Doing Math with Python

{{ (month_group|first).date|strftime('%b %Y') }} · - By Amit Saha -

set
FiniteSet
FiniteSet
>>> s1 = {1, 2, 3}
->>> s1
-{1, 2, 3}
-
>>> items = [1, 2, 3]
->>> s2 = set(items)
->>> s2
-{1, 2, 3}
-
FiniteSet
>>> from sympy import FiniteSet
->>> s1 = FiniteSet(1, 2, 3)
->>> s1
-{1, 2, 3}
-
->>> items = [1, 2, 3]
->>> s2 = FiniteSet(*items)
->>> s2
-{1, 2, 3}
-
set
>>> e = set()
->>> e
-set()
-
EmptySet
EmptySet
FiniteSet
>>> from sympy import EmptySet
->>> e = EmptySet()
->>> e
-EmptySet()
->>> e = FiniteSet()
->>> e
-EmptySet()
-
len()
x
s
x in s
union()
>>> s1 = set([1, 2, 3])
->>> s2 = set([2, 3, 4])
->>> s3 = set([2, 3, 4, 5])
->>> s1.union(s2).union(s3)
-{1, 2, 3, 4, 5}
-
>>> from sympy import FiniteSet
->>> s1 = FiniteSet(1, 2, 3)
->>> s2 = FiniteSet(2, 3, 4)
->>> s3 = FiniteSet(2, 3, 4, 5)
->>> s1.union(s2).union(s3)
-{1, 2, 3, 4, 5}
-
intersection()
>>> s1 = set([1, 2, 3])
->>> s2 = set([2, 3, 4])
->>> s3 = set([2, 3, 4, 5])
->>> s1.intersection(s2).intersection(s3)
-{2, 3}
-
>>> s1.intersection(s2).intersection(s3)
-{2, 3}
-
set
product()
>>> s1 = {1, 2, 3}
->>> s2 = {4, 5, 6}
->>> import itertools
->>> itertools.product(s1, s2)
-<itertools.product object at 0x10418c990>
-
product()
itertools.product(s1, s2).union(s3)
set(itertools.product(s1, s2)).union(s3)
FiniteSet
*
>>> s1 = FiniteSet(1, 2, 3)
->>> s2 = FiniteSet(4, 5, 6)
->>> >>> s3 = FiniteSet(7, 8, 9)
->>> (s1*s2).union(s3)
-{7, 8, 9} U {1, 2, 3} x {4, 5, 6}
-
repeat
itertools.product()
repeat
itertools.product(s1,
-repeat=2)
>>> s1 = {1, 2, 3}
->>> set(itertools.product(s1, repeat=2))
-{(1, 2), (3, 2), (1, 3), (3, 3), (3, 1), (2, 1), (2, 3), (2, 2), (1, 1)}
-
**
>>> s1 = FiniteSet(1, 2, 3)
->>> s1**2
-{1, 2, 3} x {1, 2, 3}
-
issubset()
issuperset()
s1.issubset(s2)
>>> s1 = {1, 2, 3}
->>> s2 = {1, 2, 3, 4}
->>> s1.issubset(s2) and s1 != s2
-True
-
is_proper_subset()
is_proper_superset()
s1.is_proper_subset(s2)
set
powerset
powerset()
>>> s1 = FiniteSet(1, 2, 3)
->>> s1.powerset()
-{EmptySet(), {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
-
powerset()
FiniteSet
set
FiniteSet
*
**
powerset()
set
FiniteSet
frozenset
set
frozenset
FiniteSet
FiniteSet
FiniteSet
-$ conda update conda
-$ conda install anaconda=5.0
-
doingmathwithpython@gmail.com
set
set
-print('Area: {0}, Estimated ({1}): {2}'.
-           format(area_of_circle, points, estimate(radius, points)))
-
-print('Area: {0}, Estimated ({1}): {2}'.format(area_of_circle, points, estimate(radius, points)))
-
print()
-s = 'Area: {0}, Estimated ({1}): {2}'.format(area_of_circle, points, estimate(radius, points))
-
s
-s = ('Area: {0}, Estimated ({1}): {2}'
-     .format(area_of_circle, points, estimate(radius, points)))
-
-s1 = x + x**2/2 + x**3/3 + x**4/4 + x**5/5 + x**6/6 + x**7/7 + x**8/8
-
-s3 = (x + x**2/2 + x**3/3
-     + x**4/4 + x**5/5
-     + x**6/6 + x**7/7
-     + x**8/8)
-
\
\
-s3 = x + x**2/2 + x**3/3 \
-    + x**4/4 + x**5/5 \
-    + x**6/6 + x**7/7 \
-    + x**8/8
-
\
if
-# Using parenthesis
-if (cond1 and cond2 and cond3
-    and cond4):
-    # True block
-else:
-    # False block
-
-# Using line continuation operator
-if cond1 and cond2 and cond3 \
-   and cond4:
-    # True block
-else:
-    # False block
-
-x = 1
-print(x,
-      x)
-
-print('Area: {0}, Estimated ({1}): {2}'.format(area_of_circle,
-                                              points,
-                                              estimate(radius, points)))
-
format()
n
n!
n*(n-1)*(n-2)...*1
5! = 5*4*3*2*1 = 120
n
-import math
-
-
-def is_positive_integer(x):
-    try:
-        x = float(x)
-    except ValueError:
-        return False
-    else:
-        if x.is_integer() and x > 0:
-            return True
-        else:
-            return False
-
-
-def trailing_zeros(num):
-    if is_positive_integer(num):
-        # The above function call has done all the sanity checks for us
-        # so we can just convert this into an integer here
-        num = int(num)
-
-        k = math.floor(math.log(num, 5))
-        zeros = 0
-        for i in range(1, k + 1):
-            zeros = zeros + math.floor(num/math.pow(5, i))
-        return zeros
-    else:
-        print("Factorial of a non-positive non-integer is undefined")
-
-
-if __name__ == "__main__":
-    fact_num = input(
-        "Enter the number whose factorial's trailing zeros you want to find: "
-    )
-    num_zeros = trailing_zeros(fact_num)
-    print("Number of trailing zeros: {0}".format(num_zeros))
-
