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Results tagged with polynomials
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user 508260
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.
2
votes
Accepted
Coprime polynomials and polynomial substitution
The answer is positive. Since $P,Q$ are coprime the variety $V=\{P=Q=0\}\subset\mathbb A^m$ has dimension $\le m-2$. Consider the variety $W=\{P(R_1,\ldots,R_m)=Q(R_1,\ldots,R_m)=0\}\subset\mathbb A^{ …
- 651
1
vote
Computing the minimal polynomial of roots of polynomials with algebraic coefficients
One approach would be as follows: Let $c_i^{(j)},\,j=1,\ldots,\deg q_i$ be the conjugates of $c_i$. Denote $p_{j_0,\ldots,j_n}(x)=\sum_{i=0}^nc_i^{(j_i)}x^i$ and form the product $P(x)=\prod_{j_1,\ldo …
- 651
3
votes
Accepted
Defining polynomial of compositum of splitting fields
For monic polynomials $f,g$ define $f*g=\mathrm{Res}_y(f(y),g(x-y))$. This is an associative and commutative operation on univariate monic polynomials with neutral element $x$. …
- 651
5
votes
Galois groups of truncated $\cosh(x)$ Taylor polynomials and related results?
EDIT: I initially misread the definition of $C_n$ to be $\sum_{k=0}^n\frac {x^{2k}}{k!}$ and answered the wrong question. The general approach should still apply, but additional ideas are required for …
- 651