Polynomials Enumerated

Navigation

You can move through the list using the mousewheel, the prev/next buttons, or by clicking on a lower polynomial to move down, and a higher polynomial to move up.

To jump to a particular index, enter it in the text box at the bottom left and click "lookup".

To jump to a particular polynomial, enter it in the text box at the bottom right and click "lookup".

Computational Limits

There are no limits to how high you can go simply by scrolling. Each of the lookup boxes, however, are limited:

For looking-up by index, the function is limited by how long it takes the server to compute the polynomial: if longer than 10 seconds, it times out. The amount of time is generally a function of the order of the polynomial, which isn't directly related to the size of the number. However, random numbers with much more than 250 digits will generally take too long to compute.

For looking-up by polynomial, there is a very efficient way to predict how big the index of the polynomial will be, so if it looks like the index will have more than 10,000 digits, it will not be computed. Generally, this is a function of the order of the polynomial plus the sum of the numerators and denominators in all of the coefficients. This means that it is very easy to express simple polynomials whose indices are too large, simply by choosing large values for the coefficients: e.g., (179/83)x^2 has over 12,000 digits, and so will not compute.

Shortcuts

To quickly copy the index and text-form of a polynomial in the display window, first click on it once to move it to the middle position, then double click on it to copy to the textboxes.

To expand the index-display box (when viewing polynomials with very large indices), double click on it.