def multiplyVariables(variable1, variable2, coeff):
variable = Variable()
variable.value = []
variable.value.extend(variable1.value)
variable.power = []
variable.power.extend(variable1.power)
if isNumber(variable1.coefficient):
variable.coefficient = float(variable1.coefficient)
elif isinstance(variable1.coefficient, Function):
variable.coefficient = evaluateConstant(variable1.coefficient)
else:
variable.coefficient = variable1.coefficient
for j, var in enumerate(variable.value):
found = False
for k, var2 in enumerate(variable2.value):
if var == var2:
if isNumber(variable.power[j]) and isNumber(variable2.power[k]):
variable.power[j] += variable2.power[k]
found = True
break
if not found:
variable.value.append(variable2.value[j])
variable.power.append(variable2.power[j])
variable.coefficient *= variable2.coefficient
variable.coefficient *= coeff
# removeScopes.append(tokens[i].scope)
# removeScopes.append(tokens[i+1].scope)
return variable
def __mul__(self, other):
if other.isZero():
return other
elif self.isZero():
return self
elif isinstance(other, Constant):
const = Constant(self.calculate() * other.calculate())
return const
elif isinstance(other, Variable):
variable = Variable()
variable.coefficient = self.calculate() * other.coefficient
variable.value.extend(other.value)
variable.power.extend(other.power)
self = variable
return variable
elif isinstance(other, Expression):
if other.power == 1:
other.tokens[0] = self * other.tokens[0]
for i, var in enumerate(other.tokens):
if other.tokens[i-1].value == '+' or other.tokens[i-1].value == '-':
other.tokens[i] = self * var
else:
if isinstance(other.power, Constant) or isinstance(other.power, int) or isinstance(other.power, float):
self = self ** (-1 * other.power)
for i, var in enumerate(other.tokens):
if other.tokens[i - 1].value == '+' or other.tokens[i - 1].value == '-':
other.tokens[i] = self * var
else:
other.coefficient = self * other.coefficient
else:
other.coefficient = self.calculate() * other.coefficient
return other
def integrateTokens(funclist, wrtVar):
"""Integrates given tokens wrt given variable
Arguments:
funclist {list} -- list of function tokens
wrtVar {string} -- with respect to variable
Returns:
intFunc {list} -- list of integrated tokens
animNew {list} -- equation tokens for step-by-step
commentsNew {list} -- comments for step-by-step
"""
intFunc = []
animNew = []
commentsNew = [
"Integrating with respect to " + r"$" + wrtVar + r"$" + "\n"
]
for func in funclist:
if isinstance(func, Operator): # add isfunctionOf
intFunc.append(func)
else:
newfunc = []
commentsNew[0] += r"$" + r"\int \ " + r"( " + func.__str__(
) + ")" + r" d" + wrtVar + r"$"
funcCopy = copy.deepcopy(func)
if wrtVar in funcCopy.functionOf():
if isinstance(funcCopy, Variable):
log = False
funcCopy, log = funcCopy.integrate(wrtVar)
if log:
commentsNew[0] += r"$" + r"= " + funcCopy[0].__str__(
) + r"*" + funcCopy[2].__str__() + r"\ ;\ " + r"$"
newfunc.extend(funcCopy)
else:
commentsNew[0] += r"$" + r"= " + funcCopy.__str__(
) + r"\ ;\ " + r"$"
newfunc.append(funcCopy)
elif isinstance(funcCopy, Trigonometric):
funcCopy = funcCopy.integrate(wrtVar)
newfunc.append(funcCopy)
commentsNew[0] += r"$" + r"= " + funcCopy.__str__(
) + r"\ ;\ " + r"$"
else:
if isinstance(funcCopy, Variable):
funcCopy.value.append(wrtVar)
funcCopy.power.append(1)
if isinstance(funcCopy, Constant):
coeff = funcCopy.value
funcCopy = Variable()
funcCopy.coefficient = coeff
funcCopy.value.append(wrtVar)
funcCopy.power.append(1)
newfunc.append(funcCopy)
commentsNew[0] += r"$" + r"= " + funcCopy.__str__(
) + r"\ ;\ " + r"$"
intFunc.extend(newfunc)
animNew.extend(intFunc)
return intFunc, animNew, commentsNew
def multiplyVariableConstant(constant, variable, coeff):
variable1 = Variable()
variable1.value = []
variable1.value.extend(variable.value)
variable1.power = []
variable1.power.extend(variable.power)
if isNumber(variable.coefficient):
variable1.coefficient = float(variable.coefficient)
elif isinstance(variable.coefficient, Function):
variable1.coefficient = evaluateConstant(variable.coefficient)
else:
variable.coefficient = variable1.coefficient
