How to write sigma in python

An efficient way to do this in Python is to use reduce().

To solve

3
Σ i
i=1

You can use the following:

from functools import reduce
result = reduce(lambda a, x: a + x, [0]+list(range(1,3+1)))
print(result)

reduce() will take arguments of a callable and an iterable, and return one value as specified by the callable. The accumulator is a and is set to the first value (0), and then the current sum following that. The current value in the iterable is set to x and added to the accumulator. The final accumulator is returned.

The formula to the right of the sigma is represented by the lambda. The sequence we are summing is represented by the iterable. You can change these however you need.

For example, if I wanted to solve:

Σ π*i^2
i

For a sequence I [2, 3, 5], I could do the following:

reduce(lambda a, x: a + 3.14*x*x, [0]+[2,3,5])

You can see the following two code lines produce the same result:

>>> reduce(lambda a, x: a + 3.14*x*x, [0]+[2,3,5])
119.32
>>> (3.14*2*2) + (3.14*3*3) + (3.14*5*5)
119.32

Below is a simple example of a sigma function. You can also download sigma.py and play around with it if you like. Here are the same functions and sigma applied algebraically:

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Unicode characters are very useful for engineers. A couple commonly used symbols in engineers include Omega and Delta. We can print these in python using unicode characters. From the Python interpreter we can type:

>>> print('Omega: \u03A9')
Omega: Ω
>>> print('Delta: \u0394')
Delta: Δ
>>> print('sigma: \u03C3')
sigma: σ
>>> print('mu: \u03BC')
mu: μ
>>> print('epsilon: \u03B5')
epsilon: ε
>>> print('degree: \u00B0')
degree: °
>>> print('6i\u0302 + 4j\u0302-2k\u0302')
6î + 4ĵ-2k̂

All of these are unicode characters. Python has support for unicode characters built in. You can check if your system supports it by importing the sys module and calling the sys.getdefaultencoding() function

>>> import sys
>>> sys.getdefaulencoding()
'utf-8'

If you see utf-8, then your system supports unicode characters. To print any character in the Python interpreter, use a \u to denote a unicode character and then follow with the character code. For instance, the code for β is 03B2, so to print β the command is print('\u03B2').

There are a couple of special characters that will combine symbols. A useful one in engineering is the hat ^ symbol. This is typically used to denote unit vectors. We can add a hat ^ (also called a circumflex) by putting the unicode escape after the letter you want to add a hat to. For example to add a hat to i the command is print('i\u0302').

Below is a list of symbols and greek letters and the corresponding unicode escape to produce the character in python.

Useful unicode symbols in engineering

Greek lower case letters

Greek upper case letters

How do you define a sigma in Python?

How do you write summation in Python?