又来打扰前辈们~~~AJAX的简单问题

<%@ page language="java" contentType="text/html; charset=GBK"
    pageEncoding="gbk"%>
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Insert title here</title>
<script type="text/javascript">
function check()
{
alert("test");
var url = "test?name="+name.value;
if(window.XMLHttpRequest)
   {
   req=new XMLHttpRequest();
   }
   else if(window.ActiveXobject)
   {
   req=new ActiveXobject("Microsoft.XMLHTTP");
   }
     //以GET方法传送到URL，URL在上面
   req.onreadystatechange=callback;
   req.open("GET",url,true);
   //这边会调用方法 callback()
   req.send(null);  //无用
}
function callback()
{
var state = req.readyState;
if(state==4){
alert("test");
var doms = req.responseXML;
var user = doms.getElementsByTagName("code");
alert(user[0]);//这边返回NULL
if(user[0].getElementsByTagName("name")[0].firstChild.data=="exist"){
var name = document.getElementById("name");
alert("fail");
}else{
alert("success");
}
}
}
</script>
</head>
<body>
<input type="text" name="name">
<input type="submit" onclick="check()"> 
</body>
</html>-------------------------------------------------------------------------------------package funcetion;import java.io.IOException;
import java.io.PrintWriter;import javax.servlet.ServletException;
import javax.servlet.http.HttpServlet;
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpServletResponse;public class test extends HttpServlet {
public void doGet(HttpServletRequest request, HttpServletResponse response)
throws ServletException, IOException { PrintWriter out = response.getWriter();
String code = request.getParameter("name");
String rcode = (String)request.getSession().getAttribute("rand");
System.out.println("-----------------");//这边测试有没有到这边来
if(code.equals(rcode))
out.print("<Codes>");
out.print("<code>");
out.print("<message>"+"correct"+"</message>");
out.print("</code>");
out.print("</Codes>");
}else
out.print("<Codes>");
out.print("<code>");
out.print("<message>"+"error"+"</message>");
out.print("</code>");
out.print("</Codes>");
}
}
public void doPost(HttpServletRequest request, HttpServletResponse response)
throws ServletException, IOException { PrintWriter out = response.getWriter();
String code = request.getParameter("name");
String rcode = (String)request.getSession().getAttribute("rand");
System.out.println("--------------------");
if(1==1){
out.print("<Codes>");
out.print("<code>");
out.print("<message>"+"correct"+"</message>");
out.print("</code>");
out.print("</Codes>");
}else{
out.print("<Codes>");
out.print("<code>");
out.print("<message>"+"error"+"</message>");
out.print("</code>");
out.print("</Codes>");
}
}}
我要用实现功能，就是点击按钮，能够判断出来，然后弹出对话框~~~~