def __sub__(self, other):
if isinstance(other, Constant):
self = self + Constant(-1, 1, 1) * other
return self
elif isinstance(other, Variable):
if self.value == 0:
other.coefficient *= -1
return other
expression = Expression()
expression.tokens = [self]
expression.tokens.extend([Minus(), other])
elif isinstance(other, Expression):
expression = Expression()
expression.tokens = [self]
if other.power == 1:
coeff = other.coefficient
for i, token in enumerate(other.tokens):
print(expression, " ", type(token), other.tokens[i-1])
if isinstance(token, Constant):
if other.tokens[i-1].value == '+' or i == 0:
expression.tokens[0] = Constant(self.calculate() - token.calculate()*coeff)
elif other.tokens[i-1].value == '-':
expression.tokens[0] = Constant(self.calculate() + token.calculate()*coeff)
elif isinstance(token, Variable):
if other.tokens[i-1].value == '+' or i == 0:
expression.tokens.extend([Minus(), Variable(token)])
elif other.tokens[i-1].value == '-':
expression.tokens.extend([Plus(), Variable(token)])
else:
expression.tokens.extend([Minus(), other])
self = expression
return expression
def __sub__(self, other):
from visma.functions.constant import Constant
if isinstance(other, Variable):
otherValueSorted = sorted(other.value)
selfValueSorted = sorted(self.value)
if (other.power == self.power) & (selfValueSorted
== otherValueSorted):
self = self + Constant(-1, 1, 1) * other
return self
else:
expression = Expression()
expression.tokens = [self]
expression.tokens.extend([Minus(), other])
self = expression
return expression
elif isinstance(other, Constant):
if other.isZero():
return self
expression = Expression()
expression.tokens = [self]
expression.tokens.extend([Minus(), other])
self = expression
return expression
elif isinstance(other, Expression):
expression = Expression()
expression.tokens = [self]
for i, token in enumerate(other.tokens):
if isinstance(token, Variable):
tokenValueSorted = sorted(token.value)
selfValueSorted = sorted(self.value)
if (token.power == self.power) & (tokenValueSorted
== selfValueSorted):
if other.tokens[i - 1].value == '+' or (i == 0):
self.coefficient -= other.tokens[i].coefficient
elif other.tokens[i - 1].value == '-':
self.coefficient += other.tokens[i].coefficient
else:
if other.tokens[i - 1].value == '+' or i == 0:
expression.tokens.extend([Plus(), Variable(token)])
elif other.tokens[i - 1].value == '-':
expression.tokens.extend(
[Minus(), Variable(token)])
elif not isinstance(token, Binary):
if other.tokens[i - 1].value == '+' or (i == 0):
expression.tokens.extend([Minus(), token])
elif other.tokens[i - 1].value == '-':
expression.tokens.extend([Plus(), token])
expression.tokens[0] = self
self = expression
return expression
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 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=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
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 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()
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 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 __truediv__(self, other):
from visma.functions.constant import Constant
if isinstance(other, Variable) or isinstance(other, Constant):
self = self * (other**Constant(-1, 1, 1))
return self
elif isinstance(other, Expression):
expression = Expression()
self.coefficient /= other.coefficient
other.power *= -1
expression.tokens = [self]
expression.tokens.extend([Multiply(), other])
self = expression
return expression
def differentiationProductRule(tokens, wrtVar):
resultTokens = []
for i in range(0, len(tokens), 2):
currentDiff = Expression()
currentDiffTokens, _, _, _, _ = differentiate([tokens[i]], wrtVar)
currentDiff.tokens = currentDiffTokens
tempTokens = copy.deepcopy(tokens)
tempTokens[i] = currentDiff
resultTokens.extend(tempTokens)
resultTokens.append(Plus())
resultTokens.pop()
token_string = tokensToString(resultTokens)
# TODO: Make simplify module to simplify expressions involving Trigonometric Expressions (to some extent)
# resultTokens, _, token_string, _, _ = simplify(resultTokens)
return tokens, [], token_string, [], []
