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import copy
from visma.functions.constant import Constant
from visma.functions.variable import Variable
from visma.functions.operator import Operator, Binary
from visma.simplify.simplify import simplify
from visma.functions.trigonometry import Trigonometric
from visma.calculus.differentiation import differentiate
from visma.io.parser import tokensToString
###############
# Integration #
###############
def integrate(tokens, wrtVar):
"""Simplifies and then integrates given tokens wrt given variable
Arguments:
tokens {list} -- list of function tokens
wrtVar {string} -- with respect to variable
Returns:
tokens {list} -- list of integrated tokens
availableOperations {list} -- list of operations
token_string {string} -- output equation string
animation {list} -- equation tokens for step-by-step
comments {list} -- comments for step-by-step
"""
tokens, availableOperations, token_string, animation, comments = simplify(tokens)
tokens, animNew, commentsNew = (integrateTokens(tokens, wrtVar))
animation.append(animNew)
comments.append(commentsNew)
tokens, availableOperations, token_string, animation2, comments2 = simplify(tokens)
animation2.pop(0)
comments2.pop(0)
animation.extend(animation2)
comments.extend(comments2)
return tokens, availableOperations, token_string, animation, comments
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 integrationByParts(tokens, wrtVar):
if (isinstance(tokens[1], Binary) and tokens[1].value == '*'):
u = tokens[0]
v = tokens[2]
vIntegral, _, _, _, _ = integrate(v, wrtVar)
uDerivative, _, _, _, _ = differentiate(u, wrtVar)
term1 = u * vIntegral
term2, _, _, _, _ = integrate(uDerivative * vIntegral, 'x')
resultToken = term1 - term2
token_string = tokensToString(resultToken)
return resultToken, [], token_string, [], []
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