Help with my code?

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Summary:

Help making code shorter and with the maths

Help with my code?

John (guest) 22 Feb 2013 03:55

Hey guys,
This is my first time on the forum. I am trying to code a program that factors a polynomial (up to quartic). I am using synthetic division to find factors for the polynomial. Its working pretty well, but is limited. I only have a basic understanding of programming on the nspire, so the code is very lengthy. Could anybody help me compact my code/suggest another way to factor polynomials? Also, the program has a couple bugs right now and won't tell me the correct factorization sometimes, so if anybody finds the error, please let me know.

Define syntheticdiv()=
Prgm
:Request "Power of polynomial (2-4)?",e
:If e=2 Then
:  Text "Enter Quadratic as Ax^2+Bx+C"
:  Request "A(x^2)=",d
:  Request "B(x)=",h
:  Request "C=",i
:  Lbl checkquad
:  −20→a
:  While a≤20
:  a+((1)/(12))→a
:  If i+a*(d*a+h)=0 Then
:  quadfactor:=−a
: Goto e2finish
:ElseIf a=20 Then
:quadfactor:=10000
:Goto e2finish
:EndIf
:EndWhile
:ElseIf e=3 Then
:Text "Input the Cubic Polynomial as Ax^3+Bx^2+Cx+D"
:Request "A(x^3)=",b
:Request "B(x^2)=",c
:Request "C(x)=",l
:Request "D=",m
:Lbl checkcube
:  −20→o
:  While o≤20
:  o+((1)/(12))→o
:  p:=((b*o+c)*o+l)*o+m
:  If p=0 Then
:  cubicfactor:=−o
:  d:=b
:  h:=b*o+c
:  i:=(b*o+c)*o+l
:  Goto checkquad
: ElseIf o=20 Then
: cubicfactor:=10000
: Goto e3finish
:EndIf
:EndWhile
:ElseIf e=4 Then
:Text "Input Quartic Polynomial as Ax^4+Bx^3+Cx^2+Dx+E"
:Request "Ax^4",r
:Request "Bx^3",s
:Request "Cx^2",t
:Request "Dx",u
:Request "E",v
:  −20→w
:  While w≤20
:  w+((1)/(12))→w
:q:=(((r*w+s)*w+t)*w+u)*w+v
:  If q=0 Then
:  quarticfactor:=−w
:  b:=r
:  c:=r*w+s
:  l:=t+w*(r*w+s)
:  m:=u+w*(t+w*(r*w+s))
:  Goto checkcube
: ElseIf w=20 Then
: quarticfactor:=10000
: Goto e4finish
:EndIf
:EndWhile
:EndIf
:Lbl e4finish
:If quarticfactor=10000 Then
:Disp "There are no factors"
:Goto finish
:EndIf
:Lbl e3finish
:If cubicfactor=10000 Then
:If e=4 Then
:quarticnum:=getNum(quarticfactor)
:quarticdenom:=getDenom(quarticfactor)
:Disp quarticdenom,"*(",quarticdenom,"x+",quarticnum,")(",b,"x^3+",c,"x^2+",l,"x+",m,")"
:Goto finish
:Else
:Disp "There are no factors"
:Goto finish
:EndIf
:EndIf
:Lbl e2finish
:If quadfactor=10000 Then
:If e=4 Then
:quarticnum:=getNum(quarticfactor)
:quarticdenom:=getDenom(quarticfactor)
:cubicdenom:=getDenom(cubicfactor)
:cubicnum:=getNum(cubicfactor)
:quaddenom:=getDenom(quadfactor)
:quadnum:=getNum(quadfactor)
:coefficient:=((1)/(quarticdenom*cubicdenom*quaddenom))
:Disp "(",quarticdenom,"x+",quarticnum,")(",cubicdenom,"x+",cubicnum,")(",d,"x^2",h,"x",i,")"
:Goto finish
:ElseIf e=3 Then
:cubicdenom:=getDenom(cubicfactor)
:cubicnum:=getNum(cubicfactor)
:quaddenom:=getDenom(quadfactor)
:quadnum:=getNum(quadfactor)
:coefficient:=((1)/(cubicdenom*quaddenom))
:Disp coefficient,"*(",cubicdenom,"x+",cubicnum,")(",d,"x^2+",h,"x+",i,")"
:Goto finish
:ElseIf e=2 Then
:Disp "There are no factors"
:Goto finish
:EndIf
:EndIf
:If e=4 Then
:quarticnum:=getNum(quarticfactor)
:quarticdenom:=getDenom(quarticfactor)
:cubicdenom:=getDenom(cubicfactor)
:cubicnum:=getNum(cubicfactor)
:quaddenom:=getDenom(quadfactor)
:quadnum:=getNum(quadfactor)
:coefficient:=((1)/(d))
:Disp coefficient,"*(",quarticdenom,"x+",quarticnum,")(",cubicdenom,"x+",cubicnum,")(",quaddenom,"x+",quadnum,")(",d,"x+",a*d+h,")"
:ElseIf e=3 Then
:cubicdenom:=getDenom(cubicfactor)
:cubicnum:=getNum(cubicfactor)
:quaddenom:=getDenom(quadfactor)
:quadnum:=getNum(quadfactor)
:coefficient:=((1)/(d))
:Disp coefficient,"*(",cubicdenom,"x+",cubicnum,")(",quaddenom,"x+",quadnum,")(",d,"x+",a*d+h,")"
:ElseIf e=2 Then
:quaddenom:=getDenom(quadfactor)
:quadnum:=getNum(quadfactor)
:coefficient:=((1)/(d))
:Disp coefficient,"*(",quaddenom,"x+",quadnum,")(",d,"x+",a*d+h,")"
:EndIf
:Lbl finish
:DelVar cubicdenom,cubicnum,quaddenom,quadnum,quarticnum,quarticdenom,a,b,c,d,e,f,g,h,i,l,m,o,p,q,r,s,t,u,v,w,quarticfactor,cubicfactor,quadfactor
:EndPrgm