def differentiateTokens(funclist, wrtVar):
"""Differentiates given tokens wrt given variable
Arguments:
funclist {list} -- list of function tokens
wrtVar {string} -- with respect to variable
Returns:
diffFunc {list} -- list of differentiated tokens
animNew {list} -- equation tokens for step-by-step
commentsNew {list} -- comments for step-by-step
"""
diffFunc = []
animNew = []
commentsNew = ["Differentiating with respect to " + r"$" + wrtVar + r"$" + "\n"]
for func in funclist:
if isinstance(func, Operator):
diffFunc.append(func)
else:
newExpression = Expression()
newfunc = []
while(isinstance(func, Function)):
commentsNew[0] += r"$" + "\\frac{d}{d" + wrtVar + "} ( " + func.__str__() + ")" + r"$"
funcCopy = copy.deepcopy(func)
if wrtVar in funcCopy.functionOf():
if isinstance(funcCopy, Trigonometric) or isinstance(funcCopy, Logarithm) or isinstance(funcCopy, Variable) or isinstance(funcCopy, Exponential):
funcCopy = funcCopy.differentiate(wrtVar)
newfunc.append(funcCopy)
commentsNew[0] += r"$" + r"= " + funcCopy.__str__() + r"\ ;\ " + r"$"
else:
funcCopy = Zero()
newfunc.append(funcCopy)
commentsNew[0] += r"$" + r"= " + funcCopy.__str__() + r"\ ;\ " + r"$"
newfunc.append(Multiply())
if func.operand is None:
break
else:
func = func.operand
if isinstance(func, Constant):
diffFunc = Zero()
break
newfunc.pop()
newExpression.tokens = newfunc
diffFunc.extend([newExpression])
animNew.extend(diffFunc)
return diffFunc, animNew, commentsNew
def integrate(self, wrtVar):
if wrtVar not in self.value:
self.value.append(wrtVar)
self.power.append(1)
else:
for i, val in enumerate(self.value):
if val == 'wrtVar':
break
if self.power[i] == -1:
self.power.pop(i)
self.value.pop(i)
expression = Expression()
expression.tokens = [self]
variable = Variable(1, 'wrtVar', 1)
expression.tokens.append(Logarithm(variable))
self.__class__ = Expression
self = expression
else:
self.coefficient /= self.power[i] + 1
self.power[i] += 1
def cubicRoots(lTokens, rTokens):
'''Used to get roots of a cubic equation
This functions also translates roots {list} into final result of solution
Argument:
lTokens {list} -- list of LHS tokens
rTokens {list} -- list of RHS tokens
Returns:
lTokens {list} -- list of LHS tokens
rTokens {list} -- list of RHS tokens
{empty list}
token_string {string} -- final result stored in a string
animation {list} -- list of equation solving process
comments {list} -- list of comments in equation solving process
'''
from visma.solvers.polynomial.roots import getCoefficients
animations = []
comments = []
lTokens, rTokens, _, token_string, animNew1, commentNew1 = simplifyEquation(
lTokens, rTokens)
animations.extend(animNew1)
comments.extend(commentNew1)
if len(rTokens) > 0:
lTokens, rTokens = moveRTokensToLTokens(lTokens, rTokens)
coeffs = getCoefficients(lTokens, rTokens, 3)
var = getVariables(lTokens)
roots, animNew2, commentNew2 = getRootsCubic(coeffs)
animations.extend(animNew2)
comments.extend(commentNew2)
tokens1 = []
expression1 = Expression(coefficient=1, power=3)
variable = Variable(1, var[0], 1)
tokens1.append(variable)
if roots[0][1] == 0:
binary = Binary()
if roots[0][0] < 0:
roots[0][0] *= -1
binary.value = '+'
else:
binary.value = '-'
tokens1.append(binary)
constant = Constant(round(roots[0][0], ROUNDOFF), 1)
tokens1.append(constant)
expression1.tokens = tokens1
lTokens = [expression1, Binary('*')]
if len(roots) > 1:
expression1.power = 1
for _, root in enumerate(roots[1:]):
tokens2 = []
expression2 = Expression(coefficient=1, power=1)
variable = Variable(1, var[0], 1)
tokens2.append(variable)
binary = Binary()
if root[1] == 0:
if root[0] < 0:
root[0] *= -1
binary.value = '+'
else:
binary.value = '-'
tokens2.append(binary)
constant = Constant(round(root[0], ROUNDOFF), 1)
tokens2.append(constant)
else:
binary.value = '-'
tokens2.append(binary)
expressionResult = Expression(coefficient=1, power=1)
tokensResult = []
real = Constant(round(root[0], ROUNDOFF), 1)
tokensResult.append(real)
imaginary = Constant(round(root[1], ROUNDOFF), 1)
if imaginary.value < 0:
tokensResult.append(Minus())
imaginary.value = abs(imaginary.value)
tokensResult.append(imaginary)
else:
tokensResult.extend([Plus(), imaginary])
