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Polynomial Division: more books (39)

Synthetic Division: Polynomial Long Division, Algorithm, Algebra, Polynomial, Long Division, Ruffini's Rule, Polynomial Remainder Theorem, Euclidean Domain, Gröbner Basis
The interlace polynomial: A new graph polynomial (Research report / International Business Machines Corporation. Research Division) by Richard Arratia, 2000
Generalized characteristic polynomials (Report. University of California, Berkeley. Computer Science Division) by John Canny, 1988
Root isolation and root approximation for polynomials in Bernstein form (Research report RC. International Business Machines Corporation. Research Division) by V. T Rajan, 1988
Tables for graduating orthogonal polynomials, (Commonwealth Scientific and Industrial Research Organization, Australia. Division of Mathematical Statistics technical paper) by E. A Cornish, 1962
Conditions Satisfied By Characteristic Polynomials in Fields and Division Algebras: MSRI 1000-009 by Zinovy; Boris Youssin Reichstein, 2000
A fast algorithm for rational interpolation via orthogonal polynomials (Report, CS. University of California, Berkeley. Computer Science Division) by OÌˆmer Nuri EgÌ†eciogÌ†lu, 1987
Neural networks, error-correcting codes and polynomials over the binary n-cube (Research report RJ. International Business Machines Corporation. Research Division) by Jehoshua Bruck, 1987
On the numerical condition of Bernstein Polynomials (Research Report RC. International Business Machines Corporation. Research Division) by Rida T Farouki, 1987
On the distance to the zero set of a homogeneous polynomial (Research report RC. International Business Machines Corporation. Research Division) by Michael Shub, 1989
Some algebraic and geometric computations in PSPACE (Report. University of California, Berkeley. Computer Science Division) by John Canny, 1988
On a problem of Chebyshev (Mimeograph series / Dept. of Statistics, Division of Mathematical Sciences) by W. J. (William J.) Studden, 1979
D[subscript s]-optimal designs for polynomial regression using continued fractions (Mimeograph series / Dept. of Statistics, Division of Mathematical Sciences) by W. J. (William J.) Studden, 1979
On the zeros of a polynomial vector field (Research report RC. International Business Machines Corporation. Research Division) by Takis Sakkalis, 1987

lists with details

Polynomials
3. polynomial division polynomial division is a lot like division of whole numberswhere you get a quotient and a remainder, eg 13 divided by 5 gives quotient
http://www.math.uri.edu/~pakula/111web_f02/polynomials.htm

Extractions: [UnitView] [Syllabus] Unit Guide for Polynomials Review adding, multiplying and factoring polynomials. Sections R3 and R4 are intended as a review of algebra-this should not be the first time you are seeing these things. Some special points: Multiplying polynomials: Be sure that you can multiply things like (3 x x x + x - x ). The "FOIL" method can't be used for this, so you should know how to perform this calculation by careful use of the distributive property. Special patterns: The formulas (A+B) = A + 2AB + B and (A-B)(A+B) = A - B appear very frequently and you should recognize these patterns. Factoring: Make sure you know how to factor perfect squares, difference of two squares, and situations where you must pull out common factors. You don't need to know how to factor the difference of two cubes. A very simple but common factoring situation that you should know is AB + A = A(B+1). Polynomial Functions. The main points to learn about polynomials are a. For large values of x, a polynomial behaves like the term of highest degree. This is reflected in the appearance of the graph in a very big viewing window. (The "Leading Term Test")
ThinkQuest : Library : Go Forth & Multiply: A Mathematics Adventure
Long Division. This is a method used in arithmetic and polynomial division.First, we ll take a look at an example of division in arithmetic.
http://library.thinkquest.org/C0110248/algebra/allongdiv.htm