John (guest) 22 Feb 2013 15:21

bump

Timothy Foster 22 Feb 2013 15:43

If you are looking only at degrees 2 to 4, then you can use algorithms that have already been devised to find the roots and then display them in the proper form. For instance, you can use the quadratic formula to solve for real, rational roots (that is, the discriminant is a perfect square). For instance, the expression, $x^2-3x+2$ has the roots 1 and 2, and therefore it factors to factors to $(x-2)(x-1)$.

For cubics, you can use an algorithm similar to the one here. The code is below:

+ Show code

    var p = (3*c/a-Math.pow(b/a,2))/3;
    var q = (2*Math.pow(b/a,3)-9*b*c/a/a+27*d/a)/27;
    var dis = p*p*p/27+q*q/4;
    var s = b/a/3;
    var apprx = document.getElementById("apprx");
    var answer = new Array();
    if(dis >= 0){
        var u = cbrt(-q/2+Math.sqrt(dis));
        var v = cbrt(-q/2-Math.sqrt(dis));
        answer = [roundOff(u+v-s,3),roundOff(-(u+v)/2-s,3),roundOff((u-v)*Math.sqrt(3)/2,3)];
        var disp = 4;
        if(dis == 0){
            answer.sort(sortA);
            disp = 1+(answer[1] != answer[0]+answer[2]);
        }
        switch(disp){
            case 1:
                apprx.innerHTML = "<strong>Approximation:</strong><br />x &#8776; "+answer[0];
                break;
            case 2:
                apprx.innerHTML = "<strong>Approximation:</strong><br />x &#8776; "+answer[0]+"<br />x &#8776; "+answer[2];
                break;
            case 4:
                apprx.innerHTML = "<strong>Approximation:</strong><br />x &#8776; "+answer[0]+"<br />x &#8776; "+answer[1]+"+"+answer[2]+"<b><i>i</i></b><br />x &#8776; "+answer[1]+"-"+answer[2]+"<b><i>i</i></b>";
                break;
            default:
                apprx.innerHTML = "An error may have occurred.";
        }
    }
    else if(dis < 0){
        var r = Math.acos(-q/2/Math.sqrt(Math.pow(Math.abs(p),3)/27));
        answer = [roundOff(2*Math.sqrt(Math.abs(p)/3)*Math.cos(r/3)-s,3),roundOff(-2*Math.sqrt(Math.abs(p)/3)*Math.cos((r+Math.PI)/3)-s,3),roundOff(-2*Math.sqrt(Math.abs(p)/3)*Math.cos((r-Math.PI)/3)-s,3)];
        answer.sort(sortA);
        apprx.innerHTML = "<strong>Approximation:</strong><br />x &#8776; "+answer[0]+"<br />x &#8776; "+answer[1]+"<br />x &#8776; "+answer[2];
    }
    else{
        apprx.innerHTML = "Unable to solve.  Please make sure that:<br /><ul><li>The x<sup>3</sup> coefficient is nonzero</li><li>All fields have valid real numbers</li><li>If a coefficient is 0 or 1, don't make the field blank!</li></ul>";
    }

Since you only want rational roots, the algorithms could be simplified much more; the above also searches for complex roots, which you do not need.

---

Timothy Foster - @tfAuroratide
Auroratide.com - Go here if you're nerdy like me