php代码中如何输出数学公式

<img src="http://latex.codecogs.com/gif.latex?$(a_{1})^2+(a_{3})^2geq%202(a_{2})^2$" />

<img src="http://latex.codecogs.com/gif.latex?$$%20left{%20egin{aligned}%200leq%20xleq%202%20\%200leq%20yleq%202\%20end{aligned}%20
ight.%20$$" />

$str='$$ left{
                   egin{aligned}
                   x^2+3y^2=3 \
                   y=k(x-1)\
                   end{aligned}
                   
ight.
        $$';
    //将$$转化为$$
    $str=str_replace("$$", "$", $str);
    // dd($str);
    $pattern='/$(.*)$/Us';//只能识别$$  $$
    preg_match_all($pattern,$str,$matches);
    $arr_split=preg_split($pattern,$str);
    //dd($arr_split);
    // dd($matches);
    $count=count($matches[1]);
    $str_new="";
    for($i=0;$i<count($matches[1]);$i++){
        //$arr_replace[]='<img src="http://latex.codecogs.com/gif.latex?'.$matches[1][$i].'" />';
        $matches_str=$matches[1][$i];
        // dd($str);
        //先把\n转换成\

        $matches_str=str_replace("\
", "\\
", $matches_str);
        // dd($matches_str);
        $matches_str=preg_replace('/s*/', '', $matches_str);
        // dd($matches_str);
        $str_new.=$arr_split[$i];
        $str_new.='<img src="http://latex.codecogs.com/gif.latex?'.$matches_str.'" />';
    }
    if($count>0){
        echo $str_new;
    }else{
        echo $str;
    }