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1.2.21. 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.

Example

Use R ::= Z/(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
LT(Ideal(L));
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) 
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