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) {
none(@coeff) ?? '0' !! join( '+', map { .key ~ '*' ~ .value }, grep +*.key, (@coeff Z=> map { "e($_)" }, 1 .. *) )\ .subst('+-', '-', :g)\ .subst(/<|w>1\*/, , :g);
}
say linear-combination(@$_) 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)
zkl
<lang zkl>fcn linearCombination(coeffs){
str:=[1..].zipWith(fcn(n,c){ if(c==0) "" else "%s*e(%s)".fmt(c,n) },coeffs) .filter().concat("+").replace("+-","-").replace("1*",""); if(not str) return(0); str
}</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