14,992 reputation
11940
bio website math.brown.edu/~lubinj
location Minnesota
age 78
visits member for 3 years, 2 months
seen 1 hour ago

Aged mathematician


Dec
2
answered how to construct an hyperbolic (8,3) tiling
Dec
2
comment Finding polynomial with Galois group $S_n$.
But @JyrkiLahtonen, isn’t it the case that almost any sixth-degree polynomial should give $S_6$ for the Galois group? Like, maybe $X^6-X-a$ for almost any integer $a$, like, maybe, $a=1$? Of course I would quail at the prospect of verifying this for any specific polynomial.
Dec
2
answered Compute $z^3 = -26 -18i$
Dec
2
comment Function that returns negative number for negative x and y
Couldn’t $q$ be a sum of squares? On $\mathbb R^2$, such a polynomial is never negative. I don’t think this affects your answer in any essential way…
Dec
2
comment Two doubts about squares in $\Bbb Z_p$
Well, $12$ is congruent to a square modulo $8$, but its square root is not in $\mathbb Q_2$, ’cause if it were, then $\sqrt3$ would be in $\mathbb Q_2$, which it isn’t.
Dec
2
comment A simple question on p-adic fields
I always recommend this notation and way of computation.
Dec
1
answered Which $p$-adic fields contain these numbers?
Dec
1
comment How can $\mathbb Q$ be countable, when there is no “next” rational number?
I like this approach to the confusion.
Dec
1
comment Let $y^2 = x^3 + Ax + B$ be a curve and $y = m(x - x_1) + y_1$ tangent at $x_1$. Why is $x_1$ then a double root?
Sorry, don’t understand your last two comments. Let’s continue this by e-mail, shall we?
Nov
30
answered Visualizing Balls in Ultrametric Spaces
Nov
30
comment Counting tamely ramified Galois extensions of $\mathbb{Q}_p$ with a given Galois group.
I am not familiar with that formula either, but I don‘t find your count surprising. $Q_8$ is not an easy group to find among your random collection of extensions. In fact, I’d like to see an explicit description of that quaternion-group extension of $\mathbb Q_3$.
Nov
30
comment Let $y^2 = x^3 + Ax + B$ be a curve and $y = m(x - x_1) + y_1$ tangent at $x_1$. Why is $x_1$ then a double root?
When the tangent line has a triple contact with the curve in question, the nearby secant lines have three intersections with the curve. Like $y=x^3$.
Nov
30
comment Let $y^2 = x^3 + Ax + B$ be a curve and $y = m(x - x_1) + y_1$ tangent at $x_1$. Why is $x_1$ then a double root?
Have you looked at examples? What about the simple example of $y=x^2-2x+1$ and the $x$-axis? The parabola touches the axis at only the point $(1,0)$, but when you eliminate the $y$ from the two equations $y=0$ and the $y=(x-1)^2$, you get the equation $0=(x-1)^2$. Please do some computations.
Nov
30
comment Let $y^2 = x^3 + Ax + B$ be a curve and $y = m(x - x_1) + y_1$ tangent at $x_1$. Why is $x_1$ then a double root?
You should expect the tangent line to have at least a double contact with the given curve. With pairs of ellipses, you can get double, triple, and quadruple contacts, just by arranging positions right.
Nov
29
answered Minimal Polynomial of $a +b\sqrt{2}$ as a function of a, b ∈ $\mathbb Q$
Nov
29
comment Determine the minimal polynomial of $\sqrt 3+\sqrt 5$
Good and complete.
Nov
29
comment Determine the minimal polynomial of $\sqrt 3+\sqrt 5$
Right. I did just that in detail in my response to Barry Cipra, above.
Nov
29
revised Determine the minimal polynomial of $\sqrt 3+\sqrt 5$
added 450 characters in body
Nov
29
comment Determine the minimal polynomial of $\sqrt 3+\sqrt 5$
But neither of these factors is $\mathbb R$-irreducible, as you can see by calculating the discriminant $b^2-4ac$, positive in each. So I think your argument falls.
Nov
29
comment Determine the minimal polynomial of $\sqrt 3+\sqrt 5$
@BarryCipra, that’s asking about the irreducibility of the polynomial, an issue I didn’t address. I was merely worried about an efficient way of finding the polynomial. You can’t show irreducibility by looking modulo $p$ for any single $p$, for reasons I don’t want to go into. Probably an argument prompted by galois theory would be best.