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Apr
30 |
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accepted | The roots of $t^5+1$ |
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Apr
29 |
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awarded | Commentator |
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Apr
29 |
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comment |
The roots of $t^5+1$ @CliveNewstead, so the roots are -1, -w, -w^2, -w^3, -w^4, with w=e^(2ipi/5)? |
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Apr
29 |
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asked | The roots of $t^5+1$ |
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Apr
26 |
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asked | Ramsey theory - colouring of edges |
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Apr
22 |
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comment |
Factorisation of a polynomial over $\mathbb Q(i,\sqrt 5)$ Of course..! Thank you for the point out :) |
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Apr
22 |
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asked | Factorisation of a polynomial over $\mathbb Q(i,\sqrt 5)$ |
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Apr
21 |
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accepted | Irreducible Polynomial over $\mathbb{Q}$ |
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Apr
20 |
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awarded | Scholar |
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Apr
20 |
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accepted | Irreducibility of polynomials |
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Apr
20 |
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revised |
Irreducible Polynomial over $\mathbb{Q}$ edited body |
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Apr
20 |
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comment |
Irreducibility of polynomials Thanks for the clarification, I understand the use of the primitive cube root of unity now :) |
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Apr
20 |
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comment |
Irreducible Polynomial over $\mathbb{Q}$ Thank you, Martin, this has helped a lot! Is there a way to achieve this result without looking at the poly in Z2? |
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Apr
20 |
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comment |
Irreducible Polynomial over $\mathbb{Q}$ Thank you! I would not have come across using Gauss's theorem of primitive polynomials unless after many hours! So, can we use this for any primitive polynomial, i.e. can we use this principle to find the factorisation of g(x), a primitive cubic poly? Many thanks. |
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Apr
20 |
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asked | Irreducible Polynomial over $\mathbb{Q}$ |
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Apr
20 |
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awarded | Supporter |
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Apr
20 |
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comment |
Irreducibility of polynomials Hi there, thank you for such a wonderfully detailed explanation, it was extremely helpful! I was wondering, should the quadratic in Z5 read (x^2+3x+4) rather than (x^2+2x+4)? And hence the discriminant be 9-16=-7 congruent to 3 mod 5? Also, as for the complex factorisation, could you please explain to me why we are going about it by introducing the primitive root of unity (I understand what the primitive root of unity is, etc.)? Thank you. |
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Apr
20 |
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comment |
Irreducibility of polynomials It can be expressed as such, yes. I think I understand your meaning, thank you :) |
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Apr
20 |
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comment |
Irreducibility of polynomials Btw, I now understand how we can factorise this into irreducibles over R, but what about C? If there is no imaginary part, is it still a valid factorisation in C? Sorry if that is too basic a question. |
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Apr
20 |
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comment |
Irreducibility of polynomials Thank you for explaining this! |
