规则的表示

表示方法

使用Backus-Naur Form (BNF)表示各种规则

• ::= 表示“被定义为”
• +表示“1个及以上”
• *表示“0个及以上”
• [word]表示“word为可选项”
• | 表示有可能出现的情况

基本运算符号（形式一致）

equal ::= "=" # 等于
plus ::= "+"  # 加
minus ::= "-"  # 减
multiply ::= "*"  # 乘
divide ::= "/" # 除
power ::= "**"  # 幂
basicSymbol ::= equal | plus |minus| multiply | divide | power

标记符号

comma ::= ","  # 逗号
Lparen ::= "("  # 左括号
Rparen ::= ")"  # 右括号

特殊运算符号

latex形式

max ::= "max"  # 取最大值
min ::= "min"  # 取最小值
latexFrac ::= "frac"  # 分数
latexLn ::= "ln"  # 自然对数
latexPow ::= "^"  # 指数
latexSqrt ::= "sqrt"  # 根号
latexArcsin ::="arcsin" # 反正弦
latexArccos ::="arccos" # 反余弦
latexTanh ::= "tanh"  # 双曲正切
latexCos ::= "cos" # 余弦
latexSin ::= "sin"  # 正弦
latexTan ::= "tan"  # 正切
triangleSymbol ::= latexArcsin | latexArccos | latexTanh | latexCos | latexSin | latexTan 
SpecialSymbol ::= latexFrac | latexLn | latexPow | latexSqrt | triangleSymbol

python形式

pyTanh ::= "math.tanh"
pyCos ::= "math.cos"
pySin ::= "math.sin"
pyTan ::= "math.tan"
pyLn ::= "math.log"  # 对数
pySqrt ::= "math.sqrt"
pyExp ::= "math.exp"  # e^x

参数的形式

nums ::= '0'..'9'
alphas ::= 'A'..'Z''a'..'z'
alphanums ::= nums | alphas
# 数字参数     
numPara ::= ["{"] nums+ ["." nums+] ["}"] # 12  12.13  12.13
# 字母参数
Foot ::= alphanusm+ (comma alphanums+)* # {1} {x} {x,y}
Simple AlphaPara ::= alphas+ ["_{" Foot "}"] ["'"] # A A_{x} 
Complicated AlphaPara ::= "(" alphas+ ["_{" Foot "}"]["'"] ")_{" Foot "}" # (A_{x})_{y}
alphaPara ::= Complicated AlphaPara | Simple AlphaPara # 参数

特殊计算的形式

calculatingUnit ::= SpecialSymbol | MathSymbol | alphaPara | numPara | basicSymbol | Lparen | Rparen |comma
bracketUnit ::="{" caculationUnit+ "}"
Ln ::= latexLn bracketUnit
Triangle ::= triangleSymbol bracketUnit
Power ::= latexPow bracketUnit
Sqrt ::= latexSqrt bracketUnit
Frac ::= latexFrac bracketUnit bracketUnit
Multiply ::= alphaPara Lparen | numPara Lparen | Rparen (alphaPara | numPara) | Rparen Lparen | (alphaPara | numPara) alphaPara| (alphaPara | numPara) MathSymbol

基于文法的设计公式建模

表1 设计计算公式中的符号

操作名称	Python运算符	Latex字符
plus	x+y	x+y
minus	x-y	x-y
multiply	x*y	x*y
divide	x/y	x/y
power	x**y	x^y
fraction	x/y	\frac{x}{y}
square root	math.sqrt(x)	\sqrt{x}
ln	math.log(x)	\ln{x}
max	max(x,y)	\max(x,y)
min	min(x,y)	\min(x,y)
tanh	math.tanh(x)	\tanh(x)
arccos	math.acos(x)	\arccos(x)
arcsin	math.asin(x)	\arcsin(x)
cos	math.cos(x)	\cos(x)
sin	math.sin(x)	\sin(x)
tan	math.tan(x)	\tan(x)
exponential	math.exp(x)	\exp(x)

import math, latexify

Index = {...}


@latexify.with_latex
def Formula(...):
    return ...