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Animation depicting the process of completing the square. (Details, animated GIF version)In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form + + to the form + for some values of and . [1]
In the terminology of rewriting systems, → is terminating. Every covering is bounded below. That is, if an element a in A covers elements b and c in A in the sense that a → b and a → c, then there is an element d in A such that b d and c d, where denotes the reflexive transitive closure of →. In the terminology of rewriting systems, → ...
In mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation.Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Horner himself, and can be traced back many hundreds of years to Chinese and Persian mathematicians. [1]
Plot of the Chebyshev polynomial of the first kind () with = in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D. The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as () and ().
The 10 starred equations turn out to constitute the resulting convergent rewrite system. "pm" is short for "paramodulation", implementing deduce. Critical pair computation is an instance of paramodulation for equational unit clauses. "rw" is rewriting, implementing compose, collapse, and simplify. Orienting of equations is done implicitly and ...
In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) ... which consists of rewriting the polynomial as ((( ...
Reduction of polynomials modulo an ideal is a confluent rewrite system provided one works with a Gröbner basis. Matsumoto's theorem follows from confluence of the braid relations. β-reduction of λ-terms is confluent by the Church–Rosser theorem .
A term rewriting given by a set of rules can be viewed as an abstract rewriting system as defined above, with terms as its objects and as its rewrite relation. For example, x ∗ ( y ∗ z ) → ( x ∗ y ) ∗ z {\displaystyle x*(y*z)\rightarrow (x*y)*z} is a rewrite rule, commonly used to establish a normal form with respect to the ...