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

Aged mathematician


12h
comment Given matrix P such that $P^{102 } =0 $ , to show that $P^{2} = 0$.
This is the way I see the question as well. It seems the simplest and most basic way of looking at the situation.
2d
comment Find the geodesics on the cylinder $x^2+y^2=r^2$ of radius $r>0$ in $\mathbb{R}^3$.
Slight slip in your last sentence: straight lines on the flat surface go over to helices, not ellipses.
2d
comment Why do we write $a^n$ instead of $^n\!a$ for exponentiation?
Seems to me that it’s just history, and little else. The pain caused, now at this late date, by changing the notation would be far greater than the minor annoyance that we all suffer by working with a notation that is suboptimal.
Dec
16
comment $GL_2(\mathbb{Q}_p)$ and $GL_2(\mathbb{Z}_p)\cdot\mathbb{Q}_p^\times$
Yes, the conditions are equivalent.
Dec
16
comment Are the roots of a smooth function, a smooth function?
Right. I guess the most precise way of posing your question is whether the zero-set of a smooth function contains the graph of a smooth function.
Dec
15
comment $GL_2(\mathbb{Q}_p)$ and $GL_2(\mathbb{Z}_p)\cdot\mathbb{Q}_p^\times$
Right: you guarantee this with the requirement that the determinant shall be a unit in the base ring, not merely nonzero.
Dec
14
comment Looking for GF(16), GF(32) … GF (256) tables
Do you really need a table? A exponent list (log table) should be good enough for multiplication, and addition is in some sense trivial.
Dec
14
comment Looking for GF(16), GF(32) … GF (256) tables
Why don’t you just do them yourself? As you seem to know, all you need to do is find a generator of the multiplicative group in each case.
Dec
14
comment Are the roots of a smooth function, a smooth function?
How about $f(x,y)=y^3-y-x$? Where $f=0$, you’re talking about $x=y^3-y$. Graph this.
Dec
14
comment $GL_2(\mathbb{Q}_p)$ and $GL_2(\mathbb{Z}_p)\cdot\mathbb{Q}_p^\times$
How about putting zero off-diagonal, while the diagonal entries are $1$ and $p$?
Dec
14
comment Factor $17i$ into a product of irreducible elements in $Z[i]$
Your method is flawed because $1/2 +i/2\notin\mathbb Z[i[$
Dec
13
comment Cyclotomic extension of $\mathbb{F}_p((T))$
If I may add $\varepsilon$ to @KCd’s response, when you go from $\mathbb F_p((T))$ to $\mathbb F_q((T))$, what’s going on is almost totally visible all the way down in the extension $\mathbb F_p \subset\mathbb F_q$. It’s just a constant-field extension.
Dec
12
comment Cyclotomic extension of $\mathbb{F}_p((T))$
If I may go further and climb on a soapbox, I would urge everyone to do hand computation with finite fields, especially those beyond $\mathbb F_p$.
Dec
12
comment If a=b, how does a-b=0?
I think the confusion comes from an incomplete understanding of the symbol “$=$”. It must be kept in mind that the two sides of the equals sign are different designations for a single thing.
Dec
12
comment Is there an easy way to remember the ring axioms?
Maybe there are two ways: (1) to write out the axioms 5 times; and (2) know enough examples of rings, commutative and noncommutative, as well as of nonrings (like $2\mathbb Z$).
Dec
12
comment Field algebraically closed
If you’re willing to call in the big guns, if $E$ is algebraically closed, and $[E:F]<\infty$, then the characteristic is zero, and the degree is $2$. That’s Artin-Schreier. Since $F$ is of characteristic zero, it’s automatically perfect.
Dec
10
comment Why it is not a function
I especially like your last paragraph: thank you.
Dec
8
comment Derivative=0 implies double root
Not every useful fact has a Name.
Dec
8
comment Deriving the ultrametric from the p-adic norm?
I just got a confirmation. He finished his degree in 2001, and says he heard it out of Sally’s mouth as a sophomore at Chicago. That would put the remark at around ’94, I reckon. He says it looked unprepared, and that PS seemed surprised at the class’s reaction.
Dec
8
comment If the transformation is not onto, does that mean that it is not one to one?
It’s pretty clear from your use of the word “nullity” that you were thinking of $T$ as a linear transformation of a vector space $V$. You should have said this, and also specified whether $V$ was to be finite-dimensional or not.