ideal id3=x,y;
quotient(m,id3);
==> _[1]=[1]
==> _[2]=[0,1]
==> _[3]=[0,0,x]
See fglmquot; ideal; module.