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expresión regular

En esta entrada vamos a implementar un evaluador de polinomios trigonométricos en python el cual evalúa funciones trigonométricas usando expresión regular. ¿Ya leíste mis otras entradas sobre Python? Te recomiendo que lo hagas haciendo click aquí.

En esta entrada publiqué una calculadora usando expresión regular por si lo quiere ver. El contenido que vamos a ver es el siguiente:

expresión regular

Expresión regular

En computación, una expresión regular es una secuencia de caracteres que conforma un patrón de búsqueda. Se utilizan principalmente para la búsqueda de patrones de cadenas de caracteres u operaciones de sustituciones.

Las expresiones regulares son patrones utilizados para encontrar una determinada combinación de caracteres dentro de una cadena de texto. Proporcionan una manera muy flexible de buscar o reconocer cadenas de texto.

En otras palabras: una expresión regular es una forma de representar los lenguajes regulares (finitos o infinitos) y se construye utilizando caracteres del alfabeto sobre el cual se define el lenguaje.

Tokens

Los tokens son las palabras reservadas que utiliza el lenguaje que definimos nosotros. Los que vamos a utilizar en nuestro evaluador son los siguientes:

tokens = (
    'COEFICIENTE',
    'VARIABLE',
    
    # Potencia
    'POW',
    # EQUALS
    'EQUALS',
    # Agrupacion
    'LPAREN',
    'RPAREN',
    # Operaciones binarias 
    'PLUS',
    'MINUS',
    'TIMES',
    'DIVIDE',
    # Funciones trigonometricas
    'SIN',
    'COS', 
    'TAN',
    # Funciones trigonometricas Inversas
    'SEC',
    'CSC', 
    'COT',    
    # Funcione Trigonometricas Hiperbolicas
    'SINH',
    'COSH',
    'TANH',
    # Funcione Trigonometricas Inversas Hiperbolicas
    'SECH',
    'CSCH', 
    'COTH',
    # PI
    'PI',
    # Exponente
    'EXP',
    # Logaritmo natural
    'LN',
    # Logaritmo base 2
    'LOG2',
    # Logaritmo base 10
    'LOG10',    
    # Logaritmo base 10
    'SQRT',    
    # Modulo 
    'MOD',
   
)

t_COEFICIENTE   = r'[0-9]+([.][0-9]+)?'

t_EQUALS        = r'='
t_POW           = r'\^'
t_LPAREN        = r'\('
t_RPAREN        = r'\)'
t_PLUS    = r'\+'
t_MINUS   = r'-'
t_TIMES   = r'\*'
t_DIVIDE  = r'/'
# Tokens Trigonometricas
t_SIN   = r'sin'
t_COS   = r'cos'
t_TAN   = r'tan'
# Tokens Trigonometricas Inversas
t_SEC   = r'sec'
t_CSC   = r'csc'
t_COT   = r'cot'
# Tokens Trigonometricas Hiperbolicas 
t_SINH  = r'sinh'
t_COSH  = r'cosh'
t_TANH  = r'tanh'
# Tokens Trigonometricas Inversas Hiperbolicas 
t_SECH  = r'sech'
t_CSCH  = r'csch'
t_COTH  = r'coth'
#PI
t_PI    = r'pi'
#EXP
t_EXP = r'exp'
# Logaritmo Natural
t_LN = r'ln'
# Logaritmo base 2
t_LOG2 = r'log2'
# Logaritmo base 10
t_LOG10 = r'log10'
# Raiz cuadrada
t_SQRT = r'sqrt'
# Operacion modulo
t_MOD = r'mod'

t_VARIABLE      =r'((?!(\b(sin|cos|tan|sec|csc|cot|tanh|sinh|cosh|tanh|sech|csch|cot|pi|exp|ln|log2|log10|sqrt|mod)\b)))[a-zA-Z_]'
t_ignore = " \t"
 
def t_newline(t):
    r'\n+'
    t.lexer.lineno += t.value.count("\n")
     
def t_error(t):
    print("Illegal character '%s'" % t.value[0])
    t.lexer.skip(1)

