- #1
dexterdev
- 194
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I have a small idea on what irreducible and primitive polynomials are in Abstract algebra. But what is minimal polynomial?
-Devanand T
-Devanand T
A minimal polynomial is a polynomial of the lowest degree that has a given root or set of roots. It is used in the field of algebra to find the simplest polynomial that satisfies a given set of conditions.
A minimal polynomial is important because it helps to simplify complex mathematical problems. It allows us to find the simplest polynomial that satisfies a given set of conditions, which can then be used to solve other equations or problems.
A minimal polynomial is different from other polynomials because it has the lowest possible degree while still satisfying a given set of conditions. This makes it the most efficient and simple solution for solving mathematical problems.
Minimal polynomials are commonly used in fields such as algebra, number theory, and computer science. They are used to find roots of equations, construct field extensions, and solve complex mathematical problems.
No, a polynomial can only have one minimal polynomial. This is because the minimal polynomial is unique and is determined by the given root or set of roots. Any other polynomial with the same root or roots would have a higher degree and therefore would not be the minimal polynomial.