This algorithm helps to generate the sum equation of the power function:

usage: posum.py [-h] [-d DEGREE] [-v] [-s SHOW]

optional arguments:
  -h, --help            show this help message and exit
  -d DEGREE, --degree DEGREE
  -v, --version         show version
  -s SHOW, --show SHOW  only showing the formula (f), triagle matrix (m) or both (b)[default]?

If we want to know the equation of the sum function of the nth power, we run the python script and enter the degree n of the sum function.

python posum.py -d <the degree n>

The result consists of the power sum formula of n degree and the triangle matrix. Besides, wanting to show either. Let's use the argument -s

Need help to use

python posum.py -h

To show version of algorithm.

python posum.py -v

For example, when we want to find the sum function of the power of 6, we run the command and enter the degree of the function as 6.

#input
python posum.py -d 6

#output
Sum formula of x^ 6 is:  +1/42*x^1+0*x^2-1/6*x^3+0*x^4+1/2*x^5+1/2*x^6+1/7*x^7

Matrix triagle is:

         1      2     3     4    5    6    7

  0      1
  1    1/2    1/2
  2    1/6    1/2   1/3
  3      0    1/4   1/2   1/4
  4  -1/30      0   1/3   1/2  1/5
  5      0  -1/12     0  5/12  1/2  1/6
  6   1/42      0  -1/6     0  1/2  1/2  1/7

So the equation sum of the power of the sixth power has the form:

The algorithm works by forming a triangular matrix with each value of the matrix being a coefficient of the sum equation. The coefficients of the equation of degree n are the values of the n-th row of the matrix. Values of the matrix is calculated according to the system of equations:

$$\left{ \begin{array}{l} {a_{01}} = 1\ {a_{ij}} = \frac{i}{j} \times {a_{{(i - 1)(j - 1)}}} {\rm{ ,}}\forall i\ge 1,\forall j\ge 2\ \sum\limits{k = 1}^j {{a_{ik}} = 1{\rm{ ,}}\forall i,j} \end{array} \right.$$

• Create sum formula of polinomial functions