-Enter the number whose factorial's trailing zeros you want to find: 5
-Number of trailing zeros: 1
-
-Enter the number whose factorial's trailing zeros you want to find: 5.1
-Factorial of a non-positive integer is undefined
-Number of trailing zeros: None
-
math.floor
math.log
math.pow
set
-$ sudo apt-get update
-$ sudo apt-get install python3-matplotlib python3-matplotlib-venn python3-sympy idle3
-
doingmathwithpython@gmail.com
set
-$ sudo apt-get update
-$ sudo apt-get install python3-matplotlib python3-matplotlib-venn python3-sympy idle3
-
doingmathwithpython@gmail.com
interpreter
print("Hello")
Hello
IDE
text editor
-..
-y_square = []
-for yi in y:
-    y_square.append(yi**2)
-...
-
from sympy import expand
-for i in range(2, n+1):
-    series = series + (x**i)/i
-
-from sympy import Symbol, sympify, solve, SympifyError
-
from sympy import FiniteSet
for num in s:
for num in space
probability = [1/6, 1/6, 1/3, 2/3]
probability = [1/6,
-1/6, 1/3, 1/3]
-from sympy import Derivative, Symbol, sympify, SympifyError
-
-if __name__ == '__main__':
-    u = 5
-    theta = math.radians(45)
-    x, y = components(u, theta)
-
bash <path/to/installer>
-Welcome to Anaconda3 2.1.0 (by Continuum Analytics, Inc.)
-
-In order to continue the installation process, please review the license
-agreement.
-Please, press ENTER to continue
->>> ENTER
-
-The “Anaconda END USER LICENSE AGREEMENT” will be displayed. Once you have read through it, type in “yes” to continue the installation:
-Do you approve the license terms? [yes|no]
-[no] >>> yes
-
-Anaconda3 will now be installed into this location:
-/home/testuser/anaconda3
-
-  - Press ENTER to confirm the location
-  - Press CTRL-C to abort the installation
-  - Or specify an different location below
-
-[/home/testuser/anaconda3] >>>
-PREFIX=/home/testuser/anaconda3
-installing: python-3.4.1-4 ...
-installing: conda-3.7.0-py34_0
-..
-
-creating default environment...
-installation finished.
-Do you wish the installer to prepend the Anaconda3 install location
-to PATH in your /home/testuser/.bashrc ? [yes|no]
-
-[no] >>> yes
-
-Prepending PATH=/home/testuser/anaconda3/bin to PATH in /home/testuser/.bashrc
-A backup will be made to: /home/testuser/.bashrc-anaconda3.bak
-
-
-For this change to become active, you have to open a new terminal.
-
-Thank you for installing Anaconda3!
-
sympy
sympy-0.7.6
-$ conda install sympy=0.7.6
-
-$ pip install matplotlib-venn
-
idle3
python
sympy
0.7.6
conda install sympy=0.7.6
matplotlib-venn
pip install matplotlib-venn
idle3
sympy
0.7.6
conda install sympy=0.7.6
matplotlib-venn
pip install matplotlib-venn
idle
Python 3.5
matplotlib 1.4.2
matplotlib-venn 0.11
sympy
-0.7.6
-$  conda update conda
-$  conda update anaconda
-
PYCONMATH
-$ conda update conda
-$ conda update anaconda
-
doingmathwithpython@gmail.com
n
n!
n*(n-1)*(n-2)...*1
5! = 5*4*3*2*1 = 120
n
-import math
-
-
-def is_positive_integer(x):
-    try:
-        x = float(x)
-    except ValueError:
-        return False
-    else:
-        if x.is_integer() and x > 0:
-            return True
-        else:
-            return False
-
-
-def trailing_zeros(num):
-    if is_positive_integer(num):
-        # The above function call has done all the sanity checks for us
-        # so we can just convert this into an integer here
-        num = int(num)
-
-        k = math.floor(math.log(num, 5))
-        zeros = 0
-        for i in range(1, k + 1):
-            zeros = zeros + math.floor(num/math.pow(5, i))
-        return zeros
-    else:
-        print("Factorial of a non-positive non-integer is undefined")
-
-
-if __name__ == "__main__":
-    fact_num = input(
-        "Enter the number whose factorial's trailing zeros you want to find: "
-    )
-    num_zeros = trailing_zeros(fact_num)
-    print("Number of trailing zeros: {0}".format(num_zeros))
-
-Enter the number whose factorial's trailing zeros you want to find: 5
-Number of trailing zeros: 1
-
-Enter the number whose factorial's trailing zeros you want to find: 5.1
-Factorial of a non-positive integer is undefined
-Number of trailing zeros: None
-
math.floor
math.log
math.pow
mandelbrot.py
IDLE
File >
-Open
mandelbrot.py
Run > Run Module
doingmathwithpython@gmail.com

Creating a set

Cardinality and Membership

Union and intersection

Cartesian product

Subset/super set/proper subset checking

Calculating the powerset

Choice of SymPy's FiniteSet over set

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Choice of SymPy's `FiniteSet` over `set`