What is FriCAS?¶
FriCAS is an advanced computer algebra system. Its capabilities range from calculus (integration and differentiation) to abstract algebra. It can plot functions and has an integrated help system.
What is the relation between FriCAS and Axiom?¶
FriCAS forked from Axiom in 2007. FriCAS seeks different development methodology and after fork removed several unused parts (without removing functionality). FriCAS fixed a lot of bugs and added new functionality. As of April 2013, in the src/algebra subdirectory, which hosts mathematical functionality about 25% of code was added after the fork.
What does the FriCAS name mean?¶
The prefix Fri is a deliberate misspelling of Free – FriCAS sounds like Free CAS.
There is also a second meaning: the Polish word “frykas” (which sounds similar to FriCAS) denotes generally tasty food (dainty); the French word “fricassee” and the German “Frikassee” name a particular food.
Where can I find online information about FriCAS?¶
The main entrance point to documentation about FriCAS is http://fricas.github.io.
The mailing list https://groups.google.com/group/fricas-devel?hl=en is intended both for users and developers. Please sign up before posting a message.
Where can I find documentation?¶
The main source of information about FriCAS is the “Axiom book” by Jenks and Sutor in its adaptation for FriCAS. FriCAS continues to update that contents of that book along with its development and calls it FriCAS Book. Its content is shown by the integrated HyperDoc help system. You can also access the book in .pdf form at http://fricas.github.io/book.pdf. An older version is available in in .xhtml form at http://fricas-wiki.math.uni.wroc.pl/JenksSutorInXhtml.
Where should I report bugs?¶
FriCAS moved to GitHub in March 2020. Issues should be reported to https://github.com/fricas/fricas/issues.
How one can use FriCAS in a pipe or in batch mode?¶
Currently trying to run plain
fricas command in a pipe hangs
(this is a bug, but fix requires substantial change).
Instead, one needs to pass
There several ways to let FriCAS process commands from a file.
fricas -nosman < tst.input > tst.output cat tst.input | fricas -nosman > tst.output echo ')read tst.input' | fricas -nosman > tst.output
Whereas the first two versions do not show the input in
the last command does. However, in the latter case it is hard to
distinguish input from output.
Note: Similarly to the commandline, pipe mode requires each function to be defined in a single line.
How to find where an exported function is implemented?¶
In Hyperdoc ‘Browse’ window enter the constructor name or its abbreviation and click on ‘Constructors’. In the resulting form specify all parameters. Then click on ‘Operations’ and finally on ‘Implementations’. If you are interested in a single operation, after clicking on ‘Operations’ click on an operation name and then click on ‘Implementations’.
Clef does not work. Is there an alternative?¶
If you have GNU Readline and
rlwrap installed, the
will use GNU Readline editing, tab completion, and history, i.e. call
FriCAS like this:
Default HyperDoc window is too small. How to enlarge it?¶
Put the lines like below in file called
FriCAS.hyperdoc.FormGeometry: =1200x700+40+40 FriCAS.hyperdoc.Geometry: =1200x700+40+40
They should take effect the next time you log in. If not you may have to manually run
xrdb -m ~/.Xresources
If you work with a 4K-display and want to make the font bigger, you
can add the following to your
FriCAS.hyperdoc.Geometry: =1500x800+0+0 FriCAS.hyperdoc.RmFont: -adobe-courier-bold-r-*-*-34-*-*-*-*-*-*-* FriCAS.hyperdoc.RmColor: black FriCAS.hyperdoc.ActiveFont: -adobe-courier-bold-r-*-*-34-*-*-*-*-*-*-* FriCAS.hyperdoc.ActiveColor: blue FriCAS.hyperdoc.FriCASFont: -adobe-courier-bold-r-*-*-34-*-*-*-*-*-*-* FriCAS.hyperdoc.FriCASColor: #008000 FriCAS.hyperdoc.BoldFont: -adobe-courier-bold-r-*-*-34-*-*-*-*-*-*-* FriCAS.hyperdoc.BoldColor: red FriCAS.hyperdoc.TtFont: -adobe-courier-bold-r-*-*-34-*-*-*-*-*-*-* FriCAS.hyperdoc.TtColor: black FriCAS.hyperdoc.EmphasizeFont: -adobe-courier-bold-r-*-*-34-*-*-*-*-*-*-* FriCAS.hyperdoc.EmphasizeColor: #800080 FriCAS.hyperdoc.InputBackground: #FFFF80 FriCAS.hyperdoc.InputForeground: black FriCAS.hyperdoc.BorderColor: black FriCAS.hyperdoc.Background: white
Of course, you might want to choose other fonts that are available on
your computer. Use
xfontsel to find out.
