February 20, 2017
All of these examples came from actual problems I've encountered over the last fifteen years in solving parametric polynomial systems. They involve between seven and seventeen symbolic variables. The polynomials have as many as 7000000 terms. All are quite sparse, some extremely sparse.
Most of the Magma times are the average of two runs. Fermat times do not vary much. I tried to run Magma and Fermat on the same problems in quick succession so that varying loads due to other people's jobs were not a factor.
A list of the tests and times is here.
In every case, the test is to compute GCD(^xx, ^yy) in Fermat, and time b := GCD(xx, yy) in Magma. Almost all tests run over the finite field Z/p where p is 2^31 - 19.
The files containing the Fermat code for the tests can be found here.
The files containing the Magma code for the tests can be found here.
The files are listed in the same order as they appear in the list of files and times above.
Clicking on a file name should download it to your computer. That is what happens when using Firefox or Chrome. For whatever reason, when using Safari it seems that instead the file opens in the Safari window. On versions of Fermat before 6.0, all of these tests take much much longer, often 100 - 1000 times longer.