Display a linear combination
- Task
Display a finite linear combination in an infinite vector basis .
Write a function that, when given a finite list of scalars ,
creates a string representing the linear combination in an explicit format often used in mathematics, that is:
where
The output must comply to the following rules:
- don't show null terms, unless the whole combination is null.
- e(1) is fine, e(1) + 0*e(3) or e(1) + 0 is wrong.
- don't show scalars when they are equal to one or minus one.
- e(3) is fine, 1*e(3) is wrong.
- don't prefix by a minus sign if it follows a preceding term. Instead you use subtraction.
- e(4) - e(5) is fine, e(4) + -e(5) is wrong.
Show here output for the following lists of scalars:
1) 1, 2, 3 2) 0, 1, 2, 3 3) 1, 0, 3, 4 4) 1, 2, 0 5) 0, 0, 0 6) 0 7) 1, 1, 1 8) -1, -1, -1 9) -1, -2, 0, -3 10) -1
11l
<lang 11l>F linear(x)
V a = enumerate(x).filter2((i, v) -> v != 0).map2((i, v) -> ‘#.e(#.)’.format(I v == -1 {‘-’} E I v == 1 {‘’} E String(v)‘*’, i + 1))
R (I !a.empty {a} E [String(‘0’)]).join(‘ + ’).replace(‘ + -’, ‘ - ’)
L(x) [[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]]
print(linear(x))</lang>
- Output:
e(1) + 2*e(2) + 3*e(3) e(2) + 2*e(3) + 3*e(4) e(1) + 3*e(3) + 4*e(4) e(1) + 2*e(2) 0 0 e(1) + e(2) + e(3) -e(1) - e(2) - e(3) -e(1) - 2*e(2) + 3*e(4) -e(1)
C
Accepts vector coefficients from the command line, prints usage syntax if invoked with no arguments. This implementation can handle floating point values but displays integer values as integers. All test case results shown with invocation. A multiplication sign is not shown between a coefficient and the unit vector when a vector is written out by hand ( i.e. human readable) and is thus not shown here as well. <lang C>
- include<stdlib.h>
- include<stdio.h>
- include<math.h> /*Optional, but better if included as fabs, labs and abs functions are being used. */
int main(int argC, char* argV[]) {
int i,zeroCount= 0,firstNonZero = -1; double* vector;
if(argC == 1){ printf("Usage : %s <Vector component coefficients seperated by single space>",argV[0]); }
else{
printf("Vector for ["); for(i=1;i<argC;i++){ printf("%s,",argV[i]); } printf("\b] -> ");
vector = (double*)malloc((argC-1)*sizeof(double));
for(i=1;i<=argC;i++){ vector[i-1] = atof(argV[i]); if(vector[i-1]==0.0) zeroCount++; if(vector[i-1]!=0.0 && firstNonZero==-1) firstNonZero = i-1; }
if(zeroCount == argC){ printf("0"); }
else{ for(i=0;i<argC;i++){ if(i==firstNonZero && vector[i]==1) printf("e%d ",i+1); else if(i==firstNonZero && vector[i]==-1) printf("- e%d ",i+1); else if(i==firstNonZero && vector[i]<0 && fabs(vector[i])-abs(vector[i])>0.0) printf("- %lf e%d ",fabs(vector[i]),i+1); else if(i==firstNonZero && vector[i]<0 && fabs(vector[i])-abs(vector[i])==0.0) printf("- %ld e%d ",labs(vector[i]),i+1); else if(i==firstNonZero && vector[i]>0 && fabs(vector[i])-abs(vector[i])>0.0) printf("%lf e%d ",vector[i],i+1); else if(i==firstNonZero && vector[i]>0 && fabs(vector[i])-abs(vector[i])==0.0) printf("%ld e%d ",vector[i],i+1); else if(fabs(vector[i])==1.0 && i!=0) printf("%c e%d ",(vector[i]==-1)?'-':'+',i+1); else if(i!=0 && vector[i]!=0 && fabs(vector[i])-abs(vector[i])>0.0) printf("%c %lf e%d ",(vector[i]<0)?'-':'+',fabs(vector[i]),i+1); else if(i!=0 && vector[i]!=0 && fabs(vector[i])-abs(vector[i])==0.0) printf("%c %ld e%d ",(vector[i]<0)?'-':'+',labs(vector[i]),i+1); } } }
