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