Fangyao_solutions.sagews

#Solution from FirstSteps

#Exercise 1 (ws) Evaluate the number e with 15 decimal digits
e; N(e);e.n(digits=15)

e 2.71828182845905 2.71828182845905

#Exercise 2 (ws) (a)Evaluate three built-in functions of your choice for inputs of your choice.
# (b) Explain why SageMath refuses to give the result for exp(3) and force it to evaluate the function
exp(3.);

20.0855369231877

#Exercise 3 (ws)
#Remove the pound sign before the command "parametric_plot", and create a parametric plot using the #command (choose your favorite color and specify the size of the plot).
#Save the plot in a file with name 'my_first_plot.png'
parametric_plot((cos(x),sin(x)^3),(x,0,2*pi),color="lightblue",figsize=[5 ,5 ])

#Exercise 4. Define a function that finds the minimal element of the list. Test your function on example of your choic

def minimal_el(L):
    m=L[0]
    for j in range(1,len(L)):
        if L[j]<m:
            m=L[j]
    return m
c=range(1,10)
minimal_el(c)
a=[i^2 for i in range (2,4)]
minimal_el(a)

1 4

#Exercise 5. Experiment with commands in the file sage-quickref-BasicMath.pdf. Include two examples using commands of your choice. Your commands should be different from arithmetic operations and the commands used in this worksheedef

#ex1
factor(8.)

8.00000000000000

#ex2
plot(x^3+2*x-4,-5,5,figsize=[4,3])

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#Solutions from NB

#Exercise 1. (a) Make a list L of length 10.
#(b) Select 4th element of L; make a sublist of elements with indices from 4 to 8.
#(c) Learn command "append" and append one element to your list.
L=[0,1,2,3,4,5,6,7,8,9]
L.append(10)
print L
print(L[4:8])
print(L[6])

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] [4, 5, 6, 7] 6

#Exercise 2. Design a similar exercise for tuples
tuple(n^3 for n in range(20) if n%3==0)

(0, 27, 216, 729, 1728, 3375, 5832)

#Exercise 3. Design a set of tuples
L=set({5,10,12,24,25,24,5});L

set([24, 25, 10, 12, 5])

#Exercise 4. Make a dictionary.
grade = {'cat' : 1, 'dog' : 2}; grade

{'dog': 2, 'cat': 1}

#Exercise 5. Make two strings and concatenate them to obtain a meaningful word.
str1='Dogs are ';str2='awesome!'
str1+str2

'Dogs are awesome!'

#Exercise 6. Write a snippet of code that takes an integer and determines if the integer is odd or even.
#Note: this is an example of a user-defined function.
def my_parity(n):
    if n%2==0:
        print n,'is even'
    else:
        print n,'is odd'

my_parity(17)
my_parity(88)

17 is odd 88 is even

#Exercise 7.
def add_numbers(x,y,z=None):
    if (z==None):
        return x+y
    else:
        return x+y+z

print(add_numbers(1, 2))
print(add_numbers(1, 2, 3))

3 6