Extractions: Index Education Want to learn more about the world of mathematics? Then go forth, and enter the wildest math adventure you've ever been! Learn new math concepts and refresh your knowledge for those you've already known. Understand how the formulae you use were derived from. Or, you can take a step back into the past and read about how mathematics and its concepts originated. Go forth and multiply! Visit Site 2001 ThinkQuest Internet Challenge Awards Achievement Award Students Teow Lim Raffles Junior College, Singapore, Singapore Vee San Coaches Poh Kheng Pioneer Junior College, Singapore, Singapore Jee Wah Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy
Deconv (MATLAB Functions)
. q,r = deconv(v,u) deconvolves vector u outdeconv Deconvolution and polynomial division. Syntax q,r = deconv(v,u).
http://www.mathworks.com/access/helpdesk/help/techdoc/ref/deconv.html

Extractions: [q,r] = deconv(v,u) deconvolves vector u out of vector v , using long division. The quotient is returned in vector q and the remainder in vector r such that v conv(u,q)+r If u and v are vectors of polynomial coefficients, convolving them is equivalent to multiplying the two polynomials, and deconvolution is polynomial division. The result of dividing v by u is quotient q and remainder r Examples
Cyclic Redundancy Check Polynomials Tutorial
Press the check symbol beside polynomial division. A window will appearwith the generator sequence as a divisor in a long division sum.
http://www.macs.hw.ac.uk/~pjbk/nets/crc/crctext.html

Extractions: A generator is chosen (using theory which will not be detailed here). This is a sequence of bits, of which the first and last are 1. This sequence is used with the bits of the message to calculate a check sequence which has 1 fewer bits than the generator. The check sequence is appended to the original message. At the receiver, the same calculation is performed on the message and check sequence combined. If the result is no transmission error is assumed to have occurred.
File Verification Using CRC
CRC calculations are done using a technique with the formidable nameof polynomial division . A block of data, regardless os how
http://www.dogma.net/markn/articles/crcman/crcman.htm

Extractions: Recently I have found myself thinking a lot about file verification. By file verification, I mean the process of determining whether a file on my computer has been modified unexpectedly. Whether it happened through hardware failure, program error, or malicious tampering, I like to know when a file has had its contents altered. Likewise, I would like a convenient way to check the integrity of a file to verify that it hasn't been changed. The problem of file integrity has been on my mind because of several nearly simultaneous incidents. First of all, I recently ran dozens of relatively untested programs through my home systems while I was judging the Dr. Dobb's Data Compression Contest. At least two of these programs caused inadvertent damage to the file systems on my computer, one under UNIX and one under MS-DOS. In both cases, I was able to spot a lot of the damage, but after I restored the data that looked bad, I was left feeling unsure about the rest of my system. Had other files been damaged in more subtle ways? I suddenly felt as though I couldn't trust my system. An even more alarming incident occurred a couple of weeks later. A programmer who supplies us with a product for resale called us up and casually mentioned that his office had been infested with the notorious "Stoned" virus. Had we by any chance noticed anything funny in oursystems? We see funny things on our systems on an hourly basis, sosuddenly we were once again in the position of not trusting any of the files on our computers. (Fortunately this turned out to be a false alarm).
Polynomial Expressions
The polynomial division and remainder are done using the defined monomial orderin the base ring. Parentheses are used to enforce groupings in an expression.
http://www.math.columbia.edu/online/Macaulay1-rel0994-html/node22.html

Extractions: Next: Integer lists Up: Input Syntax Previous: Integer Expressions The syntax for polynomial expressions is similar to integer expressions. The legal operators for polynomials, in order of increasing precedence, are given in the following table. The polynomial division and remainder are done using the defined monomial order in the base ring. Parentheses are used to enforce groupings in an expression. The following remarks describe certain aspects of polynomial expressions. Polynomials in Macaulay are output in an abbreviated notation: each polynomial is displayed as a number of monomials separated by ``+'' or ``-''. Each monomial is preceeded by its coefficient and each indeterminate is followed by its degree with no intervening blanks. Rational number coefficients are represented by x y . A polynomial which extends over a line boundary is displayed by using as the continuation character. If you wish to have polynomials output in Mathematica format, use the prmat command.
P04-Factor Remainder Theorems.html
f(r) = R the remainder when (xr) is divided into f(x) is R It makes a connectionbetween the remainder of a polynomial division and evaluating a polynomial.
http://www.mapleapps.com/powertools/precalc/html/P04-Factor Remainder Theorems.h
EE4253 Polynomial
The first test division by (x+1) yields a zero remainder, and a factor is found.This polynomial is not prime. Answer polynomial division in Hardware.
http://www.ee.unb.ca/tervo/ee4253/poly.htm

