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Jun
19
comment How do I do “calculations” with tensors?
@anon: I don't really understand your comment yet, I'll try again later.
Jun
19
comment How do I do “calculations” with tensors?
@YBL: I know exactly how to change coordinates, my problem is that I don't understand why $G = e_1^* \otimes e_3^* + e_2^* \otimes e_2^*$.
Jun
19
comment How do I do “calculations” with tensors?
No. I don't understand how I can represent $G$ in terms of $e_i^* \otimes e_j^*$. Once I understand how to obtain this representation and why that is the correct representation, I know how to proceed.
Jun
19
comment How do I do “calculations” with tensors?
I have no idea where to start and what I'm trying to obtain really.
Jun
19
asked How do I do “calculations” with tensors?
Apr
6
accepted A program to draw simple geometry (points, lines, dotted lines etc.)
Apr
6
comment A program to draw simple geometry (points, lines, dotted lines etc.)
Ipe is exactly what I've been looking for, thanks!
Apr
6
comment A program to draw simple geometry (points, lines, dotted lines etc.)
I'm afraid I forgot to mention that I'm looking for a program which I can run on Windows 7.
Apr
6
asked A program to draw simple geometry (points, lines, dotted lines etc.)
Mar
30
accepted Lack of understanding of the proof of the existence of an irreducible polynomial of any degree $n \geq 2$ in $\mathbb{Z}_p[x]$
Mar
30
comment Lack of understanding of the proof of the existence of an irreducible polynomial of any degree $n \geq 2$ in $\mathbb{Z}_p[x]$
3) This might be somewhat stupid but as I've never before seen these generating functions: Why exactly do we use the generating functions? What is the motivation? When will I have to use them? I mean, after all these questions and answers I think I might have understood how the proof works but I would never have come up with something even remotely related to these generating functions. However, as they are being used in this proof, I am sure that the teacher might want us to be able to use generating functions on our own to prove things...
Mar
30
comment Lack of understanding of the proof of the existence of an irreducible polynomial of any degree $n \geq 2$ in $\mathbb{Z}_p[x]$
I have given your edited response another shot and now I do indeed understand much more. However, I still have a few or say new questions: 1) In your example, did you mean to pick the term $z^3$ because $\phi_1$ appears in the third power and thus we get the term $z^3 \cdot z^2 = z^5$ to represent $\phi$, or am I missing something? 2) I understand that $\frac{1}{1-pz}$ is the generating function belonging to the set of all monic polynomials and $F$ is bijective to that set. However, why can we "just like that" set two generating functions of two bijective sets equal?
Mar
29
answered Could someone show me step by step the evaluation of this (Basic/AS Level)
Mar
29
comment Lack of understanding of the proof of the existence of an irreducible polynomial of any degree $n \geq 2$ in $\mathbb{Z}_p[x]$
Thank you very much for your answer. For me, questions 1, 2 and 4 are solved now, however, I don't quite understand your answer to my question 3. Also, you seem to use a different notation, e.g. $f_i(x)$, which is very confusing to read, as we already defined $f_n$ to be the amount of monic irreducible polynomials of $n$-th degree... I'm not sure what $\varphi_{f_1}(z)$ means either, could you maybe elaborate or change the notation to ours? Maybe, then I have better chances to understand what's going on.
Mar
29
comment Lack of understanding of the proof of the existence of an irreducible polynomial of any degree $n \geq 2$ in $\mathbb{Z}_p[x]$
@Jyrki: Regarding your first comment, I have no idea what an ideal is, so I can't really follow. Regarding your second comment, we have not anywhere defined an "index" except in this proof (if this is considered a definition). I understood if to be some integer assigned to an element of a set.
Mar
29
revised Lack of understanding of the proof of the existence of an irreducible polynomial of any degree $n \geq 2$ in $\mathbb{Z}_p[x]$
deleted 5 characters in body
Mar
29
asked Lack of understanding of the proof of the existence of an irreducible polynomial of any degree $n \geq 2$ in $\mathbb{Z}_p[x]$
Mar
29
accepted Why is this map diagonalisable?
Mar
12
asked Why is this map diagonalisable?
Mar
6
accepted How to show $\langle a, b \; | \; aba = bab \rangle \cong \langle x,y \; | \; x^3=y^2 \rangle$?