04
Apr
09

### [Javascript] Simple Polynomial Long Division

This function uses long division to divide a polynomial by a simple ax+b

The polynomial must be in the format of ax^n + bx^(n-1) + cx^(n-2)…zx^(nn)

The function itself relies upon 4 other functions in order to work, these are used to carry out basic operations on the terms in the polynomail:

```//Used to break an { ax^n } into its compontents
function extractCompontents(Term, constantChar) {
var Comps = new Array();
Comps[0] = Term.split(constantChar)[0];
Comps[1] = Term.split("^")[1];
if(Comps[0] == "") { Comps[0]=1; }
if(String(Comps[1]) == "undefined") { Comps[1]=1; }
return Comps;
}
function divideTerm(Term1, Term2, constantChar) {
var extTerm1 = extractCompontents(Term1, constantChar)
var extTerm2 = extractCompontents(Term2, constantChar)
return String(extTerm1[0]/extTerm2[0]) + constantChar + "^" + String(extTerm1[1]-extTerm2[1]);
}
function multiplyTerm(Term1, Term2, constantChar) {
var extTerm1 = extractCompontents(Term1, constantChar)
return String(extTerm1[0] * Term2) + constantChar + "^" + String(extTerm1[1]);
}
function subtractTerm(Term1, Term2, constantChar) {
var extTerm1 = extractCompontents(Term1, constantChar)
var extTerm2 = extractCompontents(Term2, constantChar)
if(extTerm1[1] != extTerm2[1]) { return null; }
return String(extTerm1[0]-extTerm2[0]) + constantChar + "^" + String(extTerm1[1]);
}```

The function itself is as follows:

```function longAlgebraicDivision(poly, division) {
//Format the equations correctly
poly = poly.replace(/(--|\+\+)/g, "+");
poly = poly.replace(/(-\+|\+-)/g, "-");
poly = poly.replace(/^\+/g, "");
poly = poly.replace(/\s/g, "");
division = division.replace(/(--|\+\+)/g, "+");
division = division.replace(/(-\+|\+-)/g, "-");
division = division.replace(/^\+/g, "");
division = division.replace(/\s/g, "");
//Add spaces to the equation to break it apart
poly = poly.replace(/([+-])/g, " \$1");
//Split the equation at the spaces
var equ = poly.split(" ");
//Begin the division
var output = ""
var lastTerm = ""
for(var i=0;i<equ.length-1;i++) {
var term = equ[i];
if(i==0) {
var dt = divideTerm(term, division.split("x")[0], "x");
output += dt + "+";
dt = multiplyTerm(dt, division.split("x")[1], "x");
lastTerm = dt;
}else{
var dt = subtractTerm(term, lastTerm, "x");
dt = divideTerm(dt, division.split("x")[0], "x");
output += dt + "+";
dt = multiplyTerm(dt, division.split("x")[1], "x");
lastTerm = dt;
}
}
//Format output
output = output.replace(/\+([+-])/g, "\$1");
output = output.replace(/x\^0\+\$/g, "");
output = output.replace(/x\^1/g, "x");
//Calculate remainder
lastTerm = lastTerm.replace(/x\^0/g, "");
output += " : Remainder [" + String(Number(equ[equ.length-1]) - Number(lastTerm)) + "]";
return output;```

Usage:

```<script language="javascript" type="text/javascript">
var poly = "14x^4-5x^3-11x^2-11x+8";
var division = "2x-1";
</script>```

Would output:

7x^3 + 1x^2 – 5x -8 : Remainder [0]