free(vector);
return 0; } </lang>
- Output:
C:\rossetaCode>vectorDisplay.exe 1 2 3 Vector for [1,2,3] -> e1 + 2 e2 + 3 e3 C:\rossetaCode>vectorDisplay.exe 0 0 0 Vector for [0,0,0] -> 0 C:\rossetaCode>vectorDisplay.exe 0 1 2 3 Vector for [0,1,2,3] -> e2 + 2 e3 + 3 e4 C:\rossetaCode>vectorDisplay.exe 1 0 3 4 Vector for [1,0,3,4] -> e1 + 3 e3 + 4 e4 C:\rossetaCode>vectorDisplay.exe 1 2 0 Vector for [1,2,0] -> e1 + 2 e2 C:\rossetaCode>vectorDisplay.exe 0 0 0 Vector for [0,0,0] -> 0 C:\rossetaCode>vectorDisplay.exe 0 Vector for [0] -> 0 C:\rossetaCode>vectorDisplay.exe 1 1 1 Vector for [1,1,1] -> e1 + e2 + e3 C:\rossetaCode>vectorDisplay.exe -1 -1 -1 Vector for [-1,-1,-1] -> - e1 - e2 - e3 C:\rossetaCode>vectorDisplay.exe -1 -2 0 -3 Vector for [-1,-2,0,-3] -> - e1 - 2 e2 - 3 e4 C:\rossetaCode>vectorDisplay.exe -1 Vector for [-1] -> - e1
C++
<lang cpp>#include <iomanip>
- include <iostream>
- include <sstream>
- include <vector>
template<typename T> std::ostream& operator<<(std::ostream& os, const std::vector<T>& v) {
auto it = v.cbegin(); auto end = v.cend();
os << '[';
if (it != end) {
os << *it;
it = std::next(it);
}
while (it != end) {
os << ", " << *it;
it = std::next(it);
}
return os << ']';
}
std::ostream& operator<<(std::ostream& os, const std::string& s) {
return os << s.c_str();
}
std::string linearCombo(const std::vector<int>& c) {
std::stringstream ss;
for (size_t i = 0; i < c.size(); i++) {
int n = c[i];
if (n < 0) {
if (ss.tellp() == 0) {
ss << '-';
} else {
ss << " - ";
}
} else if (n > 0) {
if (ss.tellp() != 0) {
ss << " + ";
}
} else {
continue;
}
int av = abs(n);
if (av != 1) {
ss << av << '*';
}
ss << "e(" << i + 1 << ')';
}
if (ss.tellp() == 0) {
return "0";
}
return ss.str();
}
int main() {
using namespace std;
vector<vector<int>> combos{
{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 (auto& c : combos) {
stringstream ss;
ss << c;
cout << setw(15) << ss.str() << " -> ";
cout << linearCombo(c) << '\n';
}
return 0;
}</lang>
- Output:
[1, 2, 3] -> e(1) + 2*e(2) + 3*e(3)
[0, 1, 2, 3] -> e(2) + 2*e(3) + 3*e(4)
[1, 0, 3, 4] -> e(1) + 3*e(3) + 4*e(4)
[1, 2, 0] -> e(1) + 2*e(2)
[0, 0, 0] -> 0
[0] -> 0
[1, 1, 1] -> e(1) + e(2) + e(3)
[-1, -1, -1] -> -e(1) - e(2) - e(3)
[-1, -2, 0, -3] -> -e(1) - 2*e(2) - 3*e(4)
[-1] -> -e(1)
C#
<lang csharp>using System; using System.Collections.Generic; using System.Text;
namespace DisplayLinearCombination {
class Program {
static string LinearCombo(List<int> c) {
StringBuilder sb = new StringBuilder();
for (int i = 0; i < c.Count; i++) {
int n = c[i];
if (n < 0) {
if (sb.Length == 0) {
sb.Append('-');
} else {
sb.Append(" - ");
}
} else if (n > 0) {
if (sb.Length != 0) {
sb.Append(" + ");
}
} else {
continue;
}
int av = Math.Abs(n);
if (av != 1) {
sb.AppendFormat("{0}*", av);
}
sb.AppendFormat("e({0})", i + 1);
}
if (sb.Length == 0) {
sb.Append('0');
}
return sb.ToString();
}
static void Main(string[] args) {
List<List<int>> combos = new List<List<int>>{
new List<int> { 1, 2, 3},
