This project is continued as a part of the 'numbering_patterns' project

linear_formula

The class LinearFormula in linear_formula.py represents a linear formula also known as first degree polynimial. The user can initialize it with a string, insert and remove segments, simplify it, substitute variables with other formulas, and find the modulo n equivalent of it

example usage

1. Initialization:

>>> LinearFormula('a + 3b - 4c')
a + 3b - 4c

(Currently the string-to-formula conversion algorithm supports only 
integer mltipliers)

>>> LinearFormula({'a': 1, 'b': 3, 'c': -4'})
a + 3b - 4c

>>> LinearFormula([1, 3, -4], ['a', 'b', 'c'])
a + 3b - 4c

>>> LinearFormula(45)
45

2. Evaluation:

>>> LinearFormula('a + 3b').evaluate(a=2, b=1})
5

3. Substitute variables:

>>> formula_1 = LinearFormula('a + 3b - 4c')
>>> formula_2 = LinearFormula('x + 2')
>>> formula_1.substitute(a=formula_2)
x + 2 + 3b - 4c

>>> formula_1.substitute(a='y - 2')
y - 2 + 3b - 4c

>>> formula_1.substitute(a='x', b='y', c='2a')
x + 3y - 8a

4. Simplify:

>>> formula_1 = LinearFormula('a + 3b - 4c + 3a - b')
>>> formula_.zip()
4a + 2b - 4c

5. Find modulo equivalent:

>>> LinearFormula('a + 5b + 6c + 4').modulo(3)
a + 2b + 1

6. Add/insert/remove segments:

>>> LinearFormula('a + 3b').add_segment(-4, 'c')
a + 3b - 4c

>>> LinearFormula('a + 3b').insert_segment(-4, 'c', 1)
a - 4c + 3b

>>> LinearFormula('a + 3b - 4c').remove_segment(1)
a - 4c

7. The methods used in points 3 - 6 can modify the formula instead of returning another formula

>>> formula_1 = LinearFormula('a + 3b')
>>> formula_1.add_segment(-4, 'c', inplace=True)
>>> formula_1
a + 3b - 4c

>>> forula_2 = formula_1.add_segment(5, 'd')
>>> formula_2
a + 3b - 4c + 5d

>>> formula_1
a + 3b - 4c

8. Operations on formulas:

>>> formula_1 = LinearFormula('a + 3b')
>>> formula_2 = LinearFormula('4c - d')

>>> -formula_1
-a - 3b

>>> fornula_1 + formula_2
a + 3b + 4c - d

>>> formula_1 + formula_2
a + 3b - 4c + d

>>> formula_1 * 2
2a + 6b

>>> formula_1 % 2
a + b

>>> formula_1[0]
(3, 'b')

8. Other:

>>> LinearFormula('a + 3b - 4c').length()
3

>>> LinearFormula('a + 3b - 4c').get_segment(1)
(3, 'b')

>>> LinearFormula('a + 3b - 4c').copy()
a + 3b - 4c