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2.2.21 Leading Term (Initial) Ideals, Generic Polynomials
The following example produces the leading term (initial) ideal of the ideal generated by three generic polynomials of degree 2 with respect to the lexicographic term-ordering.

  Use R ::= ZZ/(32003)[x[1..4]], Lex;
  F := DensePoly(2);  -- sum of all power-products of degree 2
  L := [ Randomized(F) | I In 1..3 ]; -- randomize coefficients
Ideal(x[1]^2, x[1]x[2], x[1]x[3], x[2]^3, x[1]x[4]^2, x[2]^2x[3],
x[2]^2x[4]^2, x[2]x[3]^3, x[2]x[3]^2x[4]^2, x[2]x[3]x[4]^4,
x[2]x[4]^6, x[3]^8)