new List<int> { 0, 1, 2, 3},
new List<int> { 1, 0, 3, 4},
new List<int> { 1, 2, 0},
new List<int> { 0, 0, 0},
new List<int> { 0},
new List<int> { 1, 1, 1},
new List<int> { -1, -1, -1},
new List<int> { -1, -2, 0, -3},
new List<int> { -1},
};
foreach (List<int> c in combos) {
var arr = "[" + string.Join(", ", c) + "]";
Console.WriteLine("{0,15} -> {1}", arr, LinearCombo(c));
}
}
}
}</lang>
- Output:
[1, 2, 3] -> e(1) + 2*e(2) + 3*e(3)
[0, 1, 2, 3] -> e(2) + 2*e(3) + 3*e(4)
[1, 0, 3, 4] -> e(1) + 3*e(3) + 4*e(4)
[1, 2, 0] -> e(1) + 2*e(2)
[0, 0, 0] -> 0
[0] -> 0
[1, 1, 1] -> e(1) + e(2) + e(3)
[-1, -1, -1] -> -e(1) - e(2) - e(3)
[-1, -2, 0, -3] -> -e(1) - 2*e(2) - 3*e(4)
[-1] -> -e(1)
D
<lang D>import std.array; import std.conv; import std.format; import std.math; import std.stdio;
string linearCombo(int[] c) {
auto sb = appender!string;
foreach (i, n; c) {
if (n==0) continue;
string op;
if (n < 0) {
if (sb.data.empty) {
op = "-";
} else {
op = " - ";
}
} else if (n > 0) {
if (!sb.data.empty) {
op = " + ";
}
}
auto av = abs(n);
string coeff;
if (av != 1) {
coeff = to!string(av) ~ "*";
}
sb.formattedWrite("%s%se(%d)", op, coeff, i+1);
}
if (sb.data.empty) {
return "0";
}
return sb.data;
}
void main() {
auto combos = [
[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],
];
foreach (c; combos) {
auto arr = c.format!"%s";
writefln("%-15s -> %s", arr, linearCombo(c));
}
}</lang>
- Output:
[1, 2, 3] -> e(1) + 2*e(2) + 3*e(3) [0, 1, 2, 3] -> e(2) + 2*e(3) + 3*e(4) [1, 0, 3, 4] -> e(1) + 3*e(3) + 4*e(4) [1, 2, 0] -> e(1) + 2*e(2) [0, 0, 0] -> 0 [0] -> 0 [1, 1, 1] -> e(1) + e(2) + e(3) [-1, -1, -1] -> -e(1) - e(2) - e(3) [-1, -2, 0, -3] -> -e(1) - 2*e(2) - 3*e(4) [-1] -> -e(1)
EchoLisp
<lang scheme>
- build an html string from list of coeffs
(define (linear->html coeffs)
(define plus #f)
(or*
(for/fold (html "") ((a coeffs) (i (in-naturals 1)))
(unless (zero? a)
(set! plus (if plus "+" "")))
(string-append html
(cond ((= a 1) (format "%a e%d " plus i)) ((= a -1) (format "- e%d " i)) ((> a 0) (format "%a %d*e%d " plus a i)) ((< a 0) (format "- %d*e%d " (abs a) i)) (else ""))))
"0"))
(define linears '((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)))
(define (task linears)
(html-print ;; send string to stdout
(for/string ((linear linears))
(format "%a -> %a
" linear (linear->html linear)))))
</lang>
- Output:
(1 2 3) -> e1 + 2*e2 + 3*e3
(0 1 2 3) -> e2 + 2*e3 + 3*e4
(1 0 3 4) -> e1 + 3*e3 + 4*e4
(1 2 0) -> e1 + 2*e2
(0 0 0) -> 0
(0) -> 0
(1 1 1) -> e1 + e2 + e3
(-1 -1 -1) -> - e1 - e2 - e3
(-1 -2 0 -3) -> - e1 - 2*e2 - 3*e4
(-1) -> - e1
Elixir
<lang elixir>defmodule Linear_combination do
def display(coeff) do
Enum.with_index(coeff)
|> Enum.map_join(fn {n,i} ->
{m,s} = if n<0, do: {-n,"-"}, else: {n,"+"}
case {m,i} do
{0,_} -> ""
{1,i} -> "#{s}e(#{i+1})"
{n,i} -> "#{s}#{n}*e(#{i+1})"
end
end)
|> String.trim_leading("+")
|> case do
"" -> IO.puts "0"
str -> IO.puts str
end
end
end
coeffs =
[ [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] ]
Enum.each(coeffs, &Linear_combination.display(&1))</lang>
- Output:
e(1)+2*e(2)+3*e(3) e(2)+2*e(3)+3*e(4) e(1)+3*e(3)+4*e(4) e(1)+2*e(2) 0 0 e(1)+e(2)+e(3) -e(1)-e(2)-e(3) -e(1)-2*e(2)-3*e(4) -e(1)
