<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title></title>
<body>
<div align="center">例如输入:a=3, b=6, c=-123, d=-126 e=1080</div>
<form name="form1" action="">
ax<sup>4</sup> + bx<sup>3</sup> + cx<sup>2</sup> + dx + e = 0
<table border="0" align="center" colspan="4" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td><input type="text" name="aIn" size="5" placeholder="a">x<sup>4</sup> +</td>
<td><input type="text" name="bIn" size="5" placeholder="b">x³ +</td>
<td><input type="text" name="cIn" size="5" placeholder="c">x² +</td>
<td><input type="text" name="dIn" size="5" placeholder="d">x +</td>
<td><input type="text" name="eIn" size="5" placeholder="e">e</td>
</tr>
</tbody>
</table>
<center>
<input type="button" name="button1" value="计算" onclick="quad4solve(this.form)">
</center>
<table border="0" class="innerc" cellspacing="0" cellpadding="3">
<tbody>
<tr align="center">
<td class="inner" colspan="4"><b>结果:</b></td>
</tr>
<tr>
<td>x<sub>1</sub>:
<input type="text" name="x1Re" size="25"> +
<input type="text" name="x1Im" size="25"> i
</td>
</tr>
<tr>
<td>x<sub>2</sub>:
<input type="text" name="x2Re" size="25"> +
<input type="text" name="x2Im" size="25"> i
</td>
</tr>
<tr>
<td>x<sub>3</sub>:
<input type="text" name="x3Re" size="25"> +
<input type="text" name="x3Im" size="25"> i
</td>
</tr>
<tr>
<td>x<sub>4</sub>:
<input type="text" name="x4Re" size="25"> +
<input type="text" name="x4Im" size="25"> i
</td>
</tr>
</tbody>
</table>
</form>
<script type="text/javascript">
function quad4solve(dataForm)
{
var a = parseFloat(dataForm.aIn.value);
var b = parseFloat(dataForm.bIn.value);
var c = parseFloat(dataForm.cIn.value);
var d = parseFloat(dataForm.dIn.value);
var e = parseFloat(dataForm.eIn.value);
if (a == 0)
{
alert("The coefficient of the power four of x is 0. Please use the utility for a third degree quadratic.");
return;
}
if (e == 0)
{
alert("One root is 0. Now divide through by x and use the utility for a third degree quadratic to solve the resulting equation for the other three roots.");
return;
}
if (a != 1)
{
b /= a;
c /= a;
d /= a;
e /= a;
}
//立方解算器系数
var cb, cc, cd;
var discrim, q, r, RRe, RIm, DRe, DIm, dum1, ERe, EIm, s, t, term1, r13, sqR, y1, z1Re, z1Im, z2Re;
cb = -c;
cc = -4.0*e + d*b;
cd = -(b*b*e + d*d) + 4.0*c*e;
if (cd == 0)
{
alert("cd = 0.");
}
q = (3.0*cc - (cb*cb))/9.0;
r = -(27.0*cd) + cb*(9.0*cc - 2.0*(cb*cb));
r /= 54.0;
discrim = q*q*q + r*r;
term1 = (cb/3.0);
if (discrim > 0)
{
// 1 实数, 2 复数
s = r + Math.sqrt(discrim);
s = ((s < 0) ? -Math.pow(-s, (1.0/3.0)) : Math.pow(s, (1.0/3.0)));
t = r - Math.sqrt(discrim);
t = ((t < 0) ? -Math.pow(-t, (1.0/3.0)) : Math.pow(t, (1.0/3.0)));
y1 = -term1 + s + t;
}
else
{
if (discrim == 0)
{
r13 = ((r < 0) ? -Math.pow(-r,(1.0/3.0)) : Math.pow(r,(1.0/3.0)));
y1 = -term1 + 2.0*r13;
}
else
{
q = -q;
dum1 = q*q*q;
dum1 = Math.acos(r/Math.sqrt(dum1));
r13 = 2.0*Math.sqrt(q);
y1 = -term1 + r13*Math.cos(dum1/3.0);
}
}
// 确定了y1 分解立方的实根
term1 = b/4.0;
sqR = -c + term1*b + y1;
RRe = RIm = DRe = DIm = ERe = EIm = z1Re = z1Im = z2Re = 0;
if (sqR >= 0)
{
if (sqR == 0)
{
dum1 = -(4.0*e) + y1*y1;
if (dum1 < 0){
z1Im = 2.0*Math.sqrt(-dum1);
} else {
z1Re = 2.0*Math.sqrt(dum1);
z2Re = -z1Re;
}
}
else
{
RRe = Math.sqrt(sqR);
z1Re = -(8.0*d + b*b*b)/4.0 + b*c;
z1Re /= RRe;
z2Re = -z1Re;
}
}
else
{
RIm = Math.sqrt(-sqR);
z1Im = -(8.0*d + b*b*b)/4.0 + b*c;
z1Im /= RIm;
z1Im = -z1Im;
}
z1Re += -(2.0*c + sqR) + 3.0*b*term1;
z2Re += -(2.0*c + sqR) + 3.0*b*term1;
//At this point, z1 and z2 should be the terms under the square root for D and E
if (z1Im == 0)
{ // Both z1 and z2 real
if (z1Re >= 0)
{
DRe = Math.sqrt(z1Re);
}
else
{
DIm = Math.sqrt(-z1Re);
}
if (z2Re >= 0)
{
ERe = Math.sqrt(z2Re);
}
else
{
EIm = Math.sqrt(-z2Re);
}
}
else
{
r = Math.sqrt(z1Re*z1Re + z1Im*z1Im);
r = Math.sqrt(r);
dum1 = Math.atan2(z1Im, z1Re);
dum1 /= 2; //Divide this angle by 2
ERe = DRe = r*Math.cos(dum1);
DIm = r*Math.sin(dum1);
EIm = -DIm;
}
dataForm.x1Re.value = -term1 + (RRe + DRe)/2;
dataForm.x1Im.value = (RIm + DIm)/2;
dataForm.x2Re.value = -(term1 + DRe/2) + RRe/2;
dataForm.x2Im.value = (-DIm + RIm)/2;
dataForm.x3Re.value = -(term1 + RRe/2) + ERe/2;
dataForm.x3Im.value = (-RIm + EIm)/2;
dataForm.x4Re.value = -(term1 + (RRe + ERe)/2);
dataForm.x4Im.value = -(RIm + EIm)/2;
return;
}
</script>
</body>
</html>
Incredible points. Great arguments. Keep up the good work.
Do you have any video of that? I’d like to find out some additional information.
Your style is really unique compared to other folks I’ve
read stuff from. Many thanks for posting when you have the opportunity, Guess I will just book
mark this page.
Hi this is kinda of off topic but I was wanting to know if
blogs use WYSIWYG editors or if you have to manually code with HTML.
I’m starting a blog soon but have no coding knowledge so I wanted
to get advice from someone with experience. Any help would be enormously appreciated!
Wonderful beat ! I would like to apprentice while you amend your web site, how could i subscribe for a blog
web site? The account aided me a acceptable deal. I had been a little bit acquainted of this your broadcast offered
bright clear idea