Why does FriCAS behave differently after loading new code?¶
When FriCAS loads new code, current variables become invalid. This happens when you use
or automatically when you compile a file via
You have to load and compile code before you start your computation.
Old Axiom FAQ¶
This list has been slightly adapted to match the new name FriCAS.
The fricas command fails.¶
This is likely one of two problems.
1. FriCAS uses clef as its command line editor. This has functionality similar to GNU Readline but was written independently. The fricas command uses
clef -e $FRICAS/bin/FRICASsys
Clef attempts to create new terminals and this might fail. The first thing to check is the permission bits on /dev/pty.
2. It is possible to run the fricas image, called
directly. Just type FRICASsys. It won’t have command recall or command
line editing but everything else is there.
A direct call to
FRICASsys (with the
variable set appropriately) can be done by calling
How can I create and access Lisp functions from FriCAS?¶
SExpression is the domain that handles raw lisp objects. It is possible to create SExpression elements directly.
m:=[1::SEX, 2::SEX] [1,2] Type: List SExpression n:=m::SEX (1 2) Type: SExpression car(n) 1 Type: SExpression
You can access lisp functions directly as in
Lisp is the domain, known to the interpreter and compiler, that contains lisp functions and symbols.
Notice that FriCAS is case-sensitive and that generally lisp symbols are upper case.
You can also create and call lisp functions.
)lisp (defun foo () (print "it works")) Value = FOO FOO()$Lisp "it works" it works Type: SExpression
While accessing and writing functions in Lisp is possible it is discouraged. FriCAS contains a programming language that should be able to achieve almost everything you need.
Use Lisp only when you cannot achieve your goal otherwise!
How can I see what the interpreter is trying to do?¶
)set message bottomup on
will tell you the signatures that the interpreter is trying to use.
Another method is to do
)lisp (setq |$monitorNewWorld| t)
and you can view database calls with
)lisp (setq *miss* t)
How can I record console output?¶
starts sending output to the file called
stops sending output to the file.
Graphics doesn’t work or sman fails to start ?¶
First try running
sman -debug -noclef -nonag -noht
If graphics still doesn’t work or sman fails to start then look at the error messages.
What is the purpose of the domain HACKPI?¶
HACKPI is a hack provided for the benefit of the FriCAS interpreter.
As a mathematical type, it is the simple transcendental extension
\(Q(\pi)\) of the rational numbers. This type allows interactive users to
use the name
%pi without a type both where a numerical value is
expected as in
or when the exact symbolic value is meant. The interpreter defaults a
%pi to HACKPI and then uses the various conversions to cast
it further as required by the context.
One could argue that it is unfair to single
%pi out from other
constants, but it occurs frequently enough in school examples
(specially for graphs) so it was worth a special hack. In a
non-interactive environment (library), HACKPI would not exist.
Why do .fricas.input defined functions fail in fricas?¶
You write this in your
mrd(x:Integer,v:Integer):Integer == x+y
You can’t see this function even though it appears to be defined. That’s because FriCAS is working in a new frame.
When you start
FRICASsys you are running the interpreter talking
directly to the terminal. So the
.input file is actually talking
to a frame at the top level. Your function is defined.
.fricas.input file is read in a “frame” called “initial”.
FRICASsys only uses the “initial” frame (although you can define and
use new ones). A frame contains its own variables and function definitions.
fricas command does several things that
not. In particular the
fricas shell script starts up the
process which starts
FRICASsys (which reads the
file) and then
sman creates a new frame (usually a random lisp gensym
name). In this new frame (created after
.fricas.input is read) your
mrandom function is not defined.
To see this do
fricas -nosman -- This starts FRICASsys directly. mrandom(3,3,3) -- compiles and runs the function )quit
fricas mrandom(3,3,3) -- undefined function )frame next mrandom(3,3,3) -- compiles and runs the function )frame names -- shows you all of the defined frames )quit
So with the
fricas shell script the process is
fricas start sman (done by fricas shell script) sman starts FRICASsys (done by sman) create frame "initial" (done by FRICASsys) read .fricas.input (define your function here) create frame "G00234" (done by sman) put up a command prompt (in frame G00234, no functions defined) )frame next (done by you) .... and now you're back in frame initial .... and your function is there
So your function was read and it is defined. However the function got
defined in the “initial” frame (because you defined it in the
.fricas.input file) and is not known in the frame created by
sman. The “)frame next” command will move you around the ring of
frames. (See the
)frame command in the appendix of the
How can I debug algebra code?¶
FriCAS contains some powerful commands to help with testing and
debugging library modules written in Spad and also the FriCAS system
itself. The most important of these commands is
This command is used to trace the execution of functions that make up the FriCAS system, functions defined by users, and functions from the system library. Almost all options are available for each type of function but exceptions will be noted below.
