# Sanchez

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I really appreciate it when you take time to answer my questions. Thanks!

# 934 Actions

 Jan26 comment fundamental group of the Klein bottle minus a point How would you solve the torus problem, and can you copy that solution to the Klein bottle case? Jan26 comment Typo in Marcus' $\textit{Number Fields}$? @BenjaLim, yes. But if you try to work out the contrapositive (i.e. what you can infer from $m$ being a square mod $p$), it seems natural what he wants to do. Jan26 comment Typo in Marcus' $\textit{Number Fields}$? @BenjaLim, sorry I meant to say $p > 4|m|$. Jan26 comment Independence of coordinate charts in the definition of the order of a pole of a meromorphic 1-form on a Riemann surface @Silencer, sorry for my unclear notation. $\frac{dz}{dz'}$ is by definition $\frac{d\phi}{dz'}$ here. I have edited the answer to replace all of them by $\frac{d\phi}{dz'}$. Jan26 revised Independence of coordinate charts in the definition of the order of a pole of a meromorphic 1-form on a Riemann surface added 114 characters in body Jan25 comment Inequality: $(a^3+a+1)(b^3+b+1)(c^3+c+1) \leq 27$ How is this different from Lagrange multiplier? This is just phrased in a tone-down way I suppose. Jan25 comment Symmetric inequality on positive numbers whose product is one @EwanDelanoy, I don't understand what you are saying. If we multiply as you said, we get $(n-2) + t^{n-1} \ge (n-1)t$, apparently true by AMGM. In fact, eventually I didn't use $t \ge 1$ in the whole proof. Jan25 answered Symmetric inequality on positive numbers whose product is one Jan25 comment If $H\unlhd G$ with $(|H|,[G:H])=1$ then $H$ is the unique such subgroup in $G$. Hint: let $K$ be another subgroup of this order. What can you say about $HK$? Jan25 awarded Citizen Patrol Jan25 comment How can I prove that “If $M$ is contractible differentiable manifold, then $M$ is orientable?” @Jaivir Baweja, I don't understand your hint about Poincare lemma. What homology groups are you computing? Jan24 asked $l^1$ norm estimate for inverse of Vandermonde matrix Jan24 comment Multiple choice question about a $3\times3$ invertible matrix $A$ such that $\det(A)=1$ and $\mathrm{tr}(A)=\mathrm{tr}(A^2)=0$ Do you know the Cayley Hamilton theorem? What are the coefficients in the characteristic polynomial, and how are they related to trace? Jan24 answered Independence of coordinate charts in the definition of the order of a pole of a meromorphic 1-form on a Riemann surface Jan24 comment Is multivariable calculus synonymous with differential geometry? (Multvariable) calculus is the tool to study geometry in differential geometry. So yes, they are two different things. Jan22 comment Showing that for $f(z)=\frac{1}{z^2+1}$ an upper estimate is $|f(z)|\leq \frac{1}{\rho^2-1}$ for $|z|=\rho$. No need to use complex analysis - just triangle inequality. Jan22 comment Serge Lang and categories @amWhy, it did not appear in later editions indeed :( Jan22 comment Does $d(x+u, y + v) \le d(x, y) + d(u,v)$ holds for every metric? What is the underlying space here? Jan22 comment Inequality involving partial sums of $\frac{|\sin{kx}|}{k}$ I'm not quite certain, since I guess that the phase problem is the main issue here. If you plot the graph of LHS - RHS, you can see that on $[0, \pi/n]$ it's quite positive, while there are troughs that are quite a bit smaller as we wade through $[\pi/n, \pi]$. Jan22 comment Inequality: $(a^3+a+1)(b^3+b+1)(c^3+c+1) \leq 27$ @ShaneChern, Are you sure? I don't think that Jensen's inequality tells you exactly what the equality cases are.