Using Matlab: Function Name: reversePascal Inputs: 1. (double) A vector of polyn

ID: 664434 • Letter: U

Question

Using Matlab:

Function Name: reversePascal

Inputs:

1. (double) A vector of polynomial coefficients

Outputs:

(double) A vector of binomial coefficients

(double) The exponent of the binomial

Function Description:

Write a function called reversePascal that takes the coefficients to an arbitrarily long polynomial and condenses it into the form (x+1)^n, or binomial form. The function should return [1 1] as its first output, and n as its second output.

Example: The polynomial x^2 +2x +1 has coefficients [1 2 1]. It can also be written as (x+1)^2.

While there are many ways to do this problem, the recommended method outlined below involves reversing up Pascal’s Triangle. For more information about Pascal’s Triangle, go to

http://en.wikipedia.org/wiki/Pascal%27s_triangle

Recommended Method:
Each instance of the function should check if the input is already a binomial in the form [1 1]. If it is, it should return that from the function. If it is not, the function step through the polynomial left to right and subtract the previous index from the current index.

Example:

[14641] <-- subtract 0 from 1 [13641] <-- subtract 1 from 4 [13341] <-- subtract 3 from 6 [13311] <-- subtract 3 from 4 [13310] <-- subtract 1 from 1

At this point, the function should remove the zero from the end of the vector and then call itself on this new vector.

Notes:

The input polynomial will always be reducible into a binomial.

You MUST use recursion to solve the problem.

Explanation / Answer

function y = reversePascal(pol_coeff,n)
   if n==3
       fprintf('out1 => [%d %d]',pol_coeff(1),pol_coeff(3));
       fprintf('out2 => %d',pol_coeff(2));
   else
       for i=1:n
           if i==1
               pol_coeff(i)=pol_coeff(i)-0;
           else
               pol_coeff(i)=pol_coeff(i)-pol_coeff(i-1);
           end
       end
       reversePascal(pol_coeff,n-1);
   end
end

prompt='Enter no. of polynomial coefficients';
n=input(prompt)
pol_coeff = ones(1,n);
for x=1:n
prompt='Enter the polynomial coefficient'
pol_coeff(x) = input(prompt);
end
reversePascal(pol_coeff,n);

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Using Matlab: Function Name: reversePascal Inputs: 1. (double) A vector of polyn

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