how to do polynomial division

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faa nad
faa nad 2011-11-3
回答： Ahmed J. Abougarair 2022-11-18
hi...
i wanna do polynomial divison given numerator=x^5+x^4+x^3 and
denominator=x^3+x+1 ;remainder should be x...how to implement it in matlab..
  2 个评论
Walter Roberson
Walter Roberson 2011-11-3
Will the coefficients always be either 0 or 1 ? A binary polynomial?
faa nad
faa nad 2011-11-5
yes ,it is a binary polynomial

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回答（4 个）

Daniel Baboiu
Daniel Baboiu 2011-11-3
You have two choices: 1. Use the Symbolic Math Toolbox 2. Store all coefficients as a vector (including the coefficients which are 0), then use this representation to implement division steps as described below: http://en.wikipedia.org/wiki/Polynomial_long_division
  2 个评论
faa nad
faa nad 2011-11-5
hi..
thanks for ur reply.is there any other options for dividing the polynomial directly ?what we do in mathematics.without extracting the coefficients.
Walter Roberson
Walter Roberson 2011-11-5
In mathematics, we mentally extract the coefficients in order to do the division.

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Andrei Bobrov
Andrei Bobrov 2011-11-5
[a,b]=deconv([1 1 1 0 0 0],[1 0 1 1])
add
p1=[1 1 1 0 0 0]
p2=[1 0 1 1]
[a b] = deconv(p1,p2)
syms x
k = cellfun(@(y) y*x.^(numel(y)-1:-1:0).',{a b p2},'un',0)
k = [k{:}]
out = k(1) + k(2)/k(3)
  1 个评论
faa nad
faa nad 2011-11-5
the answer given by u works well..but my aim is to divide two polynomial expressions[1+x+x^2]/[1+x] directly.the output must be polynomial expression

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Walter Roberson
Walter Roberson 2011-11-5
As you have restricted this to symbolic expressions without ever extracting the coefficients (at least not in code you write, even if it gets done "under the hood"), then the solution is to use the MuPAD Standard Library function pdivide
I could offer a very nice and efficient calculation for polynomials up to order 52 where the coefficients are all 0 or 1, if we are allowed to extract the coefficients in the code (which you could stuff in to a subroutine and never look at again), but I gather that efficiency and simplicity are not important for your purposes.
  5 个评论
显示 3更早的评论
Walter Roberson
Walter Roberson 2011-11-6
Do you have the symbolic toolbox installed and licensed? If not, then you cannot do what you are asking for, as only the symbolic toolbox hides extracting the coefficients of polynomials.
Maria Maximina
Maria Maximina 2014-2-21
hi! o have one question for you! i know it is long time ago.. but anyway.. jajaja if u do that operation that you suggested, and you get a vector like:
[a,b,polinom]
what do actually a and b mean??? thanks!

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Ahmed J. Abougarair
Ahmed J. Abougarair 2022-11-18
syms x y
p = x^3 - x*y^2 + 1;
d = x + y;
[r,q] = polynomialReduce(p,d)

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