Question: Question) Give the code for the following functions where the class below is given: a) def derivate_leaf(e, x), b) def derivate(e, x), c) def test_derivative(f,

Question) Give the code for the following functions where the class below is given: a) def derivate_leaf(e, x), b) def derivate(e, x), c) def test_derivative(f, df, x, delta=0.0001, epsilon=0.1, num_tests=1000), and d) def apply_distributive(e). It must follow the exact parameters and pass the tests assigned to each function below. Insert code where it says, "YOUR CODE HERE."

Question) Give the code for the following functions where the class below

is given: a) def derivate_leaf(e, x), b) def derivate(e, x), c) def

test_derivative(f, df, x, delta=0.0001, epsilon=0.1, num_tests=1000), and d) def apply_distributive(e). It must

follow the exact parameters and pass the tests assigned to each function

below. Insert code where it says, "YOUR CODE HERE." 4 1 ###

Derivation of a leaf expression 2. 3 def derivate_leaf(e, x): ***"This function

4 1 ### Derivation of a leaf expression 2. 3 def derivate_leaf(e, x): ***"This function takes as input an expression e and a variable x, 5 and returns the symbolic derivative of e wrt. X, as an expression." 6 ### YOUR CODE HERE 7 1 ## Derivative of a leaf expression. 2 points. 2. == 1 3 assert derivate_leaf("x", "x") 4 assert derivate_leaf("x", "y") 5 assert derivate_leaf ("y", "z" 6 assert derivate_leaf(4, "x") @ 7. 1 ## Hidden tests for derivative of a leaf expression. 3 points. 2 1 ### Implement "derivate 2. 3 def derivate(e, x): ** "Returns the derivative of e wrt x. 5 It can be done in less than 15 lines of code. 6 ### YOUR CODE HERE EFE 7 1 ### Tests for derivate for single-operator expressions. 4 points. 3 assert derivate(('+', 'x', 'x'), 'x') == ('+', 1, 1) 4 assert derivate(('-', 4, 'x'), 'x') == ('-', 0, 1) 5 assert derivate(('*', 2, 'x'), 'x') ('+', ('*', 0, 'x'), ('*', 2, 1)) 6 assert derivate(('/', 2, 'x'), 'x') == ('7', ('-', ('*', 0, 'x'), ('*', 2, 1)), ('*', 'x', 'x')) 1 ### Hidden tests for 'derivate for single-operator expressions. 6 points. [] 1 ### Tests for derivate for composite expressions. 3 points. 2 3 e1 = ('*', 'x', 'x') 4 e2 = ('*', 3, 'x') 5 num = ('-', ei, e2) 6 e3 = (*', 'a', 'x') 7 den = ('+', el, e3) 8 e = ('7', num, den) 9 10 f = ('7', 11 ('-', 12 13 14 15 16 ('+', ('*', 1, 'x'), ('*', 'x', 1)), ('+', ('*', 0, 'x'), ('*', 3, 1))), ('+', ("*', 'x', 'x'), ('*', 'a', 'x'))), 18 ('-', ('*', 'x', 'x'), ('*', 3, 'x')), 19 28 ('+', ('*', 1, 'x'), ('*', 'x', 1)), ('+', ('*', 0, 'x'), ('*', 'a', 1))))), 22 ('*', 23 ('+', ('*', 'x', 'x'), ('*', 'a', 'x')), 24 ('+', ("*', 'x', 'x'), ('*', 'a', 'x')))) 25 26 assert derivate(e, 'x') == f [ ] 1 ### Hidden tests for "derivate for composite expressions. 7 points. 2 1 ### Implementation of test_derivative 2 2 3 def test_derivative(f, df, x, delta=0.8ee1, epsilon=0.1, num_tests=1808): See above." 5. ### YOUR CODE HERE 4. 1 ### Tests for test_derivative, 4 points. 2 3 f = ("+", ("*", "cat", "cat"), ("*", "dog", "cat")) 4 df1 = ("+", ("*", 2, "cat"), "dog") 5 df2 = ("+", ("*", 2, "cat"), ("*", "dog", "cat")) 7 assert test_derivative(f, df1, "cat") 8 assert not test_derivative(f, df2,"cat") 9 assert not test_derivative(f, dfi, "dog") 10 assert not test_derivative(f, dfi, 'donkey") 11 assert test_derivative(f, o, "donkey") 12 1 ### Hidden tests for test_derivative, 6 points. 