Mathematical module for python.

This module adds the ability to work with polynomials through the Polynomial class, which contains separate terms of different degrees and the correct fraction.

To start working with polynomials, you need to create a Variable and use it to set a mathematical expression.

from PyCalc.polynomial import Variable

x = Variable("x")

a = 1 / (x**2 - 3*x + 1)
b = (x**3 + 3*x**2 + 3*x + 1) / (x + 1)
c = (4*x**6 - 8*x**5 + 9*x**4 - x**3 + 2*x**2 - 5*x + 1) * (3*x**3 - x**2 + 2*x - 6) / (x**4 + x**2 + 84)
d = a - b + c

print(a)
print()
print(b)
print()
print(c)
print()
print(d)

     1      
────────────
x^2 - 3x + 1

x^2 + 2x + 1

                                              -1620x^3 - 310x^2 + 81176x - 193458
12x^5 - 28x^4 + 31x^3 - 24x^2 - 966x + 2303 + ───────────────────────────────────
                                                        x^4 + x^2 + 84


                                              -1620x^5 + 4551x^4 + 80486x^3 - 437295x^2 + 661550x - 193374
12x^5 - 28x^4 + 31x^3 - 25x^2 - 968x + 2302 + ────────────────────────────────────────────────────────────
                                                      x^6 - 3x^5 + 2x^4 - 3x^3 + 85x^2 - 252x + 84

The Polynomial class can be used together with Numpy.

from PyCalc.polynomial import Variable
from numpy import array

x = Variable("y")

a = array([
    [1, x/2],
    [2*x, 3]
])
b = array([
    [1, 0, x**2],
    [2*x, 3, -7]
])

print(a @ b)

[[y^2 + 1 3/2y y^2 - 7/2y]
 [8y 9 2y^3 - 21]]

1. This module makes it possible to work with fractions.

   You can use 'float' type in your expression and Fraction will automatically convert it to fraction if the numerator and denominator do not exceed 10^3 (if you don't need polynominal, you can use Fraction.toFration('float')).

   Example

   from PyCalc.polynomial import Variable
   
   x = Variable("a")
   
   a = 125 / 387
   b = a * x
   
   print(a)
   print()
   print(b)

   Output:

   0.32299741602067183
   
   125 
   ───a
   387 

2. expression.evaluate_polynomial(var) is used to substitute a value instead of a variable in an expression

   Example

   from PyCalc.polynomial import Variable
   
   x = Variable("a")
   
   a = 1 / (x**2 - 3*x + 1) + (x**3 + 3*x**2 + 3*x + 1) / (x + 1)
   
   print(a)
   print("=", (a).evaluate_polynomial(2))

   Output:

                      1      
   a^2 + 2a + 1 + ────────────
                  a^2 - 3a + 1
   = 8

3. Also, in the submodule operations there is an implementation of the fft algorithm, which also allows for fast multiplication, which can be used when calculating the multiplication of polynomials that do not have huge powers or coefficients.