5.1.125 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 .Then

• quotient(I,J)= ,
• quotient(M,J)= .

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]