To list all functions, constructors, domains and packages that are traced, simply issue
To untrace everything that is traced, issue
When a function is traced, the default system action is to display the
arguments to the function and the return value when the function is
exited. Other information can be displayed or collected when a
function is traced and this is controlled by the various options. If a
domain or package is traced, the default action is to trace all
functions exported. Individual interpreter, lisp or boot functions can
be traced by listing their names after
)trace. Any options that are
present must follow the functions to be traced. For example
traces the function f. To untrace f, issue
)trace f )off
Note that if a function name contains a special character, it will be necessary to escape the character with an underscore
To trace all domains or packages that are or will be created from a
particular constructor, give the constructor name or abbreviation
)trace MATRIX )trace List Integer
The first command traces all domains currently instantiated with
Matrix. If additional domains are instantiated with this constructor
(for example, if you have used
they will be automatically traced. The second command traces
The following are the general options for the
)break after – causes a Common Lisp break loop to be entered after
exiting the traced function.
)break before – causes a Common Lisp break loop to be entered before
entering the traced function.
)break – is the same as
)count – causes the system to keep a count of the number of times the
traced function is entered.
The total can be displayed with:
and cleared with:
)trace )stats reset
)count n – causes information about the traced function to be displayed
for the first n executions. After the n-th execution, the function is
)depth n – causes trace information to be shown for only n levels of
recursion of the traced function.
)trace fib )depth 10
will cause the display of only 10 levels of trace information for the recursive execution of a user function fib.
)math causes – the function arguments and return value to be displayed
in the FriCAS monospace two-dimensional math format.
)nonquietly – causes the display of additional messages when a function
)nt – This suppresses all normal trace information. This option is useful
)timer options are used and you are interested in the
statistics but not the function calling information.
)off – causes untracing of all or specific functions. Without an argument,
all functions, constructors, domains and packages are untraced. Otherwise,
the given functions and other objects are untraced.
To immediately retrace the untraced functions, issue:
)only listOfDataToDisplay – causes only specific trace information to be
)restore – causes the last untraced functions to be retraced. If
additional options are present, they are added to those previously in
)stats – causes the display of statistics collected by the use of the
)stats reset – resets to 0 the statistics collected by the use of the
)timer – causes the system to keep a count of execution times for the
traced function. The total can be displayed with
)trace )stats and
)trace )stats reset.
)varbreak var1 ... varN – causes a Common Lisp break loop to be
entered after the assignment to any of the listed variables in the
)vars – causes the display of the value of any variable after it is
assigned in the traced function. Note that library code must have been
compiled using the
)vartrace option in order to support this option.
)vars var1 ... varN – causes the display of the value of any of
the specified variables after they are assigned in the traced function.
Note that library code must have been compiled using the
option in order to support this option.
)within executingFunction – causes the display of trace information
only if the traced function is called when the given executingFunction
The following are the options for tracing constructors, domains and packages.
)local op1 ... opN – causes local functions of the constructor to
be traced. Note that to untrace an individual local function, you must
use the fully qualified internal name, using the escape character before
the semicolon. For example:
)trace FRAC )local )trace FRAC_;cancelGcd )off
)ops op1 ... opN – By default, all operations from a domain or package
are traced when the domain or package is traced. This option allows you
to specify that only particular operations should be traced.
)trace Integer )ops min max _+ _-
traces four operations from the domain Integer. Since + and - are special characters, it is necessary to escape them with an underscore.
)lisp , and
)ltrace. Please refer to the
FriCAS Book section “FriCAS System Commands” for more detailed information.
How can I access lisp code from the FriCAS command line?¶
To run a lisp command from the command line use )lisp:
--> )lisp (+ 2 3)
If you want to run a lot of lisp commands from the command line do
--> )lisp (setq $dalymode t) --> (+ 2 3) --> (defun foo (x y) (+ x y)) --> (foo 2 3) --> 2 + 3
If the first character is a '(' then it is lisp else it is fricas
to disable it do
--> (setq $dalymode nil)
I wrote this change to the interpreter because I tend to use lisp a lot during maintenance. It breaks some syntax but you can work around that.
If you really want to “drop” into lisp do
--> )fin BOOT> (+ 2 3)
and now you are talking only to lisp at a lisp command prompt in the BOOT package. To restart FriCAS type