Extractions: EE4253 Digital Communications Manipulation of Binary Messages as Polynomials Manipulation of long binary values requires some special techniques. The polynomials notation lends itself to computation in hardware using only shift registers and exclusive-OR (XOR) gates. Once the mathematics of polynomials has been defined, the concept of prime polynomials can be introduced. Introduction to Polynomials For example, can be written as x x x x x x and simplified as: x + x + x + 1 The order of a polynomial is the power of the highest non-zero coefficient. The above example shows a polynomial of "order 5". 2. Polynomials can be manipulated using the usual arithmetic rules, and these properites (closure, associative, commutative, etc) define a field Example 1: 110011 x 10 = 1100110 can be written as: (x + x + x + 1) (x) = x + x + x + x 3. Polynomials always use modulus 2 arithmetic . This is equivalent to the exclusive-OR operation, as shown below. Example 2: 11 x 11 can be computed as: 11 x 11 11 + 110 101 Note modulus 2 addition and as a polynomial: (x + 1)(x + 1) = x + x + x + 1 = x Note that x + x = when simplifying this result.
DBLP: Dario Bini
ISSAC 1993 193200. 20, Dario Bini, Victor Y. Pan Improved Parallelpolynomial division. SIAM J. Comput. 22(3) 617-626 (1993). 1992.
http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/b/Bini:Dario.html

Extractions: List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL ACM Guide CiteSeer CSB ... EE Dario Bini, Gianna M. Del Corso Giovanni Manzini Luciano Margara : Inversion of Circulant Matrices over Z m ICALP 1998 EE Dario Bini, Victor Y. Pan : Computing Matrix Eigenvalues and Polynomial Zeros Where the Output is Real. SIAM J. Comput. 27 Dario Bini, Luca Gemignani : Erratum: Fast Parallel Computation of the Polynomial Remainder Sequence via Bezout and Hankel Matrices. SIAM J. Comput. 25 Dario Bini, Luca Gemignani : Fast Parallel Computation of the Polynomial Remainder Sequence Via Bezout and Hankel Matrices. SIAM J. Comput. 24 EE Dario Bini, Victor Y. Pan : Parallel Computations with Toeplitz-like and Hankel-like Matrices. ISSAC 1993 Dario Bini, Victor Y. Pan : Improved Parallel Polynomial Division. SIAM J. Comput. 22 Dario Bini, Victor Y. Pan : Improved Parallel Polynomial Division and Its Extensions FOCS 1992 Dario Bini, Luca Gemignani : On the Complexity of Polynomial Zeros. SIAM J. Comput. 21 Dario Bini, Luca Gemignani Victor Y. Pan
Synthetic Division
Suggested Use Study algebra of polynomial division. Topics college algebra,polynomials, gcd, synthetic division, symbolic algebra. Number of Pages 1.
http://www.mathwright.com/book_pgs/book055.html

Extractions: Been away for a while? Check out our new building by clicking the picture on the right! This WorkBook requires Mathwright Library Player 2000 to read it. To download the book, press the button on the left. A self-extracting file will be downloaded. Either save it to disk and execute it later, or simply select "Open it" from the popup dialog. This places the book, along with its documentation, on the Start, Programs, Mathwright Library menu, so that you may read it whenever you like. Size: 131 KB Find similar WorkBooks in the Rooms below: Categories: Home Study Tools Math and Computers Subjects: Algebra College Algebra Precalculus Factorization ... Rational Functions Title: Synthetic Division Book Description: In this command-line WorkBook, students may explore synthetic division of polynomials with rational coefficients. There is a command called Synthetic that returns the quotient of one polynomial by another (with rational coefficients) together with the remainder part. There are also several programs that support exploration. These are: Divide(num,den) returns the same result that synthetic would. This result can then be used by another command (for example, to define a function and draw its graph). Pquotient and Premainder returns the results (quotient and remainder) from the Euclidean algorithm. Finally, GCD returns the greatest common divisor of two rational polynomials.
Matlab Manual Page: Deconv
. q,r = deconv(b,a) deconvolves vectordeconv. Purpose. Deconvolution and polynomial division. Synopsis. q,r= deconv(b,a)
http://www.utexas.edu/math/Matlab/Manual/deconv.html

