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:
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 not isinstance(funcCopy, Constant):
for i, var in enumerate(funcCopy.value):
if var == wrtVar:
funcCopy.coefficient *= funcCopy.power[i]
funcCopy.power[i] -= 1
if(funcCopy.power[i] == 0):
del funcCopy.power[i]
del funcCopy.value[i]
if funcCopy.value == []:
funcCopy.__class__ = Constant
funcCopy.value = funcCopy.coefficient
funcCopy.coefficient = 1
funcCopy.power = 1
commentsNew[0] += r"$" + r"= " + funcCopy.__str__() + r"\ ;\ " + r"$"
newfunc.append(funcCopy)
func.differentiate()
if not(isinstance(func, Constant) and func.value == 1):
newfunc.append(func)
else:
funcCopy = (Zero())
newfunc.append(funcCopy)
commentsNew[0] += r"$" + r"= " + funcCopy.__str__() + r"\ ;\ " + r"$"
if func.operand is None:
break
else:
func = func.operand
if isinstance(func, Constant):
diffFunc = Zero()
break
diffFunc.extend(newfunc)
animNew.extend(diffFunc)
return diffFunc, animNew, commentsNew
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 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