1 ### Exercise: Implement apply distributive 2 3 def apply_distributive(e): ""Applies the distributive property to an expression e. 5 ### YOUR CODE HERE 4 *** 6 ] 1 ### Simple test for distributivity. 2 points. 2 3 ## Here is a definition of equality that disregards order. 4 def is_distributed (exp): 5 def is_plusminus(exp) : return isinstance(exp, tuple) and exp[@] in '+- if isinstance(exp, tuple): 9 op, ei, e2 = exp if op == and (is_plusminus (el) or is_plusminus (e2)): return false return is distributed (el) and is_distributed (22) 13 14 import random Boomvon 16 def value_equality(e1, e2): 17 return True 18 19 20 def applied distributivity(f, g): 21 return is_distributed(g) and value_equality(f, g) 23 # Simple test 24 ('*', ('+', 1, 2), ('-', 3, 4)) 26 f = ('+', ('-', ('*', 1, 3), ('*', 1, 4)), ('-', ('*', 2, 3), (**', 2, 4))) 27 applied_distributivity(apply_distributive(e), f) 25 e = 28 29 1 ### More complicated tests for distributivity. 2 points. 2 3 # More complex tests 4 5e = ("*', ('+', 1, 2), ('-', 3, 4)) 6 e2 = ('*', e, ('+', 5, 6)) 7 f = ('+', 8 (-', ('+', ('*', ('*', 1, 3), 5), ('*', ('*', 1, 3), 6)), 10 ('+', ('*', ('*', 1, 4), 5), ('*', ('', 1, 4), 6))), 11 (-', 12 ('+', ('*', ('*', 2, 3), 5), ('*', ('', 2, 3), 6)), 13 ('+', ('*', ('*', 2, 4), 5), ('*', ('*', 2, 4), 6)))) 14 15 applied_distributivity(apply_distributive (e2), f) 17 e = ('*', ('*', ('+', 1, 2), ('-', 3, 4)), (''', ('-', 5, 6), ('+', 7, 8))) 18 f = ('+', 19 (-", ('+', ('*', ('*', 1, 3), ('*', 5, 7)), ('*', ('*', 1, 3), ('*', 5, 8))), ('+', ('*', ('*', 1, 3), ('*', 6, 7)), ('*', ('*', 1, 3), ('*', 6, 8)))), 23 24 ('+', ('*', ('*', 1, 4), ('*', 5, 7)), ('*', ('', 1, 4), (':', 5, 8))), 25 ('+', ('*', ('*', 1, 4), (*, 6, 7)), ('*, ('*', 1, 4), ('*', 6, 8))))), 26 ('-', 27 28 ('+', (**, ('*', 2, 3), ('*', 5, 7)), ('*', ('*', 2, 3), ('*', 5, 8))), 29 ('+', ('*', ('*', 2, 3), ('*', 6, ?)), ('*', ('*', 2, 3), (**, 6, 8)))), 30 31 ('+', ('*', ('*', 2, 4), ('*', 5, 7)), ('*', ('*', 2, 4), ('*', 5, 8))), 32 ('+', ('*', ('*', 2, 4), ('*', 6, 7)), ('*', ('*', 2, 4), ('*', 6, 8)))))) 33 34 applied_distributivity(apply distributive(e), f) 35 36 4 1 ### Derivation of a leaf expression 2. 3 def derivate_leaf(e, x): ***"This function takes as input an expression e and a variable x, 5 and returns the symbolic derivative of e wrt. X, as an expression." 6 ### YOUR CODE HERE 7 1 ## Derivative of a leaf expression. 2 points. 2. == 1 3 assert derivate_leaf("x", "x") 4 assert derivate_leaf("x", "y") 5 assert derivate_leaf ("y", "z" 6 assert derivate_leaf(4, "x") @ 7. 1 ## Hidden tests for derivative of a leaf expression. 3 points. 2 1 ### Implement "derivate 2. 3 def derivate(e, x): ** "Returns the derivative of e wrt x. 5 It can be done in less than 15 lines of code. 6 ### YOUR CODE HERE EFE 7 1 ### Tests for derivate for single-operator expressions. 4 points. 3 assert derivate(('+', 'x', 'x'), 'x') == ('+', 1, 1) 4 assert derivate(('-', 4, 'x'), 'x') == ('-', 0, 1) 5 assert derivate(('*', 2, 'x'), 'x') ('+', ('*', 0, 'x'), ('*', 2, 1)) 6 assert derivate(('/', 2, 'x'), 'x') == ('7', ('-', ('*', 0, 'x'), ('*', 2, 1)), ('*', 'x', 'x')) 1 ### Hidden tests for 'derivate for single-operator expressions. 6 points. [] 1 ### Tests for derivate for composite expressions. 3 points. 