def test_Variable():
variable1 = Variable(2, 'x', 3)
assert variable1.__str__() == "2{x}^{3}"
variable1.integrate('x')
assert variable1.__str__() == "0.5{x}^{4}"
# FIXME: Optimize integrate
"""
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 test_Variable():
variable1 = Variable(2, 'x', 3)
assert variable1.__str__() == "2{x}^{3}"
variable1, _ = variable1.integrate('x')
assert variable1.__str__() == "0.5{x}^{4}"
constant = Constant(3)
variable = Variable(2, 'x', 3)
add = variable + constant
assert add.__str__() == "{(2{x}^{3}+{3})}"
variable1 = Variable(2, 'x', 3)
variable2 = Variable(4, 'x', 3)
add1 = variable1 + variable2
assert add1.__str__() == "6{x}^{3}"
variable1 = Variable(2, 'x', 3)
constant = Constant(3)
exp1 = Expression([variable1, Plus(), constant])
variable2 = Variable(4, 'x', 3)
add2 = variable2 + exp1
assert add2.__str__() == "{(6{x}^{3}+{3})}"
variable1 = Variable(2, 'x', 3)
constant = Constant(3)
exp1 = variable1 + constant
variable2 = Variable(4, 'x', 3)
add2 = variable2 - exp1
assert add2.__str__() == "{(2{x}^{3}-{3})}"
variable1 = Variable(2, 'x', 3)
constant = Constant(3)
exp1 = Expression([variable1, Plus(), constant])
variable2 = Variable(4, 'x', 3)
add2 = exp1 - variable2
assert add2.__str__() == "{(-2{x}^{3}+{3})}"
constant = Constant(3)
variable = Variable(2, 'x', 3)
add = variable - constant
assert add.__str__() == "{(2{x}^{3}-{3})}"
variable1 = Variable(2, 'x', 3)
variable2 = Variable(4, 'x', 3)
variable3 = Variable(2, 'x', 4)
variable4 = Variable(2, 'x', 3)
add1 = variable1 - variable2
add2 = variable3 - variable4
assert add1.__str__() == "-2{x}^{3}"
assert add2.__str__() == "{(2{x}^{4}-2{x}^{3})}"
constant = Constant(3)
variable = Variable(2, 'x', 3)
add = variable * constant
assert add.__str__() == "6{x}^{3}"
variable1 = Variable(2, 'x', 3)
variable2 = Variable(4, 'x', 3)
add2 = variable1 * variable2
assert add2.__str__() == "8{x}^{6}"
variable1 = Variable(2, 'x', 3)
variable2 = Variable(4, 'y', 3)
add2 = variable1 * variable2
assert add2.__str__() == "8{x}^{3}{y}^{3}"
variable1 = Variable(2, 'x', 3)
variable2 = Variable(4, 'y', 4)
add1 = variable1 / variable2
assert add1.__str__() == "0.5{x}^{3}{y}^{-4}"
variable1 = Variable(2, 'x', 3)
constant = Constant(3)
exp1 = variable1 - constant
variable2 = Variable(4, 'x', 3)
add2 = variable2 / exp1
assert add2.__str__() == "{(4.0{x}^{3}*{(2{x}^{3}-{3})}^{-1})}"
variable1 = Variable(2, 'x', 3)
constant = Constant(3)
exp1 = variable1 - constant
variable2 = Variable(4, 'x', 3)
add2 = variable2 * exp1
assert add2.__str__() == "{(8{x}^{6}-12{x}^{3})}"
variable1 = Variable(2, 'x', 3)
constant1 = Constant(3)
exp1 = variable1 - constant1
variable2 = Variable(4, 'x', 3)
constant2 = Constant(4)
exp2 = variable2 - constant2
add2 = exp1 * exp2
assert add2.__str__() == "{({(8{x}^{6}-8{x}^{3})}-{(12{x}^{3}-{12})})}"
variable2 = Variable(3, 'x', -1)
variable2, _ = variable2.integrate('x')
assert tokensToString(variable2) == '3 * log(x)'
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