create file, say F1.input like this
f(n)==n^2 f(4)
And run it using the command
fricas -nosman < F1.input > o.txt
The output will go to file o.txt
Use typeOf
r:=sqrt(-5)::Complex(Float) (3) 2.2360679774_997896964 %i (5) -> typeOf(r) (5) Complex(Float)
Home page https://fricas.github.io/index.html
To install fricas on Linux Manjaro sudo pacman -S sagemath.
in case of error while installing the package, try sudo pacman -Rs sagemath and then
repeat the previous command
If copy paste does not work between windows and Linux VBox, try VBoxClient --clipboard
To use Fricas online, go to
http://axiom-wiki.newsynthesis.org/FriCASIntegration
http://fricas-wiki.math.uni.wroc.pl/SandBox
https://wiki.fricas.org/SandBox