Extractions: Deconvolution and polynomial division. [q,r] = deconv(b,a) [q,r] = deconv(b,a) deconvolves vector a out of vector b , using long division. The quotient is returned in vector q and the remainder in vector r such that b = conv(q,a)+r If a and b are vectors of polynomial coefficients, convolving them is equivalent to multiplying the two polynomials, and deconvolution is polynomial division. The result of dividing b by a is quotient q and remainder r If a = [1 2 3 4] b = [10 20 30] the convolution is c = conv(a,b) c = Use deconvolution to divide a back out: [q,r] = deconv(c,a) q = r = gives a quotient equal to b and a zero remainder. deconv uses the filter primitive. conv residue convmtx , and f ilter in the Signal Processing Toolbox
Page7
We put the polynomial division algorithms in different classes PolynomialDivisor(one variable), PolynomialPseudoDivisor (one or many variables, but wrt a
http://mate.dm.uba.ar/~caniglia/Pablo/

Extractions: Mathematical Objects This is the change set of this work The object of this project is to solve the Implicitation Problem, i.e. given an algebraic variety described by a rational parametric equation, find a system of polynomial equations which define it in implicit form. We created classes to model multivariate polynomials: MonomialLiteral, Monomial y Polynomial. MonomialLiteral models the literal part of the monomials, i.e., products of indeterminate powers. The Monomials know a coefficient and a literal. Finally, each Polynomial represets a polynomial and stores the collection of not null monomials (Monomials). We put the polynomial division algorithms in different classes: PolynomialDivisor (one variable), PolynomialPseudoDivisor (one or many variables, but w.r.t. a variable), MultiPolynomialDivisor (many variables with fixed monomial ordering). We also have objects which are rational functions; we created the RationalFunction class, this class knows a numerator and a denominator. Class Ideal You can create ideals from a generating set Class protocol instance creation generator: anIdealGenerator Also, we can ask an ideal for a generating set accessing generators The ideals allow arithmetic operations
ThinkQuest : Library : Seeing Is Believing
polynomial Functions. Synthetic division ex. divide 3x3 4x + 3 by (x + 1), using synthetic division. 3x- 4x + 3 is equal to 3x+ 0x- 4x + 3
http://library.thinkquest.org/10030/8syndiv.htm

Extractions: Index Education Need a primer on math, science, technology, education, or art, or just looking for a new Internet search engine? This catch-all site covers them all. Maybe you're doing your homework and need to quickly look up a basic term? Here you'll find a brief yet concise reference source for all these topics. And if you're still not sure what's here, use the search feature to scan the entire site for your topic. Visit Site 1997 ThinkQuest Internet Challenge Languages English Students Suranthe H Oakhill College, Sydney, Australia Peter Oakhill College, Castle Hill, Sydney, Australia Coaches Tina Oakhill College, Castle Hill, Sydney, Australia Tina Oakhill College, Castle Hill, Sydney, Australia Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy
Learn.co.uk - Learning Resources For The National Curriculum, Online Lessons, GC
2 + 3 2 leading coefficient of product = 3 1 x 3 3 constant term of product = 12 - 4 x 3 division of a polynomial expression by a binomial The binomial
http://www.learn.co.uk/default.asp?WCI=Unit&WCU=27254
Polynomial Long Division - Wikipedia, The Free Encyclopedia
polynomial long division. From Wikipedia, the free encyclopedia. A similar shortcutmethod exists for dividing by a quadratic or higher degree monic polynomial.
http://en.wikipedia.org/wiki/Polynomial_long_division

