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import copy |
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from visma.functions.constant import Constant |
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from visma.functions.variable import Variable |
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from visma.functions.operator import Operator, Binary |
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from visma.simplify.simplify import simplify |
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from visma.functions.trigonometry import Trigonometric |
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from visma.calculus.differentiation import differentiate |
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from visma.io.parser import tokensToString |
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def integrate(tokens, wrtVar): |
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"""Simplifies and then integrates given tokens wrt given variable |
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Arguments: |
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tokens {list} -- list of function tokens |
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wrtVar {string} -- with respect to variable |
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Returns: |
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tokens {list} -- list of integrated tokens |
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availableOperations {list} -- list of operations |
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token_string {string} -- output equation string |
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animation {list} -- equation tokens for step-by-step |
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comments {list} -- comments for step-by-step |
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""" |
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tokens, availableOperations, token_string, animation, comments = simplify(tokens) |
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tokens, animNew, commentsNew = (integrateTokens(tokens, wrtVar)) |
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animation.append(animNew) |
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comments.append(commentsNew) |
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tokens, availableOperations, token_string, animation2, comments2 = simplify(tokens) |
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animation2.pop(0) |
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comments2.pop(0) |
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animation.extend(animation2) |
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comments.extend(comments2) |
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return tokens, availableOperations, token_string, animation, comments |
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def integrateTokens(funclist, wrtVar): |
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"""Integrates given tokens wrt given variable |
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Arguments: |
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funclist {list} -- list of function tokens |
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wrtVar {string} -- with respect to variable |
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Returns: |
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intFunc {list} -- list of integrated tokens |
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animNew {list} -- equation tokens for step-by-step |
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commentsNew {list} -- comments for step-by-step |
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""" |
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intFunc = [] |
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animNew = [] |
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commentsNew = ["Integrating with respect to " + r"$" + wrtVar + r"$" + "\n"] |
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for func in funclist: |
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if isinstance(func, Operator): |
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intFunc.append(func) |
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else: |
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newfunc = [] |
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commentsNew[0] += r"$" + r"\int \ " + r"( " + func.__str__() + ")" + r" d" + wrtVar + r"$" |
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funcCopy = copy.deepcopy(func) |
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if wrtVar in funcCopy.functionOf(): |
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if isinstance(funcCopy, Variable): |
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log = False |
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funcCopy, log = funcCopy.integrate(wrtVar) |
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if log: |
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commentsNew[0] += r"$" + r"= " + funcCopy[0].__str__() + r"*" + funcCopy[2].__str__() + r"\ ;\ " + r"$" |
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newfunc.extend(funcCopy) |
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else: |
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commentsNew[0] += r"$" + r"= " + funcCopy.__str__() + r"\ ;\ " + r"$" |
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newfunc.append(funcCopy) |
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elif isinstance(funcCopy, Trigonometric): |
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funcCopy = funcCopy.integrate(wrtVar) |
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newfunc.append(funcCopy) |
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commentsNew[0] += r"$" + r"= " + funcCopy.__str__() + r"\ ;\ " + r"$" |
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else: |
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if isinstance(funcCopy, Variable): |
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funcCopy.value.append(wrtVar) |
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funcCopy.power.append(1) |
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if isinstance(funcCopy, Constant): |
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coeff = funcCopy.value |
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funcCopy = Variable() |
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funcCopy.coefficient = coeff |
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funcCopy.value.append(wrtVar) |
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funcCopy.power.append(1) |
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newfunc.append(funcCopy) |
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commentsNew[0] += r"$" + r"= " + funcCopy.__str__() + r"\ ;\ " + r"$" |
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intFunc.extend(newfunc) |
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animNew.extend(intFunc) |
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return intFunc, animNew, commentsNew |
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def integrationByParts(tokens, wrtVar): |
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if (isinstance(tokens[1], Binary) and tokens[1].value == '*'): |
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u = tokens[0] |
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v = tokens[2] |
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vIntegral, _, _, _, _ = integrate(v, wrtVar) |
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uDerivative, _, _, _, _ = differentiate(u, wrtVar) |
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term1 = u * vIntegral |
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term2, _, _, _, _ = integrate(uDerivative * vIntegral, 'x') |
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resultToken = term1 - term2 |
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token_string = tokensToString(resultToken) |
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return resultToken, [], token_string, [], [] |
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