Grammar LL1简单计算器语法（+；，-，*，/，pow，root）

我想出了这个语法，它成功地在括号中添加了/子数字等等。但是，我发现很难为pow（^）和root（#）逻辑扩展它。我很感激你的帮助，因为我现在已经陷入困境

nonZeroDigit = "1"|"2"|"3"|"4"|"5"|"6"|"7"|"8"|"9";
digit = "0" | nonZeroDigit;
naturalNumber = nonZeroDigit , {digit};
secondPriorityOperators= "+" |"-";
firstPriorityOperators= "*" | "/";
syntax=expr;
expr=term, {secondPriorityOperators, term};
term=factor, {firstPriorityOperators, factor};
factor="(", expr , ")" | naturalNumber;
root = "#" , root | factor;
power = root, "^" , power| root;

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对于测试，我使用了这个站点：

只需添加另一个优先级：

thirdPriorityOperators= "+" |"-";
secondPriorityOperators= "*" | "/";
firstPriorityOperators= "#" | "^";

term3rd=term2nd, {thirdPriorityOperators, term2nd};
term2nd=term1st, {secondPriorityOperators, term1st};
term1st=factor, {firstPriorityOperators, factor};