Extractions: Server will be down for maintenance on 2004-06-11 from about 18:00 to 18:30 UTC. In algebra polynomial long division is an algorithm similar to long division for dividing a polynomial into another polynomial of a larger degree. It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones. For any polynomials f(x) and g(x) g(x) being of lesser degree than f(x) , there exist unique polynomials q(x) and r(x) such that Synthetic division will find the quotient q(x) and remainder r(x) given a dividend f(x) and divisor g(x) . The problem is written down like this: When the problem is written, all the terms with exponents less than the largest one must be written, even if their coefficients are zero. edit Find: The problem is written like this (note that the x term is included): 1. Divide the first term of the dividend by the first term of the divisor. Place the result above the bar ( x ÷ x = x 2. Multiply the divisor by the term you just wrote. Write the result under the first two terms of the dividend ( x * (x-3) = x 3. Subtract the second term of the result you just got from the second term of the dividend and write the result under both of them. This can be tricky at times, because of the sign. (
Polynomial Long Division - Wikipedia, The Free Encyclopedia
polynomial long division. (Redirected from Synthetic division). A similar shortcutmethod exists for dividing by a quadratic or higher degree monic polynomial.
http://en.wikipedia.org/wiki/Synthetic_division

Extractions: (Redirected from Synthetic division Server will be down for maintenance on 2004-06-11 from about 18:00 to 18:30 UTC. In algebra polynomial long division is an algorithm similar to long division for dividing a polynomial into another polynomial of a larger degree. It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones. For any polynomials f(x) and g(x) g(x) being of lesser degree than f(x) , there exist unique polynomials q(x) and r(x) such that Synthetic division will find the quotient q(x) and remainder r(x) given a dividend f(x) and divisor g(x) . The problem is written down like this: When the problem is written, all the terms with exponents less than the largest one must be written, even if their coefficients are zero. edit Find: The problem is written like this (note that the x term is included): 1. Divide the first term of the dividend by the first term of the divisor. Place the result above the bar ( x ÷ x = x 2. Multiply the divisor by the term you just wrote. Write the result under the first two terms of the dividend (
Mathwords: Polynomial Long Division
V. W. X. Y. Z. A to Z. polynomial Long division. A method used to divide polynomials.polynomial long division is essentially the same as long division for numbers.
http://www.mathwords.com/p/polynomial_long_division.htm

Extractions: G o o g ... e www mathwords Polynomial Long Division A method used to divide polynomials . Polynomial long division is essentially the same as long division for numbers. This method can be used to write an improper rational expression as the sum of a polynomial and a proper rational expression See also Synthetic division this page updated 7-jun-04
Beginning Algebra Tutorial On Division Of Polynomials
Divide a polynomial by a polynomial using long division. Introduction. Divide polynomialpolynomial. Using Long division. Step 1 Set up the long division.
http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut30_di

Extractions: In this tutorial we revisit something that you may not have seen since grade school: long division. I hope that your experiences with long division have been better than Nerwin's in this comic. In this tutorial we are dividing polynomials, but it follows the same steps and thought process as when you apply it numbers. Let's forge ahead.
Division Of Polynomials
Lesson Page, Math A. Steps for Dividing a polynomial by a Monomial. 1. Divide eachterm of the polynomial by the monomial. a) Divide numbers b) Subtract exponents.
http://regentsprep.org/Regents/math/divpoly/Ldiv.htm
Division Of A Polynomial By A Monomial
division OF A polynomial BY A MONOMIAL. division, like multiplication,may be distributive. division OF A polynomial BY A polynomial.
http://www.tpub.com/math1/10g.htm

Extractions: Synthetic Division DIVISION OF A POLYNOMIAL BY A MONOMIAL Division, like multiplication, may be distributive. Consider, for example, the problem 2, which may be solved by adding the numbers within the parentheses and then dividing the total by 2. Thus, Now notice that the problem may also-be solved distributively. CAUTION: Do not confuse problems of the type just described with another type which is similar in appearance but not in final result. For example, in a problem such as 2 the beginner is tempted to divide 2 successively by 4, then 6, and then -2, as follows: Notice that we have canceled the "equals" sign, because 2 + 8 is obviously not equal to 1/2 + 2/6. - 1. The distributive method applies only in those cases in which several different numerators are to be used with the same denominator When literal numbers are present in an expression, the distributive method must be used, as in the following two problems: Quite often this division may be done mentally, and the intermediate steps need not be

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