There are three versions, Linux for Intel hardware; Mac for Intel hardware; and Mac for Apple hardware (the M1 chip). See below to download.
Fermat 7.* includes everything from 6.5. The main new feature is the ability to factor multivariate polynomials over Z/p, and in a limited way, over Z. See
this document factr. (This was updated on March 3, 2024; February 28, 2024; February 11, 2024; January 11, 2024;
November 14, 2023.)
Fermat 7.5a is for Mac and Linux. This update fixes a small bug in factoring two-variable polynomials mod p.
Also, the methods in factr have been improved.
Fermat 7.5 is for Mac and Linux. This update improves factoring polynomials over Z. A bug in 7.4 was fixed concerning factoring over ground fields produced
by polymodding (i.e., the command &(P = ....)).
Also, the methods in factr have been improved.
Fermat 7.4 is for Mac and Linux. Irred has been further improved since 7.3. You have to load the file factr (available here) for factoring. (In
other words, Fermat now has the ability to load a collection of Fermat functions from an external text file and use them internally -- at least in this one case.) Similarly, the
function FCTZ there has been improved, especially when polymodding (i.e., working modulo an irreducible polynomial). It can still fail and return -1, but this probably means irreducible.
There is a new function Varsp(f) to return the number of variables in f above field depth.
There is a new function Polymod to return true/false, polymodding or not. This is not the same as using Flevel to determne the field level.
When creating a field with polymodding, the auxiliary primes are not only computed and displayed, they are stored in an array aux_prime for user's use.
Fermat 7.3 is for Mac and Linux. This update addresses factoring polynomials over Z. The built-in function Irred for irreducible polynomial sometimes fails over Z (i.e. returns -1, can't decide).
It has been improved, if you have loaded the file factr (available here) for factoring. (In other words, Fermat now has the ability to load a collection of
Fermat functions from an external text file and use them internally -- at least in this one case.) Similarly, the function FCTZ there has been improved. But it can still fail by returning -1.
Fermat 7.2 is for Mac and Linux. November 29, 2023. The implementation of Zippel-like polynomial gcd was not very good for some cases of six variable polynomials. It has been improved.
Fermat 7.1 is for Mac. October 23, 2023. It is a "bug" fix. Relatively recently the Mac system programmers changed some low-level details about reading characters from the terminal. The result was that copying
and pasting an array to the terminal no longer worked in fer64. Fermat 7.1 fixes that. No change is required in Linux.
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See also the Fermat FAQ page.
Version 7.0. July 23, 2023
- new function Nextvar: Nextvar returns the position (level) of the
second variable in the poly argument. If there is only one var, it returns 0. If the input is a
number or field element, it returns -1.
- new function Vars that returns the number of poly vars in the input. It includes vars that are part of the field if field_depth > 0.
- changes to Irred: It now works for any polynomial input. Over Z, drops into mod p for several p. Over Z/p, it uses the well known idea
to replace all vars but two with linear combinations of those two, then factor the two-var poly. See "Irreducibility of Multivariate Polynomials" by
Joachim von zur Gathen 1985. This is probabilistic, highly likely to be correct.
- new function Revpoly. It reverses the terms; i.e. if the degree is n, replaces exponent i with n-i.
- function Factor has been extended. Factor(u, [q]) now works for two-variable polys over Z/p.
- new function CIrred for irreducible with no content check. If you know the argument has no contents, use this instead of Irred. If in fact it does have contents,
the result is undefined.
Bug fix: Redrowech sometimes did not handle the auxiliary matrices correctly.
Bug fix: There was a bug in polynomial evaluation that sometimes popped up in modular mode.
Bug fix: There were several small memory leaks introduced in version 6.5.
Bug fix: You cannot call &F or &v inside a function. This is now an error.
64 bit Mac version 7.5a for Intel hardware. This was compiled with 10.15.7. It will not work on 10.5 and earlier.
Expand the tar bundle. Put Ferm7i in the right place so that the application Terminal sees it. Start up Terminal,
then cd into Ferm7i. Type ./fer64. Don't just open the folder and double-click on fer64. For me, at least, that doesn't work well.
64 bit Mac version 7.5a for Apple M1 hardware. This was compiled with 12.6.3.
64 bit Linux version 7.5a. This was compiled with the static option on Ubuntu.
Fermat is freeware. Institutions or those with grant money should contribute a total of $US 75 per machine.