More fiddles, more fun!

jsfiddles/create_room_send_msg/demo.css

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+.loggedin {
+    visibility: hidden;
+}
+
+p {
+    font-family: monospace;
+}
+
+table
+{
+    border-spacing:5px;
+}
+
+th,td
+{
+    padding:5px;
+}

jsfiddles/create_room_send_msg/demo.html

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+<div>
+    <p>This room creation / message sending demo requires a home server to be running on http://localhost:8080</p>
+</div>
+<form class="loginForm">
+    <input type="text" id="userLogin" placeholder="Username"></input>
+    <input type="password" id="passwordLogin" placeholder="Password"></input>
+    <input type="button" class="login" value="Login"></input>
+</form>
+<div class="loggedin">
+    <form class="createRoomForm">
+        <input type="text" id="roomAlias" placeholder="Room alias (optional)"></input>
+        <input type="button" class="createRoom" value="Create Room"></input>
+    </form>
+    <form class="sendMessageForm">
+        <input type="text" id="roomId" placeholder="Room ID"></input>
+        <input type="text" id="messageBody" placeholder="Message body"></input>
+        <input type="button" class="sendMessage" value="Send Message"></input>
+    </form>
+    <table id="rooms">
+        <tbody>
+            <tr>
+                <th>Room ID</th>
+                <th>My state</th>
+                <th>Room Alias</th>
+                <th>Latest message</th>
+            </tr>
+        </tbody>
+    </table>
+</div>
+    

jsfiddles/create_room_send_msg/demo.js

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+var accountInfo = {};
+
+var showLoggedIn = function(data) {
+    accountInfo = data;
+    getCurrentRoomList();
+    $(".loggedin").css({visibility: "visible"});
+};
+
+$('.login').live('click', function() {
+    var user = $("#userLogin").val();
+    var password = $("#passwordLogin").val();
+    $.ajax({
+        url: "http://localhost:8080/matrix/client/api/v1/login",
+        type: "POST",
+        contentType: "application/json; charset=utf-8",
+        data: JSON.stringify({ user: user, password: password, type: "m.login.password" }),
+        dataType: "json",
+        success: function(data) {
+            showLoggedIn(data);
+        },
+        error: function(err) {
+            alert(JSON.stringify($.parseJSON(err.responseText)));  
+        }
+    }); 
+});
+
+var getCurrentRoomList = function() {
+    var url = "http://localhost:8080/matrix/client/api/v1/im/sync?access_token=" + accountInfo.access_token + "&from=END&to=START&limit=1";
+    $.getJSON(url, function(data) {
+        for (var i=0; i<data.length; ++i) {
+            data[i].latest_message = data[i].messages.chunk[0].content.body;
+            addRoom(data[i]);   
+        }
+    }).fail(function(err) {
+        alert(JSON.stringify($.parseJSON(err.responseText)));
+    });
+};
+
+$('.createRoom').live('click', function() {
+    var roomAlias = $("#roomAlias").val();
+    var data = {};
+    if (roomAlias.length > 0) {
+        data.room_alias_name = roomAlias;   
+    }
+    $.ajax({
+        url: "http://localhost:8080/matrix/client/api/v1/rooms?access_token="+accountInfo.access_token,
+        type: "POST",
+        contentType: "application/json; charset=utf-8",
+        data: JSON.stringify(data),
+        dataType: "json",
+        success: function(data) {
+            data.membership = "join"; // you are automatically joined into every room you make.
+            data.latest_message = "";
+            addRoom(data);
+        },
+        error: function(err) {
+            alert(JSON.stringify($.parseJSON(err.responseText)));  
+        }
+    }); 
+});
+
+var addRoom = function(data) {
+    row = "<tr>" +
+        "<td>"+data.room_id+"</td>" +
+        "<td>"+data.membership+"</td>" +
+        "<td>"+data.room_alias+"</td>" +
+        "<td>"+data.latest_message+"</td>" +
+        "</tr>";
+    $("#rooms").append(row);
+};
+
+$('.sendMessage').live('click', function() {
+    var roomId = $("#roomId").val();
+    var body = $("#messageBody").val();
+    var msgId = $.now();
+    
+    if (roomId.length === 0 || body.length === 0) {
+        return;
+    }
+    
+    var url = "http://localhost:8080/matrix/client/api/v1/rooms/$roomid/messages/$user/$msgid?access_token=$token";
+    url = url.replace("$token", accountInfo.access_token);
+    url = url.replace("$roomid", encodeURIComponent(roomId));
+    url = url.replace("$user", encodeURIComponent(accountInfo.user_id));
+    url = url.replace("$msgid", msgId);
+    
+    var data = {
+        msgtype: "m.text",
+        body: body
+    };
+    
+    $.ajax({
+        url: url,
+        type: "PUT",
+        contentType: "application/json; charset=utf-8",
+        data: JSON.stringify(data),
+        dataType: "json",
+        success: function(data) {
+            $("#messageBody").val("");
+            // wipe the table and reload it. Using the event stream would be the best
+            // solution but that is out of scope of this fiddle.
+            $("#rooms").find("tr:gt(0)").remove();
+            getCurrentRoomList();
+        },
+        error: function(err) {
+            alert(JSON.stringify($.parseJSON(err.responseText)));  
+        }
+    }); 
+});