F#
The function
<lang fsharp> // Display a linear combination. Nigel Galloway: March 28th., 2018 let fN g =
let rec fG n g=match g with
|0::g -> fG (n+1) g
|1::g -> printf "+e(%d)" n; fG (n+1) g
|(-1)::g -> printf "-e(%d)" n; fG (n+1) g
|i::g -> printf "%+de(%d)" i n; fG (n+1) g
|_ -> printfn ""
let rec fN n g=match g with
|0::g -> fN (n+1) g
|1::g -> printf "e(%d)" n; fG (n+1) g
|(-1)::g -> printf "-e(%d)" n; fG (n+1) g
|i::g -> printf "%de(%d)" i n; fG (n+1) g
|_ -> printfn "0"
fN 1 g
</lang>
The Task
<lang fsharp> fN [1;2;3] </lang>
- Output:
e(1)+2e(2)+3e(3)
<lang fsharp> fN [0;1;2;3] </lang>
- Output:
e(2)+2e(3)+3e(4)
<lang fsharp> fN[1;0;3;4] </lang>
- Output:
e(1)+3e(3)+4e(4)
<lang fsharp> fN[1;2;0] </lang>
- Output:
e(1)+2e(2)
<lang fsharp> fN[0;0;0] </lang>
- Output:
0
<lang fsharp> fN[0] </lang>
- Output:
0
<lang fsharp> fN[1;1;1] </lang>
- Output:
e(1)+e(2)+e(3)
<lang fsharp> fN[-1;-1;-1] </lang>
- Output:
-e(1)-e(2)-e(3)
<lang fsharp> fN[-1;-2;0;-3] </lang>
- Output:
-e(1)-2e(2)-3e(4)
<lang fsharp> fN[1] </lang>
- Output:
e(1)
Factor
<lang factor>USING: formatting kernel match math pair-rocket regexp sequences ;
MATCH-VARS: ?a ?b ;
- choose-term ( coeff i -- str )
1 + { } 2sequence {
{ 0 _ } => [ "" ]
{ 1 ?a } => [ ?a "e(%d)" sprintf ]
{ -1 ?a } => [ ?a "-e(%d)" sprintf ]
{ ?a ?b } => [ ?a ?b "%d*e(%d)" sprintf ]
} match-cond ;
- linear-combo ( seq -- str )
[ choose-term ] map-index harvest " + " join R/ \+ -/ "- " re-replace [ "0" ] when-empty ;
{ { 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 } }
[ dup linear-combo "%-14u -> %s\n" printf ] each</lang>
- Output:
{ 1 2 3 } -> e(1) + 2*e(2) + 3*e(3)
{ 0 1 2 3 } -> e(2) + 2*e(3) + 3*e(4)
{ 1 0 3 4 } -> e(1) + 3*e(3) + 4*e(4)
{ 1 2 0 } -> e(1) + 2*e(2)
{ 0 0 0 } -> 0
{ 0 } -> 0
{ 1 1 1 } -> e(1) + e(2) + e(3)
{ -1 -1 -1 } -> -e(1) - e(2) - e(3)
{ -1 -2 0 -3 } -> -e(1) - 2*e(2) - 3*e(4)
{ -1 } -> -e(1)
Go
<lang go>package main
import (
"fmt" "strings"
)
func linearCombo(c []int) string {
var sb strings.Builder
for i, n := range c {
if n == 0 {
continue
}
var op string
switch {
case n < 0 && sb.Len() == 0:
op = "-"
case n < 0:
op = " - "
case n > 0 && sb.Len() == 0:
op = ""
default:
op = " + "
}
av := n
if av < 0 {
av = -av
}
coeff := fmt.Sprintf("%d*", av)
if av == 1 {
coeff = ""
}
sb.WriteString(fmt.Sprintf("%s%se(%d)", op, coeff, i+1))
}
if sb.Len() == 0 {
return "0"
} else {
return sb.String()
}
}
func main() {
combos := [][]int{
{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 _, c := range combos {
t := strings.Replace(fmt.Sprint(c), " ", ", ", -1)
fmt.Printf("%-15s -> %s\n", t, linearCombo(c))
}
}</lang>
- Output:
[1, 2, 3] -> e(1) + 2*e(2) + 3*e(3) [0, 1, 2, 3] -> e(2) + 2*e(3) + 3*e(4) [1, 0, 3, 4] -> e(1) + 3*e(3) + 4*e(4) [1, 2, 0] -> e(1) + 2*e(2) [0, 0, 0] -> 0 [0] -> 0 [1, 1, 1] -> e(1) + e(2) + e(3) [-1, -1, -1] -> -e(1) - e(2) - e(3) [-1, -2, 0, -3] -> -e(1) - 2*e(2) - 3*e(4) [-1] -> -e(1)
J
Implementation:
<lang J>fourbanger=:3 :0
e=. ('e(',')',~])@":&.> 1+i.#y
firstpos=. 0< {.y-.0
if. */0=y do. '0' else. firstpos}.;y gluedto e end.
)
gluedto=:4 :0 each
pfx=. '+-' {~ x<0
select. |x
case. 0 do.
case. 1 do. pfx,y
case. do. pfx,(":|x),'*',y
end.
