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Results tagged with polynomials
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user 5534
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.
5
votes
1
answer
2k
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Multivariate Hensel's Lemma, but with only one polynomial
One version of Hensel's Lemma is the following statement:
Let $R$ be a commutative ring with a unit. Given a polynomial $Q\in R[X]$ and a root $\alpha$ of $Q$ modulo some ideal $I$ (i.e. $Q(\alpha) …
- 2,019
15
votes
1
answer
788
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Can formal power series become polynomial often, when composed with polynomials?
Let $F[X]$ and $F[[X]]$ denote the ring of polynomials and power series over $F$, respectively. I'm trying to show a statement like the following:
Fix a $d > 0$. Let $g\in F[[X]]$. … If there exists a set $C\subseteq F[X]$ of polynomials (with no constant term) of degree at most $k$ such that for all $c\in C$, $g(c)$ -- $g$ composed with $c$ -- is a degree $kd$ polynomial, and $|C| …
- 2,019
0
votes
1
answer
131
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Uniqueness of Hensel factors of a polynomial (invariant to change of "basepoint")?
An important component of algorithms for factoring multivariate polynomials over a commutative ring $R$ is Hensel lifting. …
- 2,019
0
votes
3
answers
441
views
Entire function interpolation with control over multiplicities/derivatives
Let's say I have a multiset of complex numbers $\lbrace a_1,\cdots,a_n\rbrace$ (so some of the elements may be repeated) and I would like to construct an entire function $p(z)$ with those numbers as z …
- 2,019