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Aged mathematician


14h
comment Find a complex number for the splitting field
e-mail me if you’d like to discuss this further.
17h
comment Factorize x^3+3
GF(7) is $\mathbb F_7=\mathbb Z/(7)$
17h
comment Solve $z^{1+i}=4$
This is certainly the right method, just take account of the many-valuedness.
1d
comment Find a complex number for the splitting field
Well, almost any combination of the two separate things will give you a primitive element. My guess is that your process gets only some of these.
1d
comment Find a complex number for the splitting field
Yes, in the sense that for $c$ equal to either of the quoted elements, $E = \mathbb Q(c)$. But not via the procedure you were following!
1d
comment Find a complex number for the splitting field
Both are primitive elements. That is, either of them will generate your sextic extension of $\mathbb Q$
2d
comment Find a complex number for the splitting field
I made a comment that the sum $\root3\of2+\omega$ should work, but that was based on experience, not on using the method you were told to use. With the knowledge of the special properties of this field, though, I found that $(2\omega+1)/(\root3\of2+1)$ has $\mathbb Q$-polynomial $X^6-3X^4+3X^2+3$, a very pretty Eisenstein sextic, more in line with the kind of thing you were looking for.
2d
answered Laurent series for $f(z)= \frac{1}{ (z-i)(z+2i)}$
2d
comment Cyclotomic polynomial identity
This comes from the Möbius Inversion Theorem, which you should look up. Also, in your exponent, you really just wanted ordinary division: $X^{n/d}$.
Nov
21
comment How do I get the expansion of $(2x-1)^{-1} $ to the $x^3$ term
@ClaudeLeibovici, I wish long division of power series was taught in all US schools…
Nov
21
comment Ratio of an isosceles triangle to its altitude is 3:4. find the measures of the angles
When you say, “ratio of an isosceles triangle to its altitude”, are you talking about the base of the triangle versus the altitude? If so, could you edit?
Nov
21
comment How to evaluate $(0.9)^4$ without calculator
Just a matter of terminology: one solves an equation, here you want to evaluate your expression.
Nov
20
comment Is the map, $ f:(0,1)⊂ \mathbb{R}$ → $(1,∞)⊂ \mathbb{R}$ : $x ↦ 1/x $continuous?
If there were a point of discontinuity, what would it be? And what is the inverse function of $f(x)=1/x$?
Nov
20
comment Can $\pi$ be a ratio of angles?
Any real number can be the ratio between two angles.
Nov
20
comment Is there a formula for calculating the area of 2d shapes on a sphere?
multiply by $r^2$
Nov
20
comment Is there a formula for calculating the area of 2d shapes on a sphere?
For a spherical triangle (bounded by arcs of great circles: these are the geodesics on the sphere), it’s easy, and has been known for centuries: the area is proportional to the “spherical excess”, the amount by which the sum of the angles exceeds a straight angle (of $180^\circ$). So, for a sphere of unit radius, if the sum of the angles is $S$ radians, the area is precisely $S-\pi$.
Nov
20
comment Fixed fields,cyclic groups and Galois theory
Much of this is covered in the Fundamental /theorem of Galois Theory, which you should look into. For your question on $\mathbb Z$, this group is not a Galois group as this is ordinarily defined. Galois groups are profinite: compact topological groups with a neighborhood basis of open subgroups.
Nov
19
answered $\sum_{\zeta^p=1}(\zeta-1)^n$
Nov
19
comment Polynominal odd function
What is $y$? If it’s a variable, I don’t see how $x-y$ can divide a polynomial without any $y$’s in it.
Nov
19
comment Questions about poles
This is my way of doing it, but it’s really “power-series division”, ’cause you write the terms in ascending order of degree rather than descending.