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Fast Library for Number Theory
Fast Library for Number Theory

Factorising - Numeracy Workshop
Factorising - Numeracy Workshop

linked PDF version! - Math-UMN
linked PDF version! - Math-UMN

PDF Polynomial rings and their automorphisms
PDF Polynomial rings and their automorphisms

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The Theory of Polynomial Functors

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Simplifying Expressions Involving Radicals

... the simplification of expressions. Since many algorithms in Computer Algebra systems like Mathematica, Maple, and Reduce work in quite general settings they do not necessarily find a solution to a given problem described in the easiest possible way. Simplification algorithms can be applied to expres ...
A Book of Abstract Algebra
A Book of Abstract Algebra

A (biased) survey on Arithmetic Circuits
A (biased) survey on Arithmetic Circuits

... derivatives of C according to X1,…,Xk (any k) is at most s (spanned by Li,k+1(Xk+1) ⋅ … ⋅ Li,d(Xd)) Algorithm: compute a basis for all derivatives according to X1,…,Xk starting from k=1 to k=d. C≡0 if at the end all basis elements are 0 Same idea also in the general case ...
Divided powers
Divided powers

8 Square matrices continued: Determinants
8 Square matrices continued: Determinants

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characteristic 2

9 The resultant and a modular gcd algorithm in Z[x]
9 The resultant and a modular gcd algorithm in Z[x]

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Course Notes (Gross

(3) Greatest common divisor
(3) Greatest common divisor

The Mathematics of Coding: Information, Compression, Error Correction,
The Mathematics of Coding: Information, Compression, Error Correction,

COMPUTATIONS FOR ALGEBRAS AND GROUP
COMPUTATIONS FOR ALGEBRAS AND GROUP

NAVAL POSTGRADUATE SCHOOL
NAVAL POSTGRADUATE SCHOOL

Galois Field Computations A Galois field is an algebraic field that
Galois Field Computations A Galois field is an algebraic field that

Polynomials and Polynomial Functions
Polynomials and Polynomial Functions

Galois Theory - Joseph Rotman
Galois Theory - Joseph Rotman

Lectures on Applied Algebra II
Lectures on Applied Algebra II

MATH 371 - McGill University
MATH 371 - McGill University

Paul Mitchener's notes
Paul Mitchener's notes

Borel-fixed monomial ideals
Borel-fixed monomial ideals

Lecture 8: Stream ciphers - LFSR sequences
Lecture 8: Stream ciphers - LFSR sequences

1 2 3 4 5 ... 28 >

Resultant

In mathematics, the resultant of two polynomials is a polynomial expression of their coefficients, which is equal to zero if and only if the polynomials have a common root (possibly in a field extension), or, equivalently, a common factor (over their field of coefficients). In some older texts, the resultant is also called eliminant.The resultant is widely used in number theory, either directly or through the discriminant, which is essentially the resultant of a polynomial and its derivative. The resultant of two polynomials with rational or polynomial coefficients may be computed efficiently on a computer. It is a basic tool of computer algebra, and is a built-in function of most computer algebra systems. It is used, among others, for cylindrical algebraic decomposition, integration of rational functions and drawing of curves defined by a bivariate polynomial equation.The resultant of n homogeneous polynomials in n variables or multivariate resultant, sometimes called Macaulay's resultant, is a generalization of the usual resultant introduced by Macaulay. It is, with Gröbner bases, one of the main tools of effective elimination theory (elimination theory on computers).
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