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5.1.103 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
Rn.
Then
-
quotient(I,J) =
{a ∈ R∣aJ ⊂ I},
-
quotient(M,J) =
{b ∈ Rn∣bJ ⊂ 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.
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