How to resolve the algorithm Display a linear combination step by step in the FreeBASIC programming language

Published on 12 May 2024 09:40 PM
#Freebasic

How to resolve the algorithm Display a linear combination step by step in the FreeBASIC programming language

Table of Contents

Problem Statement

Display a finite linear combination in an infinite vector basis

(

e

1

,

e

2

, … )

{\displaystyle (e_{1},e_{2},\ldots )}

. Write a function that, when given a finite list of scalars

(

α

1

,

α

2

, … )

{\displaystyle (\alpha ^{1},\alpha ^{2},\ldots )}

, creates a string representing the linear combination

∑

i

α

i

e

i

{\displaystyle \sum {i}\alpha ^{i}e{i}}

in an explicit format often used in mathematics, that is: where

α

i

k

≠ 0

{\displaystyle \alpha ^{i_{k}}\neq 0}

The output must comply to the following rules:

Show here output for the following lists of scalars:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Display a linear combination step by step in the FreeBASIC programming language

Source code in the freebasic programming language

Dim scalars(1 To 10, 1 To 4) As Integer => {{1,  2,  3}, {0,  1,  2,  3}, _
{1,  0,  3,  4}, {1,  2,  0}, {0,  0,  0}, {0}, {1,  1,  1}, {-1, -1, -1}, _
{-1, -2,  0, -3}, {-1}}

For n As Integer = 1 To Ubound(scalars)
    Dim As String cadena = ""
    Dim As Integer scalar
    For m As Integer = 1 To Ubound(scalars,2)
        scalar = scalars(n, m)
        If scalar <> 0 Then
            If scalar = 1 Then
                cadena &= "+e" & m
            Elseif scalar = -1 Then
                cadena &= "-e" & m
            Else
                If scalar > 0 Then
                    cadena &= Chr(43) & scalar & "*e" & m
                Else
                    cadena &= scalar & "*e" & m
                End If
            End If
        End If   
    Next m
    If cadena = "" Then cadena = "0"
    If Left(cadena, 1) = "+" Then cadena = Right(cadena, Len(cadena)-1)
    Print cadena
Next n
Sleep

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