)</lang>
Example use:
<lang J> fourbanger 1 2 3 e(1)+2*e(2)+3*e(3)
fourbanger 0 1 2 3
e(2)+2*e(3)+3*e(4)
fourbanger 1 0 3 4
e(1)+3*e(3)+4*e(4)
fourbanger 0 0 0
0
fourbanger 0
0
fourbanger 1 1 1
e(1)+e(2)+e(3)
fourbanger _1 _1 _1
-e(1)-e(2)-e(3)
fourbanger _1 _2 0 _3
-e(1)-2*e(2)-3*e(4)
fourbanger _1
-e(1)</lang>
Java
<lang Java>import java.util.Arrays;
public class LinearCombination {
private static String linearCombo(int[] c) {
StringBuilder sb = new StringBuilder();
for (int i = 0; i < c.length; ++i) {
if (c[i] == 0) continue;
String op;
if (c[i] < 0 && sb.length() == 0) {
op = "-";
} else if (c[i] < 0) {
op = " - ";
} else if (c[i] > 0 && sb.length() == 0) {
op = "";
} else {
op = " + ";
}
int av = Math.abs(c[i]);
String coeff = av == 1 ? "" : "" + av + "*";
sb.append(op).append(coeff).append("e(").append(i + 1).append(')');
}
if (sb.length() == 0) {
return "0";
}
return sb.toString();
}
public static void main(String[] args) {
int[][] combos = new int[][]{
new int[]{1, 2, 3},
new int[]{0, 1, 2, 3},
new int[]{1, 0, 3, 4},
new int[]{1, 2, 0},
new int[]{0, 0, 0},
new int[]{0},
new int[]{1, 1, 1},
new int[]{-1, -1, -1},
new int[]{-1, -2, 0, -3},
new int[]{-1},
};
for (int[] c : combos) {
System.out.printf("%-15s -> %s\n", Arrays.toString(c), linearCombo(c));
}
}
}</lang>
- Output:
[1, 2, 3] -> e(1) + 2*e(2) + 3*e(3) [0, 1, 2, 3] -> e(2) + 2*e(3) + 3*e(4) [1, 0, 3, 4] -> e(1) + 3*e(3) + 4*e(4) [1, 2, 0] -> e(1) + 2*e(2) [0, 0, 0] -> 0 [0] -> 0 [1, 1, 1] -> e(1) + e(2) + e(3) [-1, -1, -1] -> -e(1) - e(2) - e(3) [-1, -2, 0, -3] -> -e(1) - 2*e(2) - 3*e(4) [-1] -> -e(1)
Julia
<lang julia># v0.6
linearcombination(coef::Array) = join(collect("$c * e($i)" for (i, c) in enumerate(coef) if c != 0), " + ")
for c in [[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]]
@printf("%20s -> %s\n", c, linearcombination(c))
end</lang>
- Output:
[1, 2, 3] -> 1 * e(1) + 2 * e(2) + 3 * e(3)
[0, 1, 2, 3] -> 1 * e(2) + 2 * e(3) + 3 * e(4)
[1, 0, 3, 4] -> 1 * e(1) + 3 * e(3) + 4 * e(4)
[1, 2, 0] -> 1 * e(1) + 2 * e(2)
[0, 0, 0] ->
[0] ->
[1, 1, 1] -> 1 * e(1) + 1 * e(2) + 1 * e(3)
[-1, -1, -1] -> -1 * e(1) + -1 * e(2) + -1 * e(3)
[-1, -2, 0, -3] -> -1 * e(1) + -2 * e(2) + -3 * e(4)
[-1] -> -1 * e(1)
Kotlin
<lang scala>// version 1.1.2
fun linearCombo(c: IntArray): String {
val sb = StringBuilder()
for ((i, n) in c.withIndex()) {
if (n == 0) continue
val op = when {
n < 0 && sb.isEmpty() -> "-"
n < 0 -> " - "
n > 0 && sb.isEmpty() -> ""
else -> " + "
}
val av = Math.abs(n)
val coeff = if (av == 1) "" else "$av*"
sb.append("$op${coeff}e(${i + 1})")
}
return if(sb.isEmpty()) "0" else sb.toString()
}
fun main(args: Array<String>) {
val combos = arrayOf(
intArrayOf(1, 2, 3),
intArrayOf(0, 1, 2, 3),
intArrayOf(1, 0, 3, 4),
intArrayOf(1, 2, 0),
intArrayOf(0, 0, 0),
intArrayOf(0),
intArrayOf(1, 1, 1),
intArrayOf(-1, -1, -1),
intArrayOf(-1, -2, 0, -3),
intArrayOf(-1)
)
for (c in combos) {
println("${c.contentToString().padEnd(15)} -> ${linearCombo(c)}")
}
}</lang>
- Output:
[1, 2, 3] -> e(1) + 2*e(2) + 3*e(3) [0, 1, 2, 3] -> e(2) + 2*e(3) + 3*e(4) [1, 0, 3, 4] -> e(1) + 3*e(3) + 4*e(4) [1, 2, 0] -> e(1) + 2*e(2) [0, 0, 0] -> 0 [0] -> 0 [1, 1, 1] -> e(1) + e(2) + e(3) [-1, -1, -1] -> -e(1) - e(2) - e(3) [-1, -2, 0, -3] -> -e(1) - 2*e(2) - 3*e(4) [-1] -> -e(1)
Modula-2
<lang modula2>MODULE Linear; FROM FormatString IMPORT FormatString; FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
PROCEDURE WriteInt(n : INTEGER); VAR buf : ARRAY[0..15] OF CHAR; BEGIN
FormatString("%i", buf, n);
WriteString(buf)
END WriteInt;
PROCEDURE WriteLinear(c : ARRAY OF INTEGER); VAR
buf : ARRAY[0..15] OF CHAR; i,j : CARDINAL; b : BOOLEAN;
BEGIN
b := TRUE; j := 0;
FOR i:=0 TO HIGH(c) DO
IF c[i]=0 THEN CONTINUE END;