sqrt = Sqrt(Constant(2, 1), Constant(-1, 1))
tokensResult.append(Binary('*'))
tokensResult.append(sqrt)
expressionResult.tokens = tokensResult
tokens2.append(expressionResult)
expression2.tokens = tokens2
lTokens.extend([expression2, Binary('*')])
lTokens.pop()
rTokens = [Zero()]
tokenToStringBuilder = copy.deepcopy(lTokens)
tokLen = len(lTokens)
equalTo = Binary()
equalTo.scope = [tokLen]
equalTo.value = '='
tokenToStringBuilder.append(equalTo)
tokenToStringBuilder.extend(rTokens)
token_string = tokensToString(tokenToStringBuilder)
animations.append(copy.deepcopy(tokenToStringBuilder))
comments.append([])
return lTokens, rTokens, [], token_string, animations, comments
def quadraticRoots(lTokens, rTokens):
'''Used to get quadratic roots of an equation
Argument:
lTokens {list} -- list of LHS tokens
rTokens {list} -- list of RHS tokens
Returns:
lTokens {list} -- list of LHS tokens
rTokens {list} -- list of RHS tokens
{empty list}
token_string {string} -- final result stored in a string
animation {list} -- list of equation solving process
comments {list} -- list of comments in equation solving process
'''
from visma.solvers.polynomial.roots import getCoefficients
animations = []
comments = []
lTokens, rTokens, _, token_string, animNew1, commentNew1 = simplifyEquation(lTokens, rTokens)
animations.extend(animNew1)
comments.extend(commentNew1)
if len(rTokens) > 0:
lTokens, rTokens = moveRTokensToLTokens(lTokens, rTokens)
coeffs = getCoefficients(lTokens, rTokens, 2)
var = getVariables(lTokens)
roots, animNew2, commentNew2 = getRootsQuadratic(coeffs)
animations.extend(animNew2)
comments.extend(commentNew2)
if len(roots) == 1:
tokens = []
expression = Expression(coefficient=1, power=2)
variable = Variable(1, var[0], 1)
tokens.append(variable)
binary = Binary()
if roots[0] < 0:
roots[0] *= -1
binary.value = '+'
else:
binary.value = '-'
tokens.append(binary)
constant = Constant(round(roots[0], ROUNDOFF), 1)
tokens.append(constant)
expression.tokens = tokens
lTokens = [expression]
elif len(roots) == 2:
tokens = []
expression = Expression(coefficient=1, power=1)
variable = Variable(1, var[0], 1)
tokens.append(variable)
binary = Binary()
if roots[0] < 0:
roots[0] *= -1
binary.value = '+'
else:
binary.value = '-'
tokens.append(binary)
constant = Constant(round(roots[0], ROUNDOFF), 1)
tokens.append(constant)
expression.tokens = tokens
tokens2 = []
expression2 = Expression(coefficient=1, power=1)
tokens2.append(variable)
binary2 = Binary()
if roots[1] < 0:
roots[1] *= -1
binary2.value = '+'
else:
binary2.value = '-'
tokens2.append(binary2)
constant2 = Constant(round(roots[1], ROUNDOFF), 1)
tokens2.append(constant2)
expression2.tokens = tokens2
binary3 = Binary()
binary3.value = '*'
lTokens = [expression, binary3, expression2]
elif len(roots) == 3:
binary4 = Binary()
if roots[0] < 0:
roots[0] *= -1
binary4.value = '+'
else:
binary4.value = '-'
constant3 = Constant(round(roots[0], ROUNDOFF), 1)
binary5 = Binary()
binary5.value = '*'
constant2 = Constant(round(roots[2], ROUNDOFF), 1)
tokens = []
expression = Expression(coefficient=1, power=1)
variable = Variable(1, var[0], 1)
tokens.extend([variable, binary4, constant3])
binary = Binary()
binary.value = '+'
tokens.extend([binary, constant2, binary5])
constant = Constant(round(roots[1], ROUNDOFF), 1)
sqrt = Sqrt(Constant(2, 1), constant)
tokens.append(sqrt)
expression.tokens = tokens
tokens2 = []
expression2 = Expression(coefficient=1, power=1)
variable2 = Variable(1, var[0], 1)
tokens2.extend([variable2, binary4, constant3])
binary2 = Binary()
binary2.value = '-'
tokens2.extend([binary2, constant2, binary5, sqrt])
expression2.tokens = tokens2
binary3 = Binary()
binary3.value = '*'
lTokens = [expression, binary3, expression2]
zero = Zero()
rTokens = [zero]
comments.append([])
tokenToStringBuilder = copy.deepcopy(lTokens)
tokLen = len(lTokens)
equalTo = Binary()
equalTo.scope = [tokLen]
equalTo.value = '='
tokenToStringBuilder.append(equalTo)
tokenToStringBuilder.extend(rTokens)
animations.append(copy.deepcopy(tokenToStringBuilder))
token_string = tokensToString(tokenToStringBuilder)
return lTokens, rTokens, [], token_string, animations, comments