Reglas de parsing

Las reglas de parsing se utilizan para saber en qué orden se deben recibir las entradas del usuario, utilizando los tokens, permite dividir las entradas y así reconocer cada parte.
Las que se utilizan en el evaluador de polinomios trigonométricos son los siguientes:

import ply.lex as lex
lexer = lex.lex()

# Parsing rules
 
precedence = (
    ('right','UMINUS'),
    ('left','PLUS','MINUS'),
    ('left','TIMES','DIVIDE'),
    ('right','SIN'),
    ('right','COS'),
    ('right','TAN'),
    ('right','SEC'),
    ('right','CSC'),
    ('right','COT'),
    ('right','SINH'),
    ('right','COSH'),
    ('right','TANH'),
    ('right','SECH'),
    ('right','CSCH'),
    ('right','COTH'),
    ('right','EXP'),
    ('right','LN'),
    ('right','LOG2'),
    ('right','LOG10'),
    ('right','SQRT'),
    ('left','MOD'),
    ('left','POW'),
    #('PI'),

    )  

names = { }

# 'statement : polinomio'
def p_statement_expr(t):
    'statement : polinomio'
    print(t[1])

# 'statement : VARIABLE EQUALS polinomio'
def p_statement_assign(t):  
    'statement : VARIABLE EQUALS polinomio'
    names[t[1]] = t[3]

# 'subtermino : COEFICIENTE'
def p_subtermino_individual_coeficiente(t):
    'subtermino : COEFICIENTE'
    t[0] = float(t[1])

# 'subtermino : VARIABLE'
def p_subtermino_individual_variable(t):
    'subtermino : VARIABLE'
    try:
        t[0] = names[t[1]]
    except LookupError:
        print("Undefined variable '%s'" % t[1])
        t[0] = 0

# ''subtermino : subtermino POW COEFICIENTE''
def p_subtermino_individual_potencia(t):
    'subtermino : subtermino POW COEFICIENTE'
    t[0] = t[1] ** float(t[3])

# ''subtermino : subtermino POW polinomio''
def p_subtermino_individual_potencia_polinomio(t):
    'subtermino : subtermino POW LPAREN polinomio RPAREN'
    t[0] = t[1] ** float(t[4])

def p_polinomio_pi(t):
    'subtermino : PI'
    t[0] = math.pi

# 'termino : subtermino'   
def p_termino_subtermino(t):
    'termino : subtermino'   
    t[0] = t[1]    

# 'termino : termino subtermino'
def p_termino_subtermino_producto(t):
    'termino : termino subtermino' 
    t[0] = t[1]  * t[2]

# 'polinomio: termino'
def p_polinomio_termino(t):
    'polinomio : termino' 
    t[0] = t[1] 

def p_polinomio_binop(t):
    '''polinomio : polinomio PLUS polinomio
                  | polinomio MINUS polinomio
                  | polinomio TIMES polinomio
                  | polinomio DIVIDE polinomio'''
    if t[2] == '+'  : t[0] = t[1] + t[3]
    elif t[2] == '-': t[0] = t[1] - t[3]
    elif t[2] == '*': t[0] = t[1] * t[3]
    elif t[2] == '/': t[0] = t[1] / t[3]
 
def p_polinomio_uminus(t):
    'polinomio : MINUS polinomio %prec UMINUS'
    t[0] = -t[2]
# ========================================================================================
import math

def p_polinomio_tri(t):
    '''polinomio : SIN polinomio
                  | COS polinomio
                  | TAN polinomio'''
    if   t[1] == 'sin' :  t[0] = math.sin(t[2])
    elif t[1] == 'cos' :  t[0] = math.cos(t[2])
    elif t[1] == 'tan' :  t[0] = math.tan(t[2])