IF c[i]<0 THEN
IF b THEN WriteString("-")
ELSE WriteString(" - ") END;
ELSIF c[i]>0 THEN
IF NOT b THEN WriteString(" + ") END;
END;
IF c[i] > 1 THEN
WriteInt(c[i]);
WriteString("*")
ELSIF c[i] < -1 THEN
WriteInt(-c[i]);
WriteString("*")
END;
FormatString("e(%i)", buf, i+1);
WriteString(buf);
b := FALSE;
INC(j)
END;
IF j=0 THEN WriteString("0") END;
WriteLn
END WriteLinear;
TYPE
Array1 = ARRAY[0..0] OF INTEGER; Array3 = ARRAY[0..2] OF INTEGER; Array4 = ARRAY[0..3] OF INTEGER;
BEGIN
WriteLinear(Array3{1,2,3});
WriteLinear(Array4{0,1,2,3});
WriteLinear(Array4{1,0,3,4});
WriteLinear(Array3{1,2,0});
WriteLinear(Array3{0,0,0});
WriteLinear(Array1{0});
WriteLinear(Array3{1,1,1});
WriteLinear(Array3{-1,-1,-1});
WriteLinear(Array4{-1,-2,0,-3});
WriteLinear(Array1{-1});
ReadChar
END Linear.</lang>
Perl
<lang perl>sub linear_combination {
my(@coef) = @$_;
my $e;
for my $c (1..+@coef) { $e .= "$coef[$c-1]*e($c) + " if $coef[$c-1] }
$e =~ s/ \+ $//;
$e =~ s/1\*//g;
$e =~ s/\+ -/- /g;
$e // 0;
}
print linear_combination($_), "\n" for
[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 ]</lang>
- Output:
e(1) + 2*e(2) + 3*e(3) e(2) + 2*e(3) + 3*e(4) e(1) + 3*e(3) + 4*e(4) e(1) + 2*e(2) 0 0 e(1) + e(2) + e(3) -e(1) - e(2) - e(3) -e(1) - 2*e(2) - 3*e(4) -e(1)
Perl 6
<lang perl6>sub linear-combination(@coeff) {
(@coeff Z=> map { "e($_)" }, 1 .. *)
.grep(+*.key)
.map({ .key ~ '*' ~ .value })
.join(' + ')
.subst('+ -', '- ', :g)
.subst(/<|w>1\*/, , :g)
|| '0'
}
say linear-combination($_) for [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 ]
- </lang>
- Output:
e(1) + 2*e(2) + 3*e(3) e(2) + 2*e(3) + 3*e(4) e(1) + 3*e(3) + 4*e(4) e(1) + 2*e(2) 0 0 e(1) + e(2) + e(3) -e(1) - e(2) - e(3) -e(1) - 2*e(2) - 3*e(4) -e(1)
Phix
<lang Phix>function linear_combination(sequence f)
string res = ""
for e=1 to length(f) do
integer fe = f[e]
if fe!=0 then
if fe=1 then
if length(res) then res &= "+" end if
elsif fe=-1 then
res &= "-"
elsif fe>0 and length(res) then
res &= sprintf("+%d*",fe)
else
res &= sprintf("%d*",fe)
end if
res &= sprintf("e(%d)",e)
end if
end for
if res="" then res = "0" end if
return res
end function
constant tests = {{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 i=1 to length(tests) do
sequence ti = tests[i]
printf(1,"%12s -> %s\n",{sprint(ti), linear_combination(ti)})
end for</lang>
- Output:
{1,2,3} -> e(1)+2*e(2)+3*e(3)
{0,1,2,3} -> e(2)+2*e(3)+3*e(4)
{1,0,3,4} -> e(1)+3*e(3)+4*e(4)
{1,2,0} -> e(1)+2*e(2)
{0,0,0} -> 0
{0} -> 0
{1,1,1} -> e(1)+e(2)+e(3)
{-1,-1,-1} -> -e(1)-e(2)-e(3)
{-1,-2,0,-3} -> -e(1)-2*e(2)-3*e(4)
{-1} -> -e(1)
Python
<lang python> def linear(x):
return ' + '.join(['{}e({})'.format('-' if v == -1 else if v == 1 else str(v) + '*', i + 1)
for i, v in enumerate(x) if v] or ['0']).replace(' + -', ' - ')
list(map(lambda x: print(linear(x)), [[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]]))
</lang>
- Output:
e(1) + 2*e(2) + 3*e(3) e(2) + 2*e(3) + 3*e(4) e(1) + 3*e(3) + 4*e(4) e(1) + 2*e(2) 0 0 e(1) + e(2) + e(3) -e(1) - e(2) - e(3) -e(1) - 2*e(2) + 3*e(4) -e(1)
Racket
<lang racket>#lang racket/base (require racket/match racket/string)
(define (linear-combination->string es)
(let inr ((es es) (i 1) (rv ""))
(match* (es rv)
[((list) "") "0"]
[((list) rv) rv]
[((list (? zero?) t ...) rv)
(inr t (add1 i) rv)]
[((list n t ...) rv)
(define ±n
(match* (n rv)
;; zero is handled above
[(1 "") ""]
[(1 _) "+"]
[(-1 _) "-"]
[((? positive? n) (not "")) (format "+~a*" n)]
[(n _) (format "~a*" n)]))
(inr t (add1 i) (string-append rv ±n "e("(number->string i)")"))])))
(for-each
(compose displayln linear-combination->string) '((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)))
</lang>
- Output:
