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Jul
22
revised Elements of order $3$ in $\text{Aut}\left(\mathbb{Z}/91\mathbb{Z}\right)$
word choice
Jul
22
asked Elements of order $3$ in $\text{Aut}\left(\mathbb{Z}/91\mathbb{Z}\right)$
Jul
14
accepted Show that no $T\in M_{5\times 5}(\mathbb{Q})$ has order $8$.
Jul
14
comment Show that no $T\in M_{5\times 5}(\mathbb{Q})$ has order $8$.
This one of those answers I'm gonna have to hold on to for a while and look at once I've seen some more algebra. One question that I know I have: $k$ looks like a degree-2 extension; did you mean to adjoin an $i$ or something as well?--to give us $\xi$? (I haven't done any representation theory yet, so I'm not sure where to start with my other questions! Maybe this: Is $\rho$ multiplication by $\xi$?)
Jul
14
comment Show that no $T\in M_{5\times 5}(\mathbb{Q})$ has order $8$.
Thank you! It's always nice to know I'm not crazy!
Jul
14
comment Show that no $T\in M_{5\times 5}(\mathbb{Q})$ has order $8$.
@BaronMingus: If $e_4 = 0$, then we'd need $m(x)$ to divide $x^4-1$, right? Just as a test, I tried out $m(x)=(x+1)(x^2+1)$. Once I used two copies of $x+1$ as the other invariant factors; the other time, I used $x^2+1$. Both times I got $T^4 = I$.
Jul
14
awarded  Custodian
Jul
14
asked Show that no $T\in M_{5\times 5}(\mathbb{Q})$ has order $8$.
Jul
9
comment Galois Group of $x^{4}+7$
Okay, I've convinced myself that the splitting field is what you found. However, when you can say that $\alpha = \sqrt[4]{28}$ is in $K$ because, etc. ... I mean, that shows $\mathbb{Q}(\alpha) \subseteq K$, but not necessarily equality. An easier way to think of it, I think, is that, having found the roots at the outset -- namely, $\frac{1}{2}\left(\pm\alpha\pm i\alpha\right)$ -- we know we need $K=\mathbb{Q}(\alpha,i)$. $\alpha$ has a fourth-degree minimal polynomial; $\mathbb{Q}(\alpha) \subseteq \mathbb{R}$, so $[K:\mathbb{Q}(\alpha)]=2$.
Jul
9
comment Galois Group of $x^{4}+7$
In you pre-edit post: Did you mean that the splitting field was $\mathbb{Q}(i,\sqrt[4]{7},\sqrt{2})$ -- i.e., did you forget a comma? Multiplying yields $\sqrt[4]{28}$, which you have in your edits, but I think you need both or those elements to be separate... which makes it look like $[K:\mathbb{Q}]=16$. I'm learning this too, so hopefully someone will correct me if I'm wrong.
Jul
9
revised Equation with normal distribution function
Added second half in response to OP's edit.
Jul
8
comment Equation with normal distribution function
@Eutherpy: What $z$-score did you get?
Jul
8
answered Equation with normal distribution function
May
25
revised Hypergeometric function variance
formatting
May
25
suggested approved edit on Hypergeometric function variance
May
23
comment How do I figure out how many snacks to put in a vending machine each day, given a function that predicts how many will be sold in one instant?
To be clear, do you intend for your example to be a better example of a discrete operation approximated by a continuous function? Cos I didn't notice that the first time I read your response. (And the first sentence sorta primed me to not read it that way.)
May
23
comment How do I figure out how many snacks to put in a vending machine each day, given a function that predicts how many will be sold in one instant?
I mean, sure, but would it cease to be inappropriate if OP were selling, I don't know, newspapers? The premise was that the function existed; presumably it does what it's supposed to do. (I'm guessing OP was speaking hypothetically, of course.) If the function tells us what we want it to, why not? Since OP wrote that he/she was learning, I simply wanted to point out that using a continuous function to model a discrete operation isn't on its face an invalid method.
May
23
comment How do I figure out how many snacks to put in a vending machine each day, given a function that predicts how many will be sold in one instant?
It's not at all uncommon to use continuous functions to approximate discrete-valued functions; often it simplifies matters a great deal.
May
23
comment How do I figure out how many snacks to put in a vending machine each day, given a function that predicts how many will be sold in one instant?
That's correct, at least in the case of a definite integral (meaning we evaluate our antiderivative at the endpoints of the interval and find the difference).
May
23
comment How do I figure out how many snacks to put in a vending machine each day, given a function that predicts how many will be sold in one instant?
You'd need to integrate the function over a given interval (say, one day). Have you gotten that far in your studies yet?