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Results tagged with polynomials
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user 13700
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
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Bivariate polynomial divisibility test of Spielman
One possible fix is as follows: let us write $(\deg_X(E),\deg_Y(E))=(a,b)$ and $(\deg_X(P),\deg_Y(P))=(c,d)$. Let us assume $a<c$ and $b<d$ and $E$ coprime with $P$ in the factorial ring $k[X,Y]$. Sup …
- 2,751
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2
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Bivariate polynomial divisibility test of Spielman
Setup
In his thesis (lemma 4.2.18, p. 97-98) Spielman describes a divisibility test for bivariate polynomials $E,P\in k[X,Y]$, where $k$ is a field (of positive characteristic for what I'm interested … The proof works in two steps: prove the assertion for coprime polynomials $E$ and $P$, and reduce the general case to the coprime case. …
- 2,751
45
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4
answers
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Polynomial roots and convexity
There are only 2 kinds of degree $2$ polynomials: two simple roots or a double root. Using $z\rightarrow az+b$, one only has to consider $P=X^2$ and $P=X(X-1)$. … Computing $\mathrm{Hull}(X^3-1)$ requires factorizing degree 4
polynomials, so one naturally tries to look for good values of $\omega$,
the $\omega$ that allow for easy factorization of $\Pi_{\omega}=X …