Geometry.Net - Basic_P: Polynomial Division

Polynomial Division 3
? ( ? ) ( polynomial division Version 3 ). ? ( ? ) ( polynomial division Version 1 ).
http://lpl.hkcampus.net/~lpl-wwk/Casio/Polynomial Division 3.htm
An Optimum Real-Time Systolic Polynomial Division AIgorithm
IPSJ JOURNAL Abstract Vol.27 No.03 011. An Optimum Real-Time Systolic PolynomialDivision AIgorithm. UMEO HIROSHI ?1 , SUGIOKA TOSHIYUKI ?2.
http://www.ipsj.or.jp/members/Journal/Eng/2703/article011.html
Long Polynomial Division
Problem Divide, x 4 2x 3 + 8x - 14 x 2 - 3. Set up the long division. Noticethe 0's put in as place holders for missing powers of x. x 2 =, x 4 x 2, .
http://www.sci.wsu.edu/~kentler/Fall97_101/Chapter5/lpd_3.html
Long Polynomial Division
Problem Divide, x 2 + 5x + 9 x + 2. Set up the long division. x =,x 2 x, . Choose x since x · x matches x 2 . x 2 + 2x = x(x + 2).
http://www.sci.wsu.edu/~kentler/Fall97_101/Chapter5/lpd_1.html
Polynomial Division
First Previous Next Last Index Home Text. Slide 18 of 26.
http://www.cs.berkeley.edu/~kfall/EE122/lec06/sld018.htm
Polynomial Division
polynomial division. 10011010000. 1101. 1. 1101. 1001. 1101.1. 1000. 1101. 1011. 1101. 1. 1. 1. 0. 0. 1. 1100. 1101.1000. 1101. 101.
http://www.cs.berkeley.edu/~kfall/EE122/lec06/tsld018.htm
Software: Polynomial Division
polynomial division. Home » Software Information Name, polynomial division(Download). Type, Software. Calculator, TI85. Version, 1.1.
http://endeavor.ticalc.org/objects/96.html
Software: Polynomial Division
polynomial division. Home » Software Information Name, polynomial division(Download). Type, Software. Calculator, TI85. Version, 1.0.
http://endeavor.ticalc.org/objects/340.html
4.3 Polynomial Division
4.3 polynomial division Topics polynomial division is a lot like integer division! Polynomialdivision is a lot like integer division! Integer division
http://www.austin.cc.tx.us/~powens/ ColAlg/Html/04-3/04-3.html
Polynomial Division
polynomial division. Review of Long Division. Example Use long division to calculate.495/12. and will write the steps for this process without using any numbers.
http://www.ltcconline.net/greenl/courses/103a/polynomials/polydiv.htm
Polynomial Division
polynomial division. I. Return Midterm II. II. Homework. II. Reviewof Long Division. The class will use long division to find. 495/12.
http://www.ltcconline.net/greenl/courses/103a/premid3/polydiv.htm

Extractions: Polynomial Division I. Return Midterm II II. Homework II. Review of Long Division The class will use long division to find and will write how to divide without using any numbers. We see that we follow the steps: 1) Write it in long division form. 2) Determine what we need to multiply the quotient by to get the first term. 3) Place that number on top of the long division sign. 4) Multiply that number by the quotient and place the product below. 5) Subtract 6) Repeat the process until the degree of the difference is smaller than the degree of the quotient. 7) Write as sum of the top numbers + remainder/quotient. P(x)/D(x) = Q(x) + R(x)/D(x) (A nonsintactical version of a computer program) do multiply result by denominator and place product under the remainder; subtract product from remainder for new remainder; Write expression above the quotient line + remainder/denominator; We will do the following examples: A) (3x + 5x + 7)/(x + 1) B) (2x + x - 1)/(x III. Synthetic Division For the special case that the denominator is of the form x - r, we can use a shorthand version of polynomial division called synthetic division. Here is a step by step method for synthetic division for P(x)/(x - r):
IOLTW: Abstract: Fast Configurable Polynomial Division For Error Control Coding
Fast Configurable polynomial division for Error Control Coding Applications. Itis based on a pipeline structure for the polynomial division.
http://www.computer.org/proceedings/ioltw/1290/12900158abs.htm

Extractions: University of Metz Abstract: The motivation for this paper is the need for high levels of reability in modern telecommunication systems requiring very high data transmission rates. The search for technologicaly independent solutions, easy to implement on low cost and popular devices such as FPGA is an important issue. In this paper, we present a method to improve effectively the speed performance of the polynomial division performed in most error detecting and error correcting circuits. It is based on a pipeline structure for the polynomial division. Furthermore, the proposed solution is fully configurable, both from the static and the dynamic points of view. At synthesis stage, the parallelism level (size of the pipeline structure) and the maximal size of the polynomial divisor must both be chosen. Afterwards, the actual divisor can be chosen and changed while the circuit is running. The architecture proved to be very effective, as data rates up to 2.5 Gbits/s have been reached. Proceedings of the Seventh International On-Line Testing Workshop
Polynomials: Dividing Lesson
You do the same thing with polynomial division. Since the remainderis 7 and since the divisor is 3x + 1, then turn this into
http://www.purplemath.com/modules/polydiv.htm

