Ideal gens merge

[AlexD97]

Introducing Gröbner bases/standard bases and ideal generating systems, as discussed. This PR contains the necessary amount of changes and resulting streamlining, while staying as close as possible to the status quo. Generalizations and more functionality for ideal generating systems to come as next steps.

[wdecker]

The elements of a GB are referred to using gens: julia> gens(groebner_basis(J)) How about replacing gens by elements?

Any thoughts somebody?

[simonbrandhorst]

The elements of a GB are referred to using gens: julia> gens(groebner_basis(J)) How about replacing gens by elements?

Any thoughts somebody?

I would say that groebner_basis(J) should be iterable, and groebner_basis(J)[1] should work and collect(groebner_basis(J)).

julia> S  = Set([1,2,3,4])
Set{Int64} with 4 elements:
  4
  2
  3
  1

julia> collect(S)
4-element Vector{Int64}:
 4
 2
 3
 1

We could allow both gens(groebner_basis(J)) and elements(groebner_basis(J)). Can't hurt. Maybe one user searches for gens and the other likes elements better. This way both are happy.

[tthsqe12]

Let me have one another look in 12 hours.

[tthsqe12]

I see that that the fields isGB, ord and keepordering in the old BiPolyArray are moved to the new IdealGens. Any comments on the efficacy of this two-level approach? old:

BiPolyArray:
  Ox
  O
  Sx
  S
  isGB
  ord
  keepordering

new:

BiPolyArray:
  Ox
  O
  Sx
  S

IdealGens:
  gens::BiPolyArray
  isGB
  ord
  keepordering

[ederc]

As far as I understood there will soon be more (meta) data added to IdealGens than just the ordering. I also raised the point of efficiancy some months ago but maybe @jankoboehm can give us more insight on the future plans for IdealGens.

[tthsqe12]

in any case, merge is fine with me