User blog:Nayuta Ito/Brand-new Googologism from Algebra

The googological function is written as SIR(m,n,d), where m,n,d are (nonzero) natural numbers.

The definition goes like this:

First, write every polynomial that has no more than m kinds of variables, no higher than n degrees, and no coefficients whose absolute values are bigger than d. The list will be finite.

If m=2, n=3, d=10, the list will include polynomials such as: x^3+3x^2y+3xy^2+y^3 7 x^2y-7x+3y-10 5y-10

Now, for each polynomial in the list, write the sum of the "smallest" integer roots for the polynomial, If it does not exist, leave it empty.

In this case, the "smallest" means the sum of the absolute value of all the variables. (If x=-3 and y=2, the sum is 5) (you will write that sum)

If the sum of roots are written, the list above will look like this; x^3+3x^2y+3xy^2+y^3 0 7 (blank) x^2y-7x+3y-10 6 5y-10 2

Now take the max value of the sum. That's the value of SIR(m,n,d).

(Note that the list above is just a fraction of SIR(2,3,10): x^2-10y^2-1 has the sum of 25)