latticeBasisIdeal -- construct the ideal whose generators correspond to generators of an integer lattice

Synopsis

• Usage:

  latticeBasisIdeal (R,L)

• Inputs:
  • R, a ring
  • L, an integer matrix whose columns span the lattice.
• Outputs:
  • The unital lattice basis ideal in R, defined by L

Description

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

o1 = R

o1 : PolynomialRing

i2 : L = matrix {{1,1},{-3,0},{0,1}}

o2 = | 1  1 |
     | -3 0 |
     | 0  1 |

              3       2
o2 : Matrix ZZ  <-- ZZ

i3 : latticeBasisIdeal (R, L)

               3
o3 = ideal (- y  + x, x*z - 1)

o3 : Ideal of R