-- -*- M2-comint -*- {* hash: -356330269 *}

i1 : R=ZZ/32003[a..c];

i2 : lexIdeal(R,{1,3,4,3,1})

                  2     2   3     3   2 2   5
o2 = ideal (a*b, a , a*c , b , b*c , b c , c )

o2 : Ideal of R

i3 : lexIdeal ideal(a*b,b*c)

                  2
o3 = ideal (a*b, a )

o3 : Ideal of R

i4 : lexIdeal(R,{1,3,7}) --not an O-sequence, so no lex ideal exists

i5 : Q=R/ideal(a^3,b^3,a*c^2);

i6 : lexIdeal(Q,{1,3,6,4,2})

             2      2   2    2 2   5     4
o6 = ideal (a c, a*b , a b, b c , c , b*c )

o6 : Ideal of Q

i7 : lexIdeal(Q,{1,3,6,4,4}) --value of 4 in degree 4 is too high in this ring

i8 :