bio  website  math.unice.fr/~cazanave 

location  Nice, France  
age  
visits  member for  4 years, 3 months 
seen  10 hours ago  
stats  profile views  448 
1d

awarded  SelfLearner 
1d

accepted  Easiest way to distinguish $E_8 \oplus E_8$ from $E_{16}$ 
1d

answered  Easiest way to distinguish $E_8 \oplus E_8$ from $E_{16}$ 
Jul 2 
awarded  Curious 
Jul 1 
comment 
Units of $\mathbf Z[X,Y]/(P(X,Y))$
Note that this is true only for reduced algebras. The "standard" counterexample is: $\mathbf Z[X,Y]/(X^2)$. 
Jun 25 
comment 
Easiest way to distinguish $E_8 \oplus E_8$ from $E_{16}$
@few_reps: is there an analogous command in pari/gp? (I know that there is an online Magma calculator, but for various reasons, it would be more convenient for me to do it in pari/gp). 
Jun 24 
comment 
integral equivalence classes of quadratic forms
Isn't the example of disagreement in dimension 16 due to Witt instead (and used by Milnor later for is counteraxample)? 
Jun 24 
comment 
Easiest way to distinguish $E_8 \oplus E_8$ from $E_{16}$
All this seems like a "rather complicated task". I mean: I am in front of a $16 \times 16$ matrix, with not so small integers. Pari/gp can list all 480 minimal length vectors, but analyzing this data will be tedious. I would have hoped for a trick. 
Jun 24 
asked  Easiest way to distinguish $E_8 \oplus E_8$ from $E_{16}$ 
Jun 21 
awarded  Yearling 
May 27 
comment 
Proportion of irreducible polynomials $P$ such that $\mathbf Z[X]/(P)$ is the ring of integers of $\mathbf Q[X]/(P)$
Actually the reference by AshBrakenhoffZarrabi answers exactly my question. 
May 27 
comment 
Proportion of irreducible polynomials $P$ such that $\mathbf Z[X]/(P)$ is the ring of integers of $\mathbf Q[X]/(P)$
In case it may interess someone: the proportion 60% found is conjectured by Lenstra to be $\frac 6 {\pi^2}$ (cf. the paper of AshBrakenhoffZarrabi mentionned in David Speyer answer). 
May 27 
accepted  Proportion of irreducible polynomials $P$ such that $\mathbf Z[X]/(P)$ is the ring of integers of $\mathbf Q[X]/(P)$ 
May 24 
comment 
Proportion of irreducible polynomials $P$ such that $\mathbf Z[X]/(P)$ is the ring of integers of $\mathbf Q[X]/(P)$
Thanks for the reference. Note that, however, numerical experiences seem to show that squarefree discriminants explain only half of the proportion obtained (and Stickelberger's relation does not help much). 
May 23 
awarded  Nice Question 
May 23 
revised 
Proportion of irreducible polynomials $P$ such that $\mathbf Z[X]/(P)$ is the ring of integers of $\mathbf Q[X]/(P)$
added 67 characters in body 
May 23 
asked  Proportion of irreducible polynomials $P$ such that $\mathbf Z[X]/(P)$ is the ring of integers of $\mathbf Q[X]/(P)$ 
Apr 25 
accepted  Units of $\mathbf Z[X,Y]/(P(X,Y))$ 
Apr 23 
asked  Units of $\mathbf Z[X,Y]/(P(X,Y))$ 
Oct 24 
comment 
Bass' stable range of $\mathbf Z[X]$
The answer is given in a paper of Grunewald, Mennicke and Vaserstein (On the groups $SL_2(\mathbf Z[x])$ and $SL_2(k[x,y])$). Israel J. Math. 86 (1994), no. 13, 157–193). One example of unimodular row that is not reducible is the following $(21+ 4x, 12, x^2 + 20)$. 