### 5.1.127 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,N)`= .
  - `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]
      module n=y*freemodule(2);
      quotient(m,n);
      ==> _[1]=1

See fglmquot; ideal; modQuotient; module.

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