Display a linear combination
Display a linear combination is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
The purpose of this task is to 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
Your output must comply to the following rules:
- you don't show null terms, unless the whole combination is null. For instance while the output "0" is fine, "e(0) + 0*e(3)" or "0 + e(1)" are wrong.
- you don't show scalars when they are equal to one or minus one. For instance the string "1*e(3)" is wrong.
- you don't prefix by '-' if it follows a preceding term. Instead you use subtraction. Thus "e(4) - e(5)" is correct while "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
Perl 6
<lang perl6>sub linear-combination(@coeff) {
my @terms = @coeff Z=> map { "e($_)" }, 1 .. *;
@terms.=grep(+*.key);
return '0' unless @terms;
my $result = join '+', map { .key ~ '*' ~ .value }, @terms;
$result ~~ s:g/'+-'/-/; $result ~~ s:g/<|w>1\*//; return $result;
}
say linear-combination(@$_) 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)