e(1)+2*e(2)+3*e(3) e(2)+2*e(3)+3*e(4) e(1)+3*e(3)+4*e(4) e(1)+2*e(2) 0 0 e(1)+e(2)+e(3) -e(1)-e(2)-e(3) -e(1)-2*e(2)-3*e(4) -e(1)
REXX
<lang rexx>/*REXX program displays a finite liner combination in an infinite vector basis. */ @.=.; @.1 = ' 1, 2, 3 '
@.2 = ' 0, 1, 2, 3 '
@.3 = ' 1, 0, 3, 4 '
@.4 = ' 1, 2, 0 '
@.5 = ' 0, 0, 0 '
@.6 = 0
@.7 = ' 1, 1, 1 '
@.8 = ' -1, -1, -1 '
@.9 = ' -1, -2, 0, -3 '
@.10 = -1
do j=1 while @.j\==.; n= 0 /*process each vector; zero element cnt*/
y= space( translate(@.j, ,',') ) /*elide commas and superfluous blanks. */
$= /*nullify output (liner combination).*/
do k=1 for words(y); #= word(y, k) /* ◄───── process each of the elements.*/
if #=0 then iterate; a= abs(# / 1) /*if the value is zero, then ignore it.*/
s= '+ ' ; if #<0 then s= "- " /*define the sign: plus(+) or minus(-)*/
n= n + 1; if n==1 then s= strip(s) /*if the 1st element used, remove plus.*/
if a\==1 then s= s || a'*' /*if multiplier is unity, then ignore #*/
$= $ s'e('k")" /*construct a liner combination element*/
end /*k*/
$= strip( strip($), 'L', "+") /*strip leading plus sign (1st element)*/ if $== then $= 0 /*handle special case of no elements. */ say right( space(@.j), 20) ' ──► ' strip($) /*align the output for presentation. */ end /*j*/ /*stick a fork in it, we're all done. */</lang>
- output when using the default inputs:
1, 2, 3 ──► e(1) + 2*e(2) + 3*e(3)
0, 1, 2, 3 ──► e(2) + 2*e(3) + 3*e(4)
1, 0, 3, 4 ──► e(1) + 3*e(3) + 4*e(4)
1, 2, 0 ──► e(1) + 2*e(2)
0, 0, 0 ──► 0
0 ──► 0
1, 1, 1 ──► e(1) + e(2) + e(3)
-1, -1, -1 ──► -e(1) - e(2) - e(3)
-1, -2, 0, -3 ──► -e(1) - 2*e(2) - 3*e(4)
-1 ──► -e(1)
Ring
<lang ring>
- Project : Display a linear combination
scalars = [[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=1 to len(scalars)
str = ""
for m=1 to len(scalars[n])
scalar = scalars[n] [m]
if scalar != "0"
if scalar = 1
str = str + "+e" + m
elseif scalar = -1
str = str + "" + "-e" + m
else
if scalar > 0
str = str + char(43) + scalar + "*e" + m
else
str = str + "" + scalar + "*e" + m
ok
ok
ok
next
if str = ""
str = "0"
ok
if left(str, 1) = "+"
str = right(str, len(str)-1)
ok
see str + nl
next </lang> Output:
e1+2*e2+3*e3 e2+2*e3+3*e4 e1+3*e3+4*e4 e1+2*e2 0 0 e1+e2+e3 -e1-e2-e3 -e1-2*e2-3*e4 -e1
Scala
<lang Scala>object LinearCombination extends App {
val combos = Seq(Seq(1, 2, 3), Seq(0, 1, 2, 3),
Seq(1, 0, 3, 4), Seq(1, 2, 0), Seq(0, 0, 0), Seq(0),
Seq(1, 1, 1), Seq(-1, -1, -1), Seq(-1, -2, 0, -3), Seq(-1))
private def linearCombo(c: Seq[Int]): String = {
val sb = new StringBuilder
for {i <- c.indices
term = c(i)
if term != 0} {
val av = math.abs(term)
def op = if (term < 0 && sb.isEmpty) "-"
else if (term < 0) " - "
else if (term > 0 && sb.isEmpty) "" else " + "
sb.append(op).append(if (av == 1) "" else s"$av*").append("e(").append(i + 1).append(')')
}
if (sb.isEmpty) "0" else sb.toString
}
for (c <- combos) {
println(f"${c.mkString("[", ", ", "]")}%-15s -> ${linearCombo(c)}%s")
}
}</lang>
Sidef
<lang ruby>func linear_combination(coeffs) {
var res = ""
for e,f in (coeffs.kv) {
given(f) {
when (1) {
res += "+e(#{e+1})"
}
when (-1) {
res += "-e(#{e+1})"
}
case (.> 0) {
res += "+#{f}*e(#{e+1})"
}
case (.< 0) {
res += "#{f}*e(#{e+1})"
}
}
}
res -= /^\+/
res || 0
}
var tests = [
%n{1 2 3},
%n{0 1 2 3},
%n{1 0 3 4},
%n{1 2 0},
%n{0 0 0},
%n{0},
%n{1 1 1},
%n{-1 -1 -1},
%n{-1 -2 0 -3},
%n{-1},
]
tests.each { |t|
printf("%10s -> %-10s\n", t.join(' '), linear_combination(t))
}</lang>
- Output:
1 2 3 -> e(1)+2*e(2)+3*e(3)
0 1 2 3 -> e(2)+2*e(3)+3*e(4)
1 0 3 4 -> e(1)+3*e(3)+4*e(4)
1 2 0 -> e(1)+2*e(2)
0 0 0 -> 0
0 -> 0
1 1 1 -> e(1)+e(2)+e(3)
-1 -1 -1 -> -e(1)-e(2)-e(3)
-1 -2 0 -3 -> -e(1)-2*e(2)-3*e(4)
-1 -> -e(1)
Tcl
This solution strives for legibility rather than golf.