variable1.coefficient *= evaluateConstant(constant)
variable1.coefficient *= coeff
# removeScopes.append(tokens[i].scope)
# removeScopes.append(tokens[i-1].scope)
return variable1
def division_constantVariable(constant, variable, coeff):
variable1 = Variable()
variable1.coefficient = (evaluateConstant(
constant) / variable.coefficient) * coeff
variable1.value = []
variable1.power = []
for i, var in enumerate(variable):
variable1.value.append(var)
variable1.power.append(-variable.power[i])
return variable1
def expressionDivision(variables, tokens):
removeScopes = []
comments = []
for i, token in enumerate(tokens):
if isinstance(token, Binary):
if token.value in ['/']:
prev = False
nxt = False
if i != 0:
if tokens[i - 1].__class__ in [Variable, Constant]:
prev = True
if i + 1 < len(tokens):
if tokens[i + 1].__class__ in [Variable, Constant]:
nxt = True
if nxt and prev:
if isinstance(tokens[i + 1], Constant) and isinstance(tokens[i - 1], Constant):
comments.append("Dividing " + r"$" + tokens[i - 1].__str__() + r"$" + " by " + r"$" + tokens[i + 1].__str__() + r"$")
no_1 = False
no_2 = False
if isNumber(tokens[i - 1].value):
no_1 = True
if isNumber(tokens[i + 1].value):
no_2 = True
if no_1 and no_2:
tokens[i + 1].value = evaluateConstant(
tokens[i - 1]) / evaluateConstant(tokens[i + 1])
tokens[i + 1].power = 1
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i - 1].scope)
elif no_1 and not no_2:
value = tokens[i - 1].value
power = tokens[i - 1].power
tokens[i - 1].value = [value]
tokens[i - 1].power = [power]
for val in tokens[i + 1].value:
tokens[i - 1].value.append(val)
for pows in tokens[i + 1].power:
tokens[i - 1].power.append(-pows)
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i + 1].scope)
elif not no_1 and no_2:
tokens[i - 1].value.append(tokens[i + 1].value)
tokens[i - 1].power.append(-tokens[i + 1].power)
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i + 1].scope)
elif not no_1 and not no_2:
for vals in tokens[i + 1].value:
tokens[i - 1].value.append(vals)
for pows in tokens[i + 1].power:
tokens[i - 1].power.append(pows)
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i + 1].scope)
return variables, tokens, removeScopes, comments
elif isinstance(tokens[i + 1], Variable) and isinstance(tokens[i - 1], Variable):
comments.append("Dividing " + r"$" + tokens[i - 1].__str__() + r"$" + " by " + r"$" + tokens[i + 1].__str__() + r"$")
for j, var in enumerate(tokens[i + 1].value):
found = False
for k, var2 in enumerate(tokens[i - 1].value):
tokens[i-1].coefficient /= tokens[i+1].coefficient
if var == var2:
if isNumber(tokens[i + 1].power[j]) and isNumber(tokens[i - 1].power[k]):
tokens[i - 1].power[k] -= tokens[i + 1].power[j]
if tokens[i - 1].power[k] == 0:
del tokens[i - 1].power[k]
del tokens[i - 1].value[k]
found = True
break
if not found:
tokens[i - 1].value.append(tokens[i + 1].value[j])
tokens[i - 1].power.append(-tokens[i + 1].power[j])
if len(tokens[i - 1].value) == 0:
constant = Constant()
constant.scope = tokens[i - 1].scope
constant.power = 1
constant.value = tokens[i - 1].coefficient
tokens[i - 1] = constant
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i + 1].scope)
return variables, tokens, removeScopes, comments
elif (isinstance(tokens[i + 1], Variable) and isinstance(tokens[i - 1], Constant)):
comments.append("Dividing " + r"$" + tokens[i - 1].__str__() + r"$" + " by " + r"$" + tokens[i + 1].__str__() + r"$")
val = evaluateConstant(tokens[i - 1])
scope = tokens[i - 1].scope
tokens[i - 1] = Variable()
tokens[i - 1].value = tokens[i + 1].value
tokens[i - 1].coefficient = val / \
tokens[i + 1].coefficient
tokens[i - 1].power = []
tokens[i - 1].scope = scope
for pows in tokens[i + 1].power:
tokens[i - 1].power.append(-pows)
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i + 1].scope)
return variables, tokens, removeScopes, comments
elif (isinstance(tokens[i - 1], Variable) and isinstance(tokens[i + 1], Constant)):
comments.append("Dividing " + r"$" + tokens[i - 1].__str__() + r"$" + " by " + r"$" + tokens[i + 1].__str__() + r"$")
tokens[i - 1].coefficient /= evaluateConstant(tokens[i + 1])