Extractions: Home There are two cases for dividing polynomials: either the "division" is really just simplification and reduction of a fraction, or else you need to do long division Simplification / Reduction This is just a simplification problem, because there is only one term in the polynomial you're dividing by. And, in this case, there is a common factor in the numerator (top) and denominator (bottom), so it's easy to reduce this fraction. There are two ways of proceeding. I can split the division into two fractions, each with only one term on top, and then reduce: ...or I can factor out the common factor from the top and bottom, and then cancel off: Either way, the answer is the same: x Again, I can solve this in either of two ways: by splitting up the sum and simplifying each fraction separately: ...or by taking the common factor out front and canceling it off: Either way, the answer is the same:
Synthetic Division Lesson
Synthetic division is a shorthand, or shortcut, method of polynomial division inthe special case of dividing by a linear factor (and ONLY works in this case).
http://www.purplemath.com/modules/synthdiv.htm

Extractions: Home Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor (and ONLY works in this case). It is generally used, however, not for dividing out factors but for finding zeroes (or roots) of polynomials. If you are given, say, y x , you can factor this as y x x Then you can find the zeroes of y by setting each factor equal to zero and solving. You will find that x and x are the two zeroes of y You can, however, also work backwards from the zeroes to find the originating polynomial. For instance, if you are given that x and x are zeroes of a quadratic, then you know that x , so x is a factor, and x , so x is a factor. Therefore, you know that the quadratic must be of the form y a x x (The extra number " a " in that last sentence is in there because you don't know, when working backwards from the zeroes, which quadratic you're working toward. For any non-zero value of " a ", your quadratic will still have the same zeroes. This is a technical point; as long as you see the relationship between the zeroes and the factors, that's all you really need to know for this lesson.)
Homework: Partial Fractions: Polynomial Division [MATH*2080 Online]
open this document in MS Word format.Write the following integrand in a format suitablefor the Partial Fractions technique, by performing polynomial division
http://www.uoguelph.ca/~seanscot/Web2080/Homework/PartialFractionExamples/PolyDi

Extractions: Write the following integrand in a format suitable for the Partial Fractions technique, by performing polynomial division: First step is to multiply out the bottom: Now do polynomial division. The whole trick is to always divide the highest-degree term of the divisor (here x ) into the highest degree term of the dividend (initially x You can "avoid" polynomial division by algebraically manipulating the top as follows: As before, multiply out the bottom so you know what it looks like in "standard form": Now the trick is to continually work the top into this polynomial plus a lower-degree one. If you start with a higher-powered top like we have, you first take out as high a power of x as necessary to get the same power as the bottom: x -2x = x(x Now add and subtract from that cubic to make it the same as the bottom: = x(x - x² + x² + x - x Rearrange... = x(x - x² + x - 1 + x² - x - 1) = x(x - x² + x - 1) + x(x² - x - 1) This new top can now be manipulated in a similar way, first multiply it out to see the x x(x² - x - 1) = x - x² - x This actually isn't too far away from our bottom, it's simple now:
Polynomial- And Binary-Division
Polynomial and Binary-Division with equnarray A polynomial division writing inmathmode is possible with \underline{}, \hspace{} and use of eqnarray.
http://www.educat.hu-berlin.de/~voss/lyx/equnarray/PolDiv.phtml

Extractions: open LyX-mathbox with alt-m-d hit ctrl-enter to produce an eqnarray-environment (two lines with three columns) type in your first line, put the equal-sign in the middle-box start second line with , lyx puts by default the closing parenthesis. for it's the same; try a value for the space and so on ... With alt-M-n you'll get numbering for all lines (eqnarray!), with alt-M-N you can toogle between hide and show for numbering for some lines. A binary division looks a bit different to the polynomial division, but it's possible with eqnarray, too. You can download a LyX-Samplefile which shows all the other important math stuff, too. Or show the dvi-view with package polynom
PowerPoint Presentation - 9.4 Polynomial Division
http://www2.guhsd.net/Algebra2/Alg2Show/Chapter09/9_5FindingRationalZeros.htm
PowerPoint Presentation - 9.4 Polynomial Division
http://www2.guhsd.net/Algebra2/Alg2Show/Chapter09/9_5FindingRationalZeros_files/
DBLP: Dario Bini
20, Dario Bini, Victor Y. Pan Improved Parallel polynomial division. 19, Dario Bini,Victor Y. Pan Improved Parallel polynomial division and Its Extensions.
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 Ask others: ACM CiteSeer CSB Google ... Home Page (Link generated by HomePageSearch 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
DBLP: Victor Y. Pan
46, Dario Bini, Victor Y. Pan Improved Parallel polynomial division. 44, Dario Bini,Victor Y. Pan Improved Parallel polynomial division and Its Extensions.
http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/p/Pan:Victor_Y=.html

Extractions: List of publications from the DBLP Bibliography Server FAQ Ask others: ACM CiteSeer CSB Google ... EE Victor Y. Pan: Randomized Acceleration of Fundamental Matrix Computations. STACS 2002 EE Ioannis Z. Emiris , Victor Y. Pan: Symbolic and Numeric Methods for Exploiting Structure in Constructing Resultant Matrices. JSC 33 EE Victor Y. Pan: Univariate Polynomials: Nearly Optimal Algorithms for Numerical Factorization and Root-finding. JSC 33 EE Victor Y. Pan: Univariate polynomials: nearly optimal algorithms for factorization and rootfinding. ISSAC 2001 EE Victor Y. Pan, Yanqiang Yu : Certification of Numerical Computation of the Sign of the Determinant of a Matrix. Algorithmica 30 EE Keqin Li , Victor Y. Pan: Parallel Matrix Multiplication on a Linear Array with a Reconfigurable Pipelined Bus System. IEEE Transactions on Computers 50 Victor Y. Pan: Computation of Approximate Polynomial GCDs and an Extension. Information and Computation 167 EE Victor Y. Pan: Matrix structure, polynomial arithmetic, and erasure-resilient encoding/decoding. ISSAC 2000 EE Victor Y. Pan: A Homotopic Residual Correction Process.

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