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import math
import copy
from visma.functions.structure import FuncOp, Expression
from visma.functions.operator import Multiply, Plus
from visma.functions.constant import Constant
from visma.functions. exponential import NaturalLog
##########################
# Trignometric Functions #
##########################
class Trigonometric(FuncOp):
"""Parent Class for all the Trigonometric Classes like Sine, Cosine, Tangent etc.
"""
pass
class Sine(Trigonometric):
"""Class for sin function -- sin(...)
Extends:
Trigonometric
"""
def __init__(self):
super().__init__()
self.value = 'sin'
def inverse(self, rToken, wrtVar, inverseFunction=None):
inverseFunction = ArcSin()
super().inverse(self, rToken, wrtVar, inverseFunction)
def calculate(self, val):
return self.coefficient * ((math.sin(val))**self.power)
def differentiate(self, wrtVar=None):
super().differentiate()
result = copy.deepcopy(self)
result.__class__ = Cosine
result.value = 'cos'
result.coefficient = 1
return result
def integrate(self, wrtVar=None):
term1 = Constant(-1, 1, 1)
term2 = copy.deepcopy(self)
term2.__class__ = Cosine
term2.value = 'cos'
term2.coefficient = 1
result = Expression()
result.tokens = [term1, Multiply(), term2]
return result
class Cosine(Trigonometric):
"""Class for cos function -- cos(...)
Extends:
Trigonometric
"""
def __init__(self):
super().__init__()
self.value = 'cos'
def inverse(self, RHS):
super().inverse(RHS)
self.__class__ = ArcCos
def differentiate(self, wrtVar):
term1 = Constant(-1, 1, 1)
term2 = copy.deepcopy(self)
term2.__class__ = Sine
term2.value = 'sin'
result = Expression()
result.tokens = [term1, Multiply(), term2]
return result
def integrate(self, wrtVar):
result = copy.deepcopy(self)
result.__class__ = Sine
result.value = 'sin'
result.coefficient = 1
return result
def calculate(self, val):
return self.coefficient * ((math.cos(val))**self.power)
class Tangent(Trigonometric):
"""Class for tan function -- tan(...)
Extends:
Trigonometric
"""
def __init__(self):
super().__init__()
self.value = 'tan'
def inverse(self, RHS):
super().inverse(RHS)
self.__class__ = ArcTan
def differentiate(self, wrtVar):
result = copy.deepcopy(self)
result.__class__ = Secant
result.value = 'sec'
result.coefficient = 1
result.power = 2
return result
def integrate(self, wrtVar):
term1 = Constant(-1, 1, 1)
term2 = NaturalLog()
term3 = Cosine()
term3.operand = self.operand
term2.operand = term3
term2.power = 1
term2.coefficient = 1
result = Expression()
result.tokens = [term1, Multiply(), term2]
return result
def calculate(self, val):
return self.coefficient * ((math.tan(val))**self.power)
class Cotangent(Trigonometric):
"""Class for cot function -- cot(...)
Extends:
Trigonometric
"""
def __init__(self):
super().__init__()
self.value = 'cot'
def inverse(self, RHS):
super().inverse(RHS)
self.__class__ = ArcCot
def differentiate(self, wrtVar):
term1 = Constant(-1, 1, 1)
term2 = copy.deepcopy(self)
term2.__class__ = Cosecant
term2.value = 'csc'
term2.coefficient = 1
term2.power = 2
result = Expression()
result.tokens = [term1, Multiply(), term2]
return result
def integrate(self, wrtVar):
result = NaturalLog()
term1 = Sine()
term1.operand = self.operand
term1.power = 1
term1.coefficient = 1
result.operand = term1
return result
def calculate(self, val):
return self.coefficient * ((math.cot(val))**self.power)
class Cosecant(Trigonometric):
"""Class for csc function -- csc(...)
Extends:
Trigonometric
"""
def __init__(self):
super().__init__()
self.value = 'csc'
def inverse(self, RHS):
super().inverse(RHS)
self.__class__ = ArcCosec
def differentiate(self, wrtVar):
term1 = Constant(-1, 1, 1)
term2 = Cosecant()
term2.operand = self.operand
term2.coefficient = 1
term3 = Cotangent()
term3.operand = self.operand
term3.coefficient = 1
result = Expression()
result.tokens = [term1, Multiply(), term2, Multiply(), term3]
return result
def integrate(self, wrtVar):
term1 = Constant(-1, 1, 1)
term2 = NaturalLog()
result = Expression()
term3 = Cosecant()
term3.operand = self.operand
term4 = Cotangent()
term4.operand = self.operand
inExpression = Expression()
inExpression.tokens = [term3, Plus(), term4]
term2.operand = inExpression
term2.power = 1
term2.coefficient = 1
result.tokens = [term1, Multiply(), term2]
return result
def __mul__(self, other):
if isinstance(other, Cotangent):
result = Expression()
result.coefficient = self.coefficient * other.coefficient
c = copy.deepcopy(self)
d = copy.deepcopy(other)
result.tokens.extend([c, Multiply(), d])
return result
def calculate(self, val):
return self.coefficient * ((math.cosec(val))**self.power)
class Secant(Trigonometric):
"""Class for sec function -- sec(...)
Extends:
Trigonometric
"""
def __init__(self):
super().__init__()
self.value = 'sec'
def inverse(self, RHS):
super().inverse(RHS)
self.__class__ = ArcSec
def differentiate(self, wrtVar):
term1 = Tangent()
term1.operand = self.operand
term2 = Secant()
term2.operand = self.operand
resultTerm = term2 * term1
return resultTerm
def integrate(self, wrtVar):
resultTerm = NaturalLog()
term3 = Secant()
term3.operand = self.operand
term4 = Tangent()
term4.operand = self.operand
inExpression = Expression()
inExpression.tokens = [term3, Plus(), term4]
resultTerm.operand = inExpression
resultTerm.power = 1
resultTerm.coefficient = 1
return resultTerm
def __mul__(self, other):
if isinstance(other, Tangent):
result = Expression()
Expression.coefficient = self.coefficient * other.coefficient
c = copy.deepcopy(self)
d = copy.deepcopy(other)
result.tokens.extend([c, Multiply(), d])
return result
def calculate(self, val):
return self.coefficient * ((math.sec(val))**self.power)
##################################
# Inverse Trignometric Functions #
##################################
class ArcSin(Trigonometric):
pass
class ArcCos(Trigonometric):
pass
class ArcTan(Trigonometric):
pass
class ArcCot(Trigonometric):
pass
class ArcSec(Trigonometric):
pass
class ArcCsc(Trigonometric):
pass
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