php代码中如何输出数学公式

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

<img src="http://latex.codecogs.com/gif.latex?$$%20\left\{%20\begin{aligned}%200\leq%20x\leq%202%20\\%200\leq%20y\leq%202\\%20\end{aligned}%20\right.%20$$" />

$str='$$ \left\{
 \begin{aligned}
 x^2+3y^2=3 \\
 y=k(x-1)\\
 \end{aligned}
 \right.
 $$';
 //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\\\n
 $matches_str=str_replace("\\\n", "\\\\\n", $matches_str);
 // dd($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;
 }