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import copy |
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from visma.functions.structure import Function, Expression |
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from visma.functions.constant import Constant, Zero |
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from visma.functions.operator import Operator, Multiply, Plus |
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from visma.simplify.simplify import simplify |
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from visma.functions.variable import Variable |
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from visma.functions.exponential import Logarithm, Exponential |
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from visma.functions.trigonometry import Trigonometric |
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from visma.io.parser import tokensToString |
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def differentiate(tokens, wrtVar): |
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"""Simplifies and then differentiates 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 differentiated 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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animation = [] |
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comments = [] |
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tokens, availableOperations, token_string, animation, comments = simplify(tokens) |
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tokens, animNew, commentsNew = differentiateTokens(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 differentiateTokens(funclist, wrtVar): |
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"""Differentiates 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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diffFunc {list} -- list of differentiated 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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diffFunc = [] |
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animNew = [] |
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commentsNew = ["Differentiating 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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diffFunc.append(func) |
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else: |
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newExpression = Expression() |
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newfunc = [] |
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while(isinstance(func, Function)): |
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commentsNew[0] += r"$" + "\\frac{d}{d" + wrtVar + "} ( " + func.__str__() + ")" + r"$" |
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funcCopy = copy.deepcopy(func) |
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if wrtVar in funcCopy.functionOf(): |
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if isinstance(funcCopy, Trigonometric) or isinstance(funcCopy, Logarithm) or isinstance(funcCopy, Variable) or isinstance(funcCopy, Exponential): |
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funcCopy = funcCopy.differentiate(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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funcCopy = Zero() |
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newfunc.append(funcCopy) |
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commentsNew[0] += r"$" + r"= " + funcCopy.__str__() + r"\ ;\ " + r"$" |
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newfunc.append(Multiply()) |
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if func.operand is None: |
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break |
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else: |
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func = func.operand |
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if isinstance(func, Constant): |
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diffFunc = Zero() |
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break |
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newfunc.pop() |
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newExpression.tokens = newfunc |
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diffFunc.extend([newExpression]) |
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animNew.extend(diffFunc) |
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return diffFunc, animNew, commentsNew |
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def differentiationProductRule(tokens, wrtVar): |
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resultTokens = [] |
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for i in range(0, len(tokens), 2): |
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currentDiff = Expression() |
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currentDiffTokens, _, _, _, _ = differentiate([tokens[i]], wrtVar) |
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currentDiff.tokens = currentDiffTokens |
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tempTokens = copy.deepcopy(tokens) |
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tempTokens[i] = currentDiff |
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resultTokens.extend(tempTokens) |
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resultTokens.append(Plus()) |
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resultTokens.pop() |
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token_string = tokensToString(resultTokens) |
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return tokens, [], token_string, [], [] |
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