2 3 e1 = ('*', 'x', 'x') 4 e2 = ('*', 3, 'x') 5 num = ('-', ei, e2) 6 e3 = (*', 'a', 'x') 7 den = ('+', el, e3) 8 e = ('7', num, den) 9 10 f = ('7', 11 ('-', 12 13 14 15 16 ('+', ('*', 1, 'x'), ('*', 'x', 1)), ('+', ('*', 0, 'x'), ('*', 3, 1))), ('+', ("*', 'x', 'x'), ('*', 'a', 'x'))), 18 ('-', ('*', 'x', 'x'), ('*', 3, 'x')), 19 28 ('+', ('*', 1, 'x'), ('*', 'x', 1)), ('+', ('*', 0, 'x'), ('*', 'a', 1))))), 22 ('*', 23 ('+', ('*', 'x', 'x'), ('*', 'a', 'x')), 24 ('+', ("*', 'x', 'x'), ('*', 'a', 'x')))) 25 26 assert derivate(e, 'x') == f [ ] 1 ### Hidden tests for "derivate for composite expressions. 7 points. 2 1 ### Implementation of test_derivative 2 2 3 def test_derivative(f, df, x, delta=0.8ee1, epsilon=0.1, num_tests=1808): See above." 5. ### YOUR CODE HERE 4. 1 ### Tests for test_derivative, 4 points. 2 3 f = ("+", ("*", "cat", "cat"), ("*", "dog", "cat")) 4 df1 = ("+", ("*", 2, "cat"), "dog") 5 df2 = ("+", ("*", 2, "cat"), ("*", "dog", "cat")) 7 assert test_derivative(f, df1, "cat") 8 assert not test_derivative(f, df2,"cat") 9 assert not test_derivative(f, dfi, "dog") 10 assert not test_derivative(f, dfi, 'donkey") 11 assert test_derivative(f, o, "donkey") 12 1 ### Hidden tests for test_derivative, 6 points. 1 ### Exercise: Implement apply distributive 2 3 def apply_distributive(e): ""Applies the distributive property to an expression e. 5 ### YOUR CODE HERE 4 *** 6 ] 1 ### Simple test for distributivity. 2 points. 2 3 ## Here is a definition of equality that disregards order. 4 def is_distributed (exp): 5 def is_plusminus(exp) : return isinstance(exp, tuple) and exp[@] in '+- if isinstance(exp, tuple): 9 op, ei, e2 = exp if op == and (is_plusminus (el) or is_plusminus (e2)): return false return is distributed (el) and is_distributed (22) 13 14 import random Boomvon 16 def value_equality(e1, e2): 17 return True 18 19 20 def applied distributivity(f, g): 21 return is_distributed(g) and value_equality(f, g) 23 # Simple test 24 ('*', ('+', 1, 2), ('-', 3, 4)) 26 f = ('+', ('-', ('*', 1, 3), ('*', 1, 4)), ('-', ('*', 2, 3), (**', 2, 4))) 27 applied_distributivity(apply_distributive(e), f) 25 e = 28 29 1 ### More complicated tests for distributivity. 2 points. 2 3 # More complex tests 4 5e = ("*', ('+', 1, 2), ('-', 3, 4)) 6 e2 = ('*', e, ('+', 5, 6)) 7 f = ('+', 8 (-', ('+', ('*', ('*', 1, 3), 5), ('*', ('*', 1, 3), 6)), 10 ('+', ('*', ('*', 1, 4), 5), ('*', ('', 1, 4), 6))), 11 (-', 12 ('+', ('*', ('*', 2, 3), 5), ('*', ('', 2, 3), 6)), 13 ('+', ('*', ('*', 2, 4), 5), ('*', ('*', 2, 4), 6)))) 14 15 applied_distributivity(apply_distributive (e2), f) 17 e = ('*', ('*', ('+', 1, 2), ('-', 3, 4)), (''', ('-', 5, 6), ('+', 7, 8))) 18 f = ('+', 19 (-", ('+', ('*', ('*', 1, 3), ('*', 5, 7)), ('*', ('*', 1, 3), ('*', 5, 8))), ('+', ('*', ('*', 1, 3), ('*', 6, 7)), ('*', ('*', 1, 3), ('*', 6, 8)))), 23 24 ('+', ('*', ('*', 1, 4), ('*', 5, 7)), ('*', ('', 1, 4), (':', 5, 8))), 25 ('+', ('*', ('*', 1, 4), (*, 6, 7)), ('*, ('*', 1, 4), ('*', 6, 8))))), 26 ('-', 27 28 ('+', (**, ('*', 2, 3), ('*', 5, 7)), ('*', ('*', 2, 3), ('*', 5, 8))), 29 ('+', ('*', ('*', 2, 3), ('*', 6, ?)), ('*', ('*', 2, 3), (**, 6, 8)))), 30 31 ('+', ('*', ('*', 2, 4), ('*', 5, 7)), ('*', ('*', 2, 4), ('*', 5, 8))), 32 ('+', ('*', ('*', 2, 4), ('*', 6, 7)), ('*', ('*', 2, 4), ('*', 6, 8)))))) 33 34 applied_distributivity(apply distributive(e), f) 35 36

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