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i + 1].scope)
return variables, tokens, removeScopes, comments
return variables, tokens, removeScopes, comments
def getLevelVariables(tokens):
"""Returns tokens of Function class from a list of function tokens
Arguments:
tokens {list} -- list of function tokens
Returns:
variables {list} -- list of tokens of Function class(Variable/Constant)
"""
variables = []
for i, term in enumerate(tokens):
if isinstance(term, Variable):
skip = False
for var in variables:
if var.value == term.value and var.power[0] == term.power:
var.power.append(term.power)
var.scope.append(term.scope)
var.coefficient.append(term.coefficient)
if i != 0 and isinstance(tokens[i - 1], Binary):
var.before.append(tokens[i - 1].value)
var.beforeScope.append(tokens[i - 1].scope)
else:
var.before.append('')
var.beforeScope.append('')
if i + 1 < len(tokens) and isinstance(tokens[i + 1], Binary):
var.after.append(tokens[i + 1].value)
var.afterScope.append(tokens[i + 1].scope)
else:
var.after.append('')
var.afterScope.append('')
skip = True
break
if not skip:
variable = Variable()
variable.value = term.value
variable.scope = [term.scope]
variable.power = []
variable.coefficient = []
variable.before = []
variable.beforeScope = []
variable.after = []
variable.afterScope = []
variable.power.append(term.power)
variable.coefficient.append(term.coefficient)
if i != 0 and isinstance(tokens[i - 1], Binary):
variable.before.append(tokens[i - 1].value)
variable.beforeScope.append(tokens[i - 1].scope)
else:
variable.before.append('')
variable.beforeScope.append('')
if i + 1 < len(tokens) and isinstance(tokens[i + 1], Binary):
variable.after.append(tokens[i + 1].value)
variable.afterScope.append(tokens[i + 1].scope)
else:
variable.after.append('')
variable.afterScope.append('')
variables.append(variable)
elif isinstance(term, Constant):
skip = False
for var in variables:
if isinstance(var.value, list) and isNumber(var.value[0]):
if var.power[0] == term.power:
var.value.append(term.value)
var.power.append(term.power)
var.scope.append(term.scope)
if i != 0 and isinstance(tokens[i - 1], Binary):
var.before.append(tokens[i - 1].value)
var.beforeScope.append(tokens[i - 1].scope)
else:
var.before.append('')
var.beforeScope.append('')
if i + 1 < len(tokens) and isinstance(tokens[i + 1], Binary):
var.after.append(tokens[i + 1].value)
var.afterScope.append(tokens[i + 1].scope)
else:
var.after.append('')
var.afterScope.append('')
skip = True
break
if not skip:
variable = Constant()
variable.power = []
if isinstance(term.value, list):
variable.value = [evaluateConstant(term)]
variable.power.append(1)
else:
variable.value = [term.value]
variable.power.append(term.power)
variable.scope = [term.scope]
variable.before = []
variable.beforeScope = []
variable.after = []
variable.afterScope = []
if i != 0 and isinstance(tokens[i - 1], Binary):
variable.before.append(tokens[i - 1].value)
variable.beforeScope.append(tokens[i - 1].scope)
else:
variable.before.append('')
variable.beforeScope.append('')
if i + 1 < len(tokens) and isinstance(tokens[i + 1], Binary):
variable.after.append(tokens[i + 1].value)
variable.afterScope.append(tokens[i + 1].scope)
else:
variable.after.append('')
variable.afterScope.append('')
variables.append(variable)
elif isinstance(term, Expression):
var = getLevelVariables(term.tokens)
retType, val = extractExpression(var)
if retType == "expression":
variable = Expression()
variable.value = val
variable.tokens = term.tokens
variables.append(variable)
elif retType == "constant":
skip = False
for var in variables:
if isinstance(var.value, list) and isNumber(var.value[0]):
if var.power == val.power:
var.value.append(val.value)
var.power.append(val.power)
var.scope.append(val.scope)
var.before.append(val.before)
var.beforeScope.append(val.beforeScope)
var.after.append(val.after)
var.afterScope.append(val.afterScope)
skip = True
break
if not skip:
var = Constant()
var.value = [val.value]
var.power = [val.power]
var.scope = [val.scope]
var.before = [val.before]
var.beforeScope = [val.beforeScope]
var.after = []
var.afterScope = ['']
variables.append(var)
