All Questions
Tagged with ho.history-overview polynomials
15 questions
0
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69
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Evaluating the coprimality in a bivariate polynomial equation
Given a prime $p>2$, let $x$ and $y$ be real numbers such that $x>y>0$ and
$$ \begin{equation} x^p-y^p=(x-y)^p+pxy(x-y)R \tag{1} \label{eq:one} \end{equation} $$
where $R$ is a bivariate ...
- 125
6
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141
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Historical background of finding the roots of cubic equations using continued fractions
I came across an algebra problem book written in 1899 for students of Dar al-Fonun ([dɒːɾolfʊˈnuːn], meaning, "polytechnic college",) the only modern educational institute in Iran at the ...
- 2,437
4
votes
1
answer
123
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How are Lie groups and polynomial resolvents related?
I came across the following sentence in Stevenhagen and Lenstra's wonderful little article Chebotarëv and his density theorem:
Nikolai's interest in [polynomial] resolvents led him to study Lie ...
- 185
2
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168
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Geometric construction of real root of quintic using marked ruler and compass
My question is motivated by a geometry problem about special folded rectangle:
'A rectangle with sides a, b (a<b) is folded along the line that passes through the center of the rectangle in order ...
13
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243
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Galois group of polynomials related to Fibonacci and Catalan numbers
Let $F_n$ be the Fibonacci and $C_n$ the Catalan numbers.
Define a polynomial by $F_n(x):=\sum\limits_{k=1}^{n}{F_k x^{n-k}}$.
For example $F_8(x)=x^7+x^6+2x^5+3x^4+5x^3+8x^2+13x+21$.
And another ...
- 26.5k
9
votes
1
answer
331
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Hahn's approach to Hilbert's 17th problem?
The Wikipedia article on Hahn Series mentions mentioned that these were studied by Hahn "in his approach to Hilbert's seventeenth problem".
Is this correct? If so, what was this approach, ...
- 6,406
1
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273
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Alexander Ostrowski's argument for filling the gap in Gauss's proof of the FTA
I've read in Smale "The fundamental theorem of algebra and complexity theory" and Cain "C. F. Gauss’s Proofs of the Fundamental Theorem of Algebra" regarding how there was a gap in Gauss's proof in ...
- 387
-1
votes
1
answer
315
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Resolvent in French [closed]
First, I apologize if the question doesn't fit this forum.
In a thread about Galois theory on a French math forum, I read "le sextique résolvent" and the spelling looks odd to me. I would have ...
- 6,976
19
votes
3
answers
4k
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What is the story behind the Chebyshev polynomials?
Is there anything reliable known about who actually discovered the Chebyshev polynomials and what the motivation and circumstances were?
The reason why I am interested in knowing, is that I needed a ...
- 13.2k
19
votes
2
answers
5k
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Why is a matrix pencil called a pencil?
I'm trying to understand the historical context behind the word pencil in matrix pencils, or pencil of curves so on.
I am aware that even Gantmacher 1959 has this terminology however I don't know ...
- 295
1
vote
0
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139
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First Description of how to Remove Radicals from Equations
Who first described the technique of removing radicals as indicated in the answers to questions Tools for Removing Radicals from Equations and Rewrite sum of radicals equation as polynomial equation ? ...
- 13.2k
16
votes
2
answers
2k
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Giant Rat of Sumatra singularity
I would be grateful for explanations of the issues raised in any
of these three questions, or pointers to the relevant literature
(now updated with answers):
How did a particular singularity come to ...
- 151k
22
votes
1
answer
2k
views
Primes represented by two-variable quadratic polynomials
I'm looking over a paper, "Primes represented by quadratic polynomials in two variables" [1] which attempts to characterize the density of the primes in two-variable quadratic polynomials. ...
- 9,114
1
vote
1
answer
1k
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Unique factorization in polynomial rings
Everybody knows that polynomial rings over fields have unique factorization, and that if $R$ has unique factorization, then so does $R[X]$. And everybody knows who proved these results first.
Well, ...
10
votes
1
answer
835
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what was Hilbert's geometric construction in his 17th problem?
Hilbert's 17th problem asked if a nonnegative real polynomial is the sum of squares of rational functions. It was answered affirmative by Artin in around 1920. However, in his speech, he also asked if ...
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