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Apr
18
comment Integrating a vector field over curve in R^2 with differential forms
Thanks. I guess that's pretty straightforward.
Apr
18
asked Integrating a vector field over curve in R^2 with differential forms
Oct
24
comment Tips for finding the Galois Group of a given polynomial
I think it's helpful to first consider the size of the Galois group, then ask which group of that size it could be. For example, if $|G|=6$, then it suffices to figure out whether $G$ is abelian
Oct
24
answered A question on Newton's “theorem about ovals”
Oct
24
comment A question on Newton's “theorem about ovals”
Or I should ask -- at the end of your answer, you say "For sufficiently smooth curves, if the area cut off is algebraic at all, it has to be algebraic over the whole domain of the angle." Why must it be algebraic over the whole domain of the angle?
Oct
24
comment A question on Newton's “theorem about ovals”
Isn't that precisely the definition of "$f$ is an algebraic function"? Further, I wouldn't claim $f$ and $g$ measure the same thing, merely that they agree for $\theta\in[2\pi ]$. For example, if we take the unit circle and a ray from the origin making angle $\theta$ with the poisitive $x-$axis, I would say that the area of the sector is $f(\theta) = \theta$ for $\theta \in [0, 2\pi)$ and is continued to the real line via $f(\theta + 2\pi) = f(\theta).$
Oct
23
comment A question on Newton's “theorem about ovals”
Ok, then I agree. But I still have my original question. The theorem states, as I understand it, that there is no polynomial $P$ with $P(f,r,s,t)=0$, where $f(r,s,t)$ is the area of the curve cut off by the line $rx+sy=t.$ The proof seems to provide a function $g(r,s,t)$ which has that property, but $g\neq f$
Oct
23
comment A question on Newton's “theorem about ovals”
How can a function be both periodic and monotone (and not be constant)?
Oct
23
awarded  Student
Oct
22
asked A question on Newton's “theorem about ovals”
Mar
6
comment Representation of a fundamental group.
It should be pointed out that a representation doesn't have to have the same order as the group. For example, the map g $\mapsto$ Id is a rep.
Jun
8
comment What do you call a number that represents 20 Percent written as “0.2” and “20%” respectively
I call them $1/5$
Jun
8
comment What does the notation $x \in \mathbb{R}^V$ mean where V is a set?
To elaborate further, one can see that this is in some way consistent with the notation $\mathbb{R}^n$ which can be viewed as the set of functions from a set of $n$ elements to $\mathbb{R}.$
Jun
6
comment Need help proving least upper bound property for non-empty subsets of N
Does $N = \mathbb{N}$? If so, then if $b$ is a least upper bound for a set $S,$ but $b \notin S,$ then $b-1$ is an upper bound for $S.$
May
29
comment How do I find the intersections of 2 circles on earths surface?
What do you mean the circles' center? Edit for clarity: is a circle on the Earth a set of points on the surface of the earth equidistant from some point, that point being the "center"?
May
24
comment Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian
I think you actually have the most obvious way of doing this
May
23
comment Groups acting on polynomials
@badatmath It's good to remember that a homomorphism $F \rightarrow F$ extends naturally to one $F[X] \rightarrow F[X].$ In fact, many people use the same symbol for both homomorphisms.
May
14
comment $x^p -a$ is irreducible in a field of char $0$
What happens when you compare divisors of $P \,$ to those of its derivative?
Apr
8
awarded  Commentator
Apr
8
comment Question about topology
You can! Your reasoning is entirely right. You even have written on one line, $(a,b) \cap Y = (a,b)$ if $(a,b) \in Y$. Without this you have not specified the topology completely. (I do think you have specified a correct subbasis for the topology)