elif retType == "variable":
skip = False
for var in variables:
if var.value == val.value:
var.power.append(val.power)
var.before.append('')
var.beforeScope.append('')
var.after.append('')
var.afterScope.append('')
var.coefficient.append(val.coefficient)
var.scope.append(val.scope)
skip = True
break
if not skip:
var = Constant()
var.coefficient = [val.coefficient]
var.value = val.value
var.power = [val.power]
var.scope = [val.scope]
var.before = ['']
var.beforeScope = ['']
var.after = ['']
var.afterScope = ['']
variables.append(var)
elif retType == "mixed":
for v in val:
if isinstance(v, Variable):
skip = False
for var in variables:
if var.value == v.value:
var.power.extend(v.power)
var.before.extend(v.before)
var.beforeScope.extend(v.beforeScope)
var.after.extend(v.after)
var.afterScope.extend(v.afterScope)
var.coefficient.extend(v.coefficient)
var.scope.extend(v.scope)
skip = True
break
if not skip:
var = Constant()
var.coefficient = [v.coefficient]
var.value = v.value
var.power = [v.power]
var.scope = [v.scope]
var.before = [v.before]
var.beforeScope = [v.beforeScope]
var.after = [v.after]
var.afterScope = [v.afterScope]
variables.append(var)
elif isinstance(v, Constant):
for var in variables:
if isinstance(var.value, list) and isNumber(var.value[0]):
if var.power == v.power:
var.value.extend(v.value)
var.power.extend(v.power)
var.before.extend(v.before)
var.beforeScope.extend(
v.beforeScope)
var.after.extend(v.after)
var.afterScope.extend(v.afterScope)
var.coefficient.extend(v.coefficient)
var.scope.extend(v.scope)
skip = True
break
if not skip:
var = Constant()
var.coefficient = [v.coefficient]
var.value = [v.value]
var.power = [v.power]
var.scope = [v.scope]
var.before = [v.before]
var.beforeScope = [v.beforeScope]
var.after = [v.after]
var.afterScope = [v.afterScope]
variables.append(var)
elif isinstance(v, Expression):
variables.append(v)
return variables
def integrateTokens(funclist, wrtVar):
"""Integrates given tokens wrt given variable
Arguments:
funclist {list} -- list of funtion tokens
wrtVar {string} -- with respect to variable
Returns:
intFunc {list} -- list of integrated tokens
animNew {list} -- equation tokens for step-by-step
commentsNew {list} -- comments for step-by-step
"""
intFunc = []
animNew = []
commentsNew = [
"Integrating with respect to " + r"$" + wrtVar + r"$" + "\n"
]
for func in funclist:
if isinstance(func, Operator): # add isFuntionOf
intFunc.append(func)
else:
newfunc = []
while (isinstance(func, Function)):
commentsNew[0] += r"$" + "\int \ " + "( " + func.__str__(
) + ")" + " d" + wrtVar + r"$"
funcCopy = copy.deepcopy(func)
if wrtVar in funcCopy.functionOf():
if not isinstance(funcCopy, Constant):
for i, var in enumerate(funcCopy.value):
log = False
if var == wrtVar:
if (funcCopy.power[i] == -1):
log = True
funcLog = Logarithm()
funcLog.operand = Variable()
funcLog.operand.coefficient = 1
funcLog.operand.value.append(
funcCopy.value[i])
funcLog.operand.power.append(1)
del funcCopy.power[i]
del funcCopy.value[i]
if funcCopy.value == []:
funcCopy.__class__ = Constant
funcCopy.value = funcCopy.coefficient
funcCopy.coefficient = 1
funcCopy.power = 1
funcCopy = [funcCopy]
funcJoin = Binary()
funcJoin.value = '*'
funcCopy.append(funcJoin)
funcCopy.append(funcLog)
else:
funcCopy.power[i] += 1
funcCopy.coefficient /= funcCopy.power[i]
if log:
commentsNew[0] += r"$" + "= " + funcCopy[0].__str__(
) + "*" + funcCopy[2].__str__() + "\ ;\ " + r"$"
newfunc.extend(funcCopy)
else:
commentsNew[0] += r"$" + "= " + funcCopy.__str__(
) + "\ ;\ " + r"$"
newfunc.append(funcCopy)
else:
if isinstance(funcCopy, Variable):
funcCopy.value.append(wrtVar)
funcCopy.power.append(1)
if isinstance(funcCopy, Constant):
coeff = funcCopy.value
funcCopy = Variable()
funcCopy.coefficient = coeff
funcCopy.value.append(wrtVar)
funcCopy.power.append(1)
newfunc.append(funcCopy)
commentsNew[0] += r"$" + "= " + funcCopy.__str__(
) + "\ ;\ " + r"$"
if func.operand is None:
break
else:
func = func.operand
if isinstance(func, Constant):
intFunc = Zero()
break
intFunc.extend(newfunc)
animNew.extend(intFunc)
return intFunc, animNew, commentsNew