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- linear algebra - Irreducible polynomials in $\mathbb F_3 [x . . .
By looking for what's missing from the $9$ monic polynomials of degree $2$, you can find the monic irreducible polynomials of degree $2$ For degree $3$, things get more complicated, but you're considering either products of three linear terms or a linear term with a degree $2$ factor
- Monic $\iff$ every component is monic? - Mathematics Stack Exchange
Monic $\iff$ every component is monic? Ask Question Asked 5 months ago Modified 5 months ago
- Monic and epic implies isomorphism in an abelian category?
Split monic and epic implies iso; as does split epic and monic But monic and epic does not always imply iso The counterexample is the monoid of natural numbers, since every number considered as a morphism is both monic and epic, but there's only one number, 0, with an inverse
- linear algebra - Characteristic polynomial of a matrix is monic . . .
The characteristic polynomial is the product of monic degree-1 or degree-2 terms, corresponding to eigenvalues and eigenpairs, respectively The set of monic polynomials is closed under multiplication
- Monic Irreducible Polynomials over Finite Field
Monic Irreducible Polynomials over Finite Field Ask Question Asked 12 years, 8 months ago Modified 12 years, 1 month ago
- Injective vs. monic (in categories where it makes sense)
Is the reason why [ monic $\implies $ injective ] true in categories of algebras (but not in other categories whose objects are sets (possibly with some structure) - let's call their objects qwertis) that for the latter categories there is no notion of "free qwerty on a set"? What are some examples (without proof)?
- abstract algebra - Mathematics Stack Exchange
7 With regards to your question, this paper has a formula for counting the number of monic irreducibles over a finite field
- Finding the monic gcd of 2 polynomials [duplicate]
Use Euclid’s Algorithm to find the monic gcd of (i) X^3 + 3X^2 + 4X + 2 and 2X^2 + 7X + 5 I ended up with 13 4X+13 4 = 45 13 (169 180X +169 180), but these are not monic and I don't know where I went wrong as I just followed Euclid's algorithm
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