PPT-Testing Low-Degree Polynomials over GF(2)

Noga Alon Simon Litsyn Michael Krivelevich Tali Kaufman Dana Ron Danny Vainstein Definitions Definitions Let P k be all polynomials over 01 n with degree at most k without a free term over GF2. Polynomials and Polynomial Functions. Definitions. Terms. Degree of terms and polynomials. Polynomial Functions. Evaluating. Graphing. Simplifying by Combining Like Terms. Adding & Subtracting Polynomials. Arnab. Bhattacharyya. Indian Institute of Science. Property Testing. Distinguish between. and. and. Property . P. -far from property . P.  . Testing and Learning. Proper learning (with membership queries) is as hard as testing, for any property. scalability . improvements . and . applications . to . difference . of convex programming.. Georgina . Hall. Princeton, . ORFE. Joint work with . Amir Ali Ahmadi. Princeton, ORFE. 1. Nonnegative polynomials. Chapter 6. Polynomial Functions. Polynomial Functions. A polynomial is a monomial or the sum of monomials.. A Polynomial Function:. P(x) = . a. n. x. n. + a. n-1. x. n-1 . + … + a. 1. x + a. 0. Where n is a nonnegative integer and the coefficients a. Classify polynomials and write polynomials in standard form. . Evaluate . polynomial expressions. .. Add and subtract polynomials. . Objectives. monomial. degree of a monomial. polynomial. degree of a polynomial. Lesson Objective: NCSCOS 1.01 – Write the equivalent forms of algebraic expressions to solve problems. Students will know the terms for polynomials.. Students will know how to arrange polynomials in ascending and descending order.. Algebra 2. Chapter 5. This Slideshow was developed to accompany the textbook. Larson Algebra 2. By Larson. , R., Boswell, L., . Kanold. , T. D., & Stiff, L. . 2011 . Holt . McDougal. Some examples and diagrams are taken from the textbook.. Polynomials. Monomials in one variable. The product of a constant and a variable raised to a nonnegative integer power.. 2x. 4. 2 is the coefficient degree is 4. What does it mean to be raised to a nonnegative integer power?. Definitions. Coefficient. : the numerical factor of each term.. Constant. : the term without a variable.. Term. : a number or a product of a number and variables raised . to a power.. Polynomial. : a finite sum of terms of the form . Georgina . Hall. Princeton, . ORFE. Joint work with . Amir Ali Ahmadi. Princeton, ORFE. 1. 5/4/2016. IBM May 2016. Nonnegative and convex polynomials. A polynomial . is nonnegative if . How does . nonnegativity. What is a Polynomial?. Here are some definitions….. Definition of Polynomial. An . expression. that can have constants, variables and exponents, but:. * no division by a variable . (. can’t have something . Plot both x & y intercepts to graph.. A-APR.A.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, multiplication and division.. What is a Polynomial?. Here are some definitions….. Definition of Polynomial. An . expression. that can have constants, variables and exponents, but:. * no division by a variable . (. can’t have something . Chandan. . Saha. Indian Institute of Science. Workshop on Algebraic Complexity Theory 2016. Tel-Aviv University. Background. Arithmetic Circuit. +. x. x. x. x. +. +. +. +.