There are three versions, Linux for Intel hardware; Mac for Intel hardware; and Mac for Apple hardware (the M1-2-3 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 April 6, 2026; Sept 19, 2025; June 25, 2024; March 3, 2024; February 28, 2024; February 11, 2024.)
Fermat 7.9b is for Mac and Linux. June 28, 2026
1. Analagous to recently implemented commands d:+(....), d:/(...), etc, there is now a command d:#(x=...) for polynomial evaluation. This means d := d#(x=...)
2. There have long been commands Terms(...) and Termsf(...) for the number of terms in an expression. (Termsf is useful when polymodding.) There are now analogous functions Termsa[d] and Termsaf[d] to take an array [d] and return an array of the same dimensions with the number of terms of the entries in [d].
3. A user wants to display extremely long lines to standard output. He noticed that a line break will be inserted at 5600 characters no matter what &_d has been set to. Indeed, this was true. When I wrote the code for I/O 30 years ago I was focused on displaying to the terminal for human readability. Lines can now be up to 2^31 - 1 characters before a line break.
4. A user commented that Redrowech can be speeded up, sometimes by an order of magnitude, if the "smaller, lighter" columns of the matrix are moved to the front. That's true, but you can't switch columns in Redrowech, you'd break invariance. However, you can do that for solving linear equations if you keep track of the column permutations. Also, playing with the setting for &u can have a big effect. Experiment!
5. The file Qerrs has changed.
Fermat 7.9a is for Mac and Linux. May 26, 2026
Bug fix: There was a flaw in sparse LaGrange interpolation for matrix determinant. This is very powerful command when it is applicable. The account in the manual is incomplete. Use Det([m], dr) when dr is a polynomial known to divide the determinant. This command returns Det[m]/dr. If the degree of the determinant in the highest variable is known to be D1, and that of dr is d1, use Det([m], dr, D1-d1). Similarly if you also know the degrees in the second highest variable, D2 and d2, use Det([m], dr, D1-d1, D2-d2). However,
if you also know that Det[m]/dr has the form p^n, use Det([m], dr, D1, D2, n) and p will be returned. This situation does indeed often occur when computing the resultant of
a system of polynomial equations with symmetry. Enormous speedups are possible. If the arguments dr, D1, D2, etc are not correct, execution may fall into an infinite loop.
In the last situtation, consider turning on both &V and &W. [BTW, in case it's not obvious, you compute D1, D2, d1, d2, n by running mod prime and plugging in constants for most of the vars.]
Fermat 7.9 is for Mac and Linux. April 6, 2026
Reminder: It is no longer an error to name a variable (ordinary sense) the same name as a polynomial variable. This is convenient inside functions. Just beware of it!
Fixes: Several revisions and tweaks of the Zippel mathod for multivariate polynomial GCD. It's very hard to get really "right". Some tweaks to polynomial factoring (the file factr).
Feature: Deleting a file or variable used to automatically return 0. Now it returns 1 if that item existed and was deleted, else it returns 0.
For the Mac, time moves on. This will probably be the last revision for Intel chips. The M1-2-3 family of Apple chips is great!
Fermat 7.8 is for Mac and Linux. September 20, 2025
Bug fix: Redrowech on a non-sparse matrix with unassigned entries crashed.
Bug fix: A very small number of GCD computations with the Zippel method were grossly slow.
Bug fix: On rare occasions GCD would return the wrong answer, missing a factor. This was not dependent on Zippel.
New feature: A variable (in programming sense) now has precedence over a symbolic polynomial variable. So, if there is a polynomial variable named i [I hope not], you can write a loop for i = 1, 10 ...
New feature: Saving the previous computation after an assignment statement on the terminal is now optional. Change this with &_S. This was implemented because on big problems you might have x := ... producing a huge x -- and therefore a huge previous value.
New feature: It's now an error to do &z (changing Zippel status) unless you're at the lowest level.
New function Xist: Xist(..name..) or Xist[..name..] tells if that item exists. You cannot ask if a certain entry in a matrix exists.
The programs in factr have been improved a bit.
Fermat 7.6 is for Mac and Linux. The increment command has been greatly extended. One can now write x:+y, x:-y; x:*y, x:/y for any y. Also arrays auch as x[n]:+y, x[n]:*y, etc. These mean x := x + y; x := x - y; etc. I got tired of writing ans[n] := ans[n] + deg, etc. Also, the methods in factr have been improved.
The function cancel (implemented with @) has been changed slightly. When calling @(var), if var does not exist, it is no longer an error, the function simply returns 0. If var does exist, it is deleted and @ returns 1. When cancelling a list, if any does not exist, it returns 0.
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 7.9b for Intel hardware. This was compiled with 11.7.10. It should work on 10.6 and later.
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 7.9b for Apple M1-4 hardware. This was compiled with Tahoe 26.2. Put Ferm7a in the right place so that the application Terminal sees it. Start up Terminal, then cd into Ferm7a. Type ./fer64. Don't just open the folder and double-click on fer64. For me, at least, that doesn't work well.
64 bit Linux version 7.9b. 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.
Suggested donation $60, using PayPal. (You don't have to have a PayPal account.)