<lang Tcl>proc lincom {factors} {
set exp 0
set res ""
foreach f $factors {
incr exp
if {$f == 0} {
continue
} elseif {$f == 1} {
append res "+e($exp)"
} elseif {$f == -1} {
append res "-e($exp)"
} elseif {$f > 0} {
append res "+$f*e($exp)"
} else {
append res "$f*e($exp)"
}
}
if {$res eq ""} {set res 0}
regsub {^\+} $res {} res
return $res
}
foreach test {
{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}
} {
puts [format "%10s -> %-10s" $test [lincom $test]]
}</lang>
- Output:
1 2 3 -> e(1)+2*e(2)+3*e(3)
0 1 2 3 -> e(2)+2*e(3)+3*e(4)
1 0 3 4 -> e(1)+3*e(3)+4*e(4)
1 2 0 -> e(1)+2*e(2)
0 0 0 -> 0
0 -> 0
1 1 1 -> e(1)+e(2)+e(3)
-1 -1 -1 -> -e(1)-e(2)-e(3)
-1 -2 0 -3 -> -e(1)-2*e(2)-3*e(4)
-1 -> -e(1)
Visual Basic .NET
<lang vbnet>Imports System.Text
Module Module1
Function LinearCombo(c As List(Of Integer)) As String
Dim sb As New StringBuilder
For i = 0 To c.Count - 1
Dim n = c(i)
If n < 0 Then
If sb.Length = 0 Then
sb.Append("-")
Else
sb.Append(" - ")
End If
ElseIf n > 0 Then
If sb.Length <> 0 Then
sb.Append(" + ")
End If
Else
Continue For
End If
Dim av = Math.Abs(n)
If av <> 1 Then
sb.AppendFormat("{0}*", av)
End If
sb.AppendFormat("e({0})", i + 1)
Next
If sb.Length = 0 Then
sb.Append("0")
End If
Return sb.ToString()
End Function
Sub Main()
Dim combos = New List(Of List(Of Integer)) From {
New List(Of Integer) From {1, 2, 3},
New List(Of Integer) From {0, 1, 2, 3},
New List(Of Integer) From {1, 0, 3, 4},
New List(Of Integer) From {1, 2, 0},
New List(Of Integer) From {0, 0, 0},
New List(Of Integer) From {0},
New List(Of Integer) From {1, 1, 1},
New List(Of Integer) From {-1, -1, -1},
New List(Of Integer) From {-1, -2, 0, -3},
New List(Of Integer) From {-1}
}
For Each c In combos
Dim arr = "[" + String.Join(", ", c) + "]"
Console.WriteLine("{0,15} -> {1}", arr, LinearCombo(c))
Next
End Sub
End Module</lang>
- Output:
[1, 2, 3] -> e(1) + 2*e(2) + 3*e(3)
[0, 1, 2, 3] -> e(2) + 2*e(3) + 3*e(4)
[1, 0, 3, 4] -> e(1) + 3*e(3) + 4*e(4)
[1, 2, 0] -> e(1) + 2*e(2)
[0, 0, 0] -> 0
[0] -> 0
[1, 1, 1] -> e(1) + e(2) + e(3)
[-1, -1, -1] -> -e(1) - e(2) - e(3)
[-1, -2, 0, -3] -> -e(1) - 2*e(2) - 3*e(4)
[-1] -> -e(1)
zkl
<lang zkl>fcn linearCombination(coeffs){
[1..].zipWith(fcn(n,c){ if(c==0) "" else "%s*e(%s)".fmt(c,n) },coeffs)
.filter().concat("+").replace("+-","-").replace("1*","")
or 0
}</lang> <lang zkl>T(T(1,2,3),T(0,1,2,3),T(1,0,3,4),T(1,2,0),T(0,0,0),T(0),T(1,1,1),T(-1,-1,-1),
T(-1,-2,0,-3),T(-1),T)
.pump(Console.println,linearCombination);</lang>
- Output:
e(1)+2*e(2)+3*e(3) e(2)+2*e(3)+3*e(4) e(1)+3*e(3)+4*e(4) e(1)+2*e(2) 0 0 e(1)+e(2)+e(3) -e(1)-e(2)-e(3) -e(1)-2*e(2)-3*e(4) -e(1) 0