quotient

quotient(I,J,options) -- computes the ideal or submodule quotient (I:J).
(I : J) -- a nicer notation, but you cannot provide options
quotient(Ideal,Ideal)
quotient(Ideal,RingElement)
quotient(Module,Ideal)
quotient(Module,RingElement)
quotient(Module,Module)

If I and J are ideals, this is (I:J) = {x in R | xJ in I}. If I is a submodule of a (either free or quotient) module M, and J is an ideal, this is the set of m in M s.t. mJ in I. Finally, if I and J are submodules of the same module M, then the result is the set of all a in the base ring R, s.t. aJ in I.

     i1 = R = ZZ/32003[a..d]
     
     o1 = R
     
     o1 : PolynomialRing
     
     i2 = I = monomialCurve(R,{1,4,7})
     
     o2 = ideal | c2-bd b3c-a3d b4-a3c |
     
     o2 : Ideal
     
     i3 = J = ideal(I_1-a^2*I_0,I_2-d*c*I_0)
     
     o3 = ideal | b3c-a2c2-a3d+a2bd b4-a3c-c3d+bcd2 |
     
     o3 : Ideal
     
     i4 = J : I
     
     o4 = ideal | b3-a2c+cd2 a3-a2b+c2d |
     
     o4 : Ideal

Allowable options include:

  • Strategy
  • MinimalGenerators


    • The strategy option value (if any) should be one of the following:

  • Iterate
  • Linear


    • The computation is currently not stored anywhere: this means that the computation cannot be continued after an interrupt.. This will be changed in a later version

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