| Koeffitsenta of a polynomial divided by gaps |
| Integer value of degree |
|
|
| The received polynom as a result of exponentiation |
We develop our work on the study of polynomials. So, we already know how to multiply them and it works out well with us. Now our task is the construction of an arbitrary polynomial of the form
where b, c .... z, w - are coefficients of the polynomial.
to an integer power.
In fact, the stated task turns into the problem of multiplying the original polynomial by itself as many times as the degree matters
If the degree is eleven, then you need to multiply the polynomial 11 times by yourself.
And as already mentioned in the first lines of the article, we can multiply.
I would like to note that the polynomial can contain both real and imaginary numbers, which undoubtedly increases the chances of this calculator to be seen on the Internet.
The number of polynomial coefficients is not limited, but the degree is limited from above by the number 30, in order to avoid increased load on the server.
Consider an example of raising to a power of 3 a polynomial
^3)
The answer that the bot will give
=x^{6}+(9)*x^{5}+(12)*x^{4}+(-63)*x^{3}+(-60)*x^{2}+(225)x+(-125))
Another example, we raise to the 13th degree such a complex polynomial
^{13})
The answer is as follows
=(0+i)*x^{26}+(0-13i)*x^{25}+(0+91i)*x^{24}+(0-442i)*x^{23}+(0+1651i)*x^{22}+(0-5005i)*x^{21}+(0+12727i)*x^{20}+(0-27742i)*x^{19}+(0+52624i)*x^{18}+(0-87802i)*x^{17}+(0+129844i)*x^{16}+(0-171106i)*x^{15}+(0+201643i)*x^{14}+(0-212941i)*x^{13}+(0+201643i)*x^{12}+(0-171106i)*x^{11}+(0+129844i)*x^{10}+(0-87802i)*x^{9}+(0+52624i)*x^{8}+(0-27742i)*x^{7}+(0+12727i)*x^{6}+(0-5005i)*x^{5}+(0+1651i)*x^{4}+(0-442i)*x^{3}+(0+91i)*x^{2}+(0-13i)x+(0+i))
As you can see, the resulting polynomial is symmetric with respect to the number 212941. Perhaps you can somehow connect these coefficients with the famous Pascal triangle.
Good luck!