| Assignment | Due date | Read | Turn in. |
|---|---|---|---|
| I | Wed. 1/25 | IVA I.1 #1-5 IVA I.2 #1-9, 13-15 |
IVA I.1 #5 IVA I.2 #2, 4d, 5, 6, 8, 13, 15d |
| II | Mon. 2/6 | IVA I.3 #1-6 IVA I.4 #1-12 IVA I.5 #1, 3-9 |
IVA I.3 #4, 5, 6 IVA I.4 #5, 8, 9, 11 (or 12) IVA I.5 #14, 15, 16 |
| III | Fri. 2/17 | IVA II.1 #1-3 IVA II.2 #1-7, 10-12 IVA II.3 #1-10 |
IVA II.1 #1d, 2b, 3b, 3c IVA II.2 #1b, 12 Probs. A, B, C, D IVA II.3 #5, 6, 9 |
| IV | Wed. 3/1 | IVA I.6 #1-12 IVA II.7 #1-11 IVA II.8 #1-7 IVA II.9 #1-8, 12, 13 |
IVA II.6 #10, 12 IVA II.7 #2b, 3b IVA II.8 #6, 7 IVA II.9 #2, 3, 12 |
| V | Mon. 3/27 | IVA III.1 #1-9 IVA III.2 #5 IVA III.3 #1-15 IVA III.5 #2,3, 6-16 IVA III.6 #1-5, 8-13 | IVA III.3 (one of #6, 7, 8, 9), (one of #14, 15, or Bezier cubic) IVA III.5 #13, 16 IVA III.6 #9, 11 |
| VI | Mon. 4/17 | IVA IV.1 #5-9 IVA IV.2 #8-10, 13, 15 IVA IV.3 #6-15 IVA IV.4 #1-4, 8, 9, 10 IVA IV.5 #1-5, 12, 6-16 IVA IV.6 #1-4 |
IVA IV.2 #15 IVA IV.3 #11, 12 IVA IV.4 #3, 4 IVA IV.6 #7 |
A. Give the grevlex and the grlex orderings for n=3 and for monomials up to degree 2. This is enough to show they are different orderings.
B. Let n=3 . For each of the monomial orderings lex, grlex and grevlex orders, find vectors u_1, u_2, u_3 which determine that ordering.
C. Find a total ordering on N_0^3 which is determined by a single vector u_1 .D. What condition(s) on the u_i are necessary to ensure that a group ordering on N_0^n is also a well-ordering and therefore a monomial ordering?
E. (optional) Prove one of the steps in Robbiano's classification of group orderings discussed in class on Mon. 2/6.