How to resolve the algorithm Polynomial long division step by step in the Ursala programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Polynomial long division step by step in the Ursala programming language

Table of Contents

Problem Statement

Let us suppose a polynomial is represented by a vector,

x

{\displaystyle x}

(i.e., an ordered collection of coefficients) so that the

i

{\displaystyle i}

th element keeps the coefficient of

x

i

{\displaystyle x^{i}}

, and the multiplication by a monomial is a shift of the vector's elements "towards right" (injecting ones from left) followed by a multiplication of each element by the coefficient of the monomial. Then a pseudocode for the polynomial long division using the conventions described above could be: Note: vector * scalar multiplies each element of the vector by the scalar; vectorA - vectorB subtracts each element of the vectorB from the element of the vectorA with "the same index". The vectors in the pseudocode are zero-based.

Example for clarification

This example is from Wikipedia, but changed to show how the given pseudocode works.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Polynomial long division step by step in the Ursala programming language

Source code in the ursala programming language

#import std
#import flo

polydiv =

zeroid~-l~~; leql?rlX\~&NlX ^H\(@rNrNSPXlHDlS |\ :/0.) @NlX //=> ?(
   @lrrPX ==!| zipp0.; @x not zeroid+ ==@h->hr ~&t,
   (^lryPX/~&lrrl2C minus^*p/~&rrr times*lrlPD)^/div@bzPrrPlXO ~&,
   @r ^|\~& ~&i&& :/0.)

#cast %eLW

example = polydiv(<-42.,0.,-12.,1.>,<-3.,1.,0.,0.>)

  

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