
Define a ring

  k=QQ[x,y,z,MonomialOrder=>Lex]

Fields:
 * ZZ
 * RR
 * CC
 * ZZ/p

Orderings
 * GRevLex
 * Lex
 * RevLex
 * GroupLex
 * GroupRevLex
 * Eliminate N

describe

Define an ideal

  I=ideal(x^2+y^2-1, x=y)

Eliminate a variable

  eliminate(x, I)

Compute some stuff

  * dim
  * degree

ideal(y-x+1, x^2+y^2-1)
intersect
ass -- associated primes
radical

toString

Create a Grobner basis

  * gg

Stuff to work on

  * generators (gens)


EXAMPLE:


i1 : R=QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : I=ideal(x^2+y^2-1, z^2-1,y^2-1)

             2    2       2       2
o2 = ideal (x  + y  - 1, z  - 1, y  - 1)

o2 : Ideal of R

i3 : G=gb(I)

o3 = GroebnerBasis[status: done; S-pairs encountered up to degree 1]

o3 : GroebnerBasis

i4 : gens(G)

o4 = | z2-1 y2-1 x2 |

             1       3
o4 : Matrix R  <--- R

I=ideal((x-1)^2+y^2-1,(x+1)^2+y^2-1)
