Polynomial division by convolution - quotient and reminder

Division of two polynomials to get quotient and reminder using convolution matrix.

Description

Polynomial division by convolution matrix approach.

Given b(x) and a(x), and find q(x) and r(x) in
    b(x) = a(x)*q(x) + r(x)
where
 b(x) = b(0)+ ... +b(k)*x^k + ... +b(n)*x^n
 a(x) = a(0)+ ... +a(k)*x^k + ... +a(m)*x^m
 q(x) = q(0)+ ...+ q(k)*x^k + ... +q(n-m)*x^(n-m)
 r(x) = r(0)+ ...+ r(k)*x^k + ... +r(m-1)*x^(m-1)

If coefficients of b(x) and a(x) are all integers, then the entire process may involve mostly integer arithmetric operations. The roundoff errors may thus be eliminated.

This code is similar to the MATLAB's built-in function: 'deconv.m'.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Calculates inverse Z-transform by long division
This submission has inspired the following:
Polynomial division - derived form covolution

• MATLAB release: MATLAB 6.5 (R13)

[Krishna Prasad]

 

[Krishna Prasad]

This programme is not working when the coefficient of the polynomial are zeros.
e.g a(x)=x^4+1
        b(x)=x^2

[Feng Cheng Chang]

Krishia Prasad:
Please try it again. It should have worked perfectly for both polynomials b(x) and a(x) with trailing zeros.
For the example you gave: b(x)=x^4+1 and a(x)=x^2, yielding the desired results: q(x)=x^2 and r(x)=1.
>> b = [1 0 0 0 1]; a = [1 0 0];
>> [q,r,qc,rc,c] = PolyDiv(b,a)
  q = 1 0 0
  r = 1
  qc = 1 0 0
  rc = 0 1
  c = 1
Also it should be OK for b(x) with leading zero coefficients; however, not for a(x) with trailing zero coefficients.
>> b = [0 0 1 0 0 0 1 0]; a = [1 0 1 0 0];
>> [q,r,qc,rc,c] = PolyDiv(b,a)
 q = 1 0
 r = -1 0 1 0
 qc = 0 0 1 0
 rc = -1 0 1 0
 c = 1
Anyway I thank you for giving me this peculiar case to work with.
I will update the code involving any polynomials with both leading and trailing zero coefficients.
                    Feng Cheng Chang

[Zeeshan Shareef]

Thank you...
It help me alot.