def p_polinomio_tri_inv(t):
    '''polinomio : SEC polinomio
                  | CSC polinomio
                  | COT polinomio'''
    if t[1] == 'sec' :  t[0] = 1/math.cos(float(t[2]))
    elif t[1] == 'csc' :  t[0] = 1/math.sin(float(t[2]))
    elif t[1] == 'cot' :  t[0] = 1/math.tan(float(t[2]))

def p_polinomio_hyper(t):
    '''polinomio : SINH polinomio
                  | COSH polinomio
                  | TANH polinomio'''
    if   t[1] == 'sinh' :  t[0] = math.sinh(float(t[2]))
    elif t[1] == 'cosh' :  t[0] = math.cosh(float(t[2]))
    elif t[1] == 'tanh' :  t[0] = math.tanh(float(t[2]))

def p_polinomio_inv_hyper(t):
    '''polinomio : SECH polinomio
                  | CSCH polinomio
                  | COTH polinomio'''
    if   t[1] == 'sech' :  t[0] = 1/math.cosh(float(t[2]))
    elif t[1] == 'csch' :  t[0] = 1/math.sinh(float(t[2]))
    elif t[1] == 'coth' :  t[0] = math.cosh(float(t[2]))/math.sinh(float(t[2]))

def p_expresion_exponencial(t):
    'polinomio : EXP polinomio'
    try: 
        t[0] = math.e ** t[2]
    except LookupError:
        print("Result too large");
        t[0] = 0

def p_expresion_logaritmo_natural(t):
    'polinomio : LN polinomio'
    t[0] = math.log(t[2])

def p_expresion_logaritmo_base2(t):
    'polinomio : LOG2 polinomio'
    t[0] = math.log2(t[2])

def p_expresion_logaritmo_base10(t):
    'polinomio : LOG10 polinomio'
    t[0] = math.log10(t[2])

def p_expresion_sqrt(t):
    'polinomio : SQRT polinomio'
    t[0] = math.sqrt(t[2])

def p_expresion_modulo(t):
    'polinomio : polinomio MOD polinomio'
    t[0] = t[1] % t[3]

# 'polinomio : LPAREN polinomio RPAREN'   
def p_polinomio_agroup(t):
    'polinomio : LPAREN polinomio RPAREN'   
    t[0] = t[2]

# 'polinomio : polinomio polinomio'   
def p_polinomio_polinomio(t):
    'polinomio : polinomio polinomio'   
    t[0] = t[1]*t[2]

# 'polinomio : LPAREN polinomio RPAREN POW LPAREN polinomio RPAREN'   
def p_polinomio_pow_polinomio(t):
    'polinomio : LPAREN polinomio RPAREN POW LPAREN polinomio RPAREN'   
    t[0] = t[1]**t[5]

def p_error(t):
    print("Syntax error at '%s'" % t.value)

# ========================================================================================
# YACC
# ========================================================================================
import ply.yacc as yacc
parser = yacc.yacc()

Y por último:

while True:
    try:
        s = input('polinomio > ')   # Use raw_input en Python 2
    except EOFError:
        break
    parser.parse(s)

En python copiar y pegar código es una pesadilla para los programadores ya que si no está bien estructurado, marca error o hace otra cosa. Pensé en eso y por eso, descarga el código de forma segura haciendo click aquí.

Si te marca error de ply, lo puedes instalar con este comando dependiendo de tu versión de pip.

pip3 install ply

¡No te vayas sin ponerte a prueba! Responde mis trivias sobre JavaScript, MySQL y Python haciendo click en este enlace. Cualquier duda deja un comentario y en breve te contesto.

Acerca del autor

Saintus Zephir

Ingeniero en Sistemas Computacionales y estudiante de Maestría en Ciencias en Ingeniería y Tecnologías Computacionales en el Centro de Investigación y de Estudios Avanzados del IPN (CINVESTAV-IPN).

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