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Results tagged with polynomials
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user 5495
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.
19
votes
3
answers
787
views
What is the shortest polynomial divisible by $(x-1)(y-1)(x^2y-1)$
I am interested in polynomials with few terms ("short polynomials", "fewnomials") in ideals. … Are there polynomials with six or seven terms in $I$? …
- 13.6k
12
votes
Accepted
Is an ideal generated by multilinear, irreducible, homogeneous polynomials of different degr...
One general fact that comes to mind: If an ideal $I\subset \mathbb{k}[x_1,\dots,x_n]$ contains an element of the form $f = gx_1 + h$ where $g,h$ don't use $x_1$, and $g$ is a nonzerodivisor mod $I$, …
- 1,961
5
votes
1
answer
1k
views
Is there an algorithm to decide if an ideal contains monomials?
Let $I\subset k[x_1,\dots,x_n]$ be an ideal in a polynomial ring in commuting variables. Is there a procedure to decide if $I$ contains a monomial and possibly to find one?
Gröbner bases come to min …
- 27.9k