polynomial multilayer

As Chibill posted we are making a polynomial multilayer.
We are going to use a basic "algorithm", I guess you could call it.
I mean all we are doing is multiplying by repetitively adding.

SOME Background...

For this examples I'm going to be using a max of x^3.

    First let look at a normal polynomial.
        A1x2+B1x+C1   and A2x2+B2x+C2
    So we multiply the second polynomial by the first .
        (A1x2)X(A2x2+B2x+c2) = A1A2x4+A1B2x3+A1C2X
    And now we repeat for the other and add them all up and we end up with
        A1A2x4+A1B2x3+A1C2x+B1A2x3+B1B2x2+B1C2x+C1A2x2+C1B2x+C1C2
      now group alike terms
        A1A2x4+(A1B2x3+B1A2x3)+(B1B2x2+C1A2x2)+(A1C2x+B1C2x+C1B2x+C1C2)

    As you can see these thing get big FAST!!!!
    Another BIG problem is that they come in many different sizes.
      like x6,x4,x8

You may have noticed that i used ”A”,”B”,”C” in the polynomial this is standard practice.
By taking these NUMBERS/VARIABLES and putting them into a list we can do some cool stuff.
    Lets look at a few examples of this.
             x2 + x + 6            would be [1,1,6]
           3x2+3x + 3           would be [3,3,3]
       x6 + 4x5 +2x2 +3       would be [1,4,0,0,2,0,3] (hime check your math,chib)
    You may have noticed that I filled in some extra zeros in that list. this is because you start on the largest number exponent.and continue down to no exponent and if you hit a exponent where the coefficient is zero you put a zero.

Now we start having fun! :) ( I,himehowareu, am a complete math and algorithm nut )
  when i was working on some math problems for a different project i was doing some polynomial multiplication and noticed a pattern. By using these lists we can use some simple addition and a “equal to” test to multiply the two polynomials.