2016-04-04.sagews

Math 480: Open Source Mathematical Software

2016-04-04

William Stein

Lectures 4: Basic Python (part 1/3)

Organization:

• hmwk from last week graded and returned

• hmwk for this week available now

• office hours ta discussion

• I will leave immediately after class to do a basic demo of SMC for another class today

• stickers

• remind me to turn on the screencast, since I definitely forgot!

Key things to learn this week:

1. Basics: functions, whitespace is significant, if, while, for, list comprehensions

2. Data structures: lists, tuples, dicts, sets

3. (maybe) Classes: class, methods, inheritence

Functions

def name_of_function(argument1, argument2):
    # This is a function. I changed
    print "the first argument is ", argument1, " and the second is ", argument2
    return argument1 + argument2

output = name_of_function(15, 19)

the first argument is 15 and the second is 19

True

True

False

False

None

print output

34

name_of_function('math', '480')

the first argument is math and the second is 480 'math480'

# This should fail -- you can't add a string and a number in  Python.
name_of_function('abc', 123)

the first argument is abc and the second is 123

Error in lines 2-2 Traceback (most recent call last): File "/projects/sage/sage-6.10/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 904, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> File "", line 4, in name_of_function File "sage/structure/element.pyx", line 1651, in sage.structure.element.RingElement.__add__ (/projects/sage/sage-6.10/src/build/cythonized/sage/structure/element.c:15852) return coercion_model.bin_op(left, right, add) File "sage/structure/coerce.pyx", line 1069, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (/projects/sage/sage-6.10/src/build/cythonized/sage/structure/coerce.c:9736) raise TypeError(arith_error_message(x,y,op)) TypeError: unsupported operand parent(s) for '+': '<type 'str'>' and 'Integer Ring'

%python
name_of_function('abc', 123)

the first argument is abc and the second is 123

Error in lines 1-1 Traceback (most recent call last): File "/projects/sage/sage-6.10/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 904, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> File "", line 4, in name_of_function TypeError: cannot concatenate 'str' and 'int' objects

Exercise now: Write a function avg that takes four arguments (which you may assume are numbers) and returns their average.

def avg(x1, x2, x3, x4):
    # write code here.

# test code here (etc.)
avg(1,2,3,4)

If/else Statements

if [condition]:
    [some code]
elif [condition]:
    [some code]
...
else:
    [some code]

The condition can use ==, !=, and, or, not, and so on.

(Note: Python has no switch statement.)

def parity(n):
    if n % 2 == 0:
        print "even"
    elif n == 2017:
        print "odd, that is next year!"
    else:
        print "odd"

parity(3)

odd

parity(6)

even

parity(2017)

odd, that is next year!

Exercise now: Write a function that takes a number as input and prints "negative" if it is less than 0, "positive" if it is bigger than 0, and "zero" if it is equal to 0.

def my_sign(n):
    # write your code here

For loops

`range(n)` is the list of integers from 0 up to n-1.


for [variable name] in [list or anything "iterable"]:
    [code...]

range(10)

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

for i in range(10):
    print "Hello", i

Hello 0 Hello 1 Hello 2 Hello 3 Hello 4 Hello 5 Hello 6 Hello 7 Hello 8 Hello 9

i

9

def sum_up_to(n):
    s = 0
    for i in range(n+1):
        s = s + i
    return s

sum_up_to(3)

6

sum_up_to(10)

55

sum_up_to(100)

5050

range(7, 50, 3)

[7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49]

range?

File: 
Docstring :
range(stop) -> list of integers range(start, stop[, step]) -> list of
integers

Return a list containing an arithmetic progression of integers.
range(i, j) returns [i, i+1, i+2, ..., j-1]; start (!) defaults to 0.
When step is given, it specifies the increment (or decrement). For
example, range(4) returns [0, 1, 2, 3].  The end point is omitted!
These are exactly the valid indices for a list of 4 elements.

[5..15]

[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]

[5, 5.7, .., 15]

[5.00000000000000, 5.70000000000000, 6.40000000000000, 7.10000000000000, 7.80000000000000, 8.50000000000000, 9.20000000000000, 9.90000000000000, 10.6000000000000, 11.3000000000000, 12.0000000000000, 12.7000000000000, 13.4000000000000, 14.1000000000000, 14.8000000000000]

Exercise now: Write a function sum_pow_up_to(n, k) that returns the sum $1^k + 2^k + \cdots + n^k$. You may assume that $n$ and $k$ are positive integers.

4^5

1024

4**5

1024

%python
4^5

1

def sum_pow_up_to(n, k):
    # put code here...

sum_pow_up_to(100,2)

While loops

while [condition]:
    [code...]

(You can put break in the code to immediately exit the while loop.)

i = 5
while i > 0:
    print i
    i -= 1

5 4 3 2 1

def my_factor(n):
    while not is_prime(n):       # is_prime is part of Sage (not Python)
        k = n.trial_division()   # trial_division is part of Sage (not Python)
        n = n//k
        print "found a factor=", k
    print "finished; prime number remaining=", n

my_factor(20)

found a factor= 2 found a factor= 2 finished; prime number remaining= 5

my_factor(2016)

found a factor= 2 found a factor= 2 found a factor= 2 found a factor= 2 found a factor= 2 found a factor= 3 found a factor= 3 finished; prime number remaining= 7

Exercise now:

Use a while loop to write a function largest_power_of_2 that takes an input a positive integer $n$ and returns the largest power of $2$ that is less than $n$. Your loop should start with pow=1 and while pow*2 is less than $n$ replaces pow by pow*2. When the condition fails, just return pow.

def largest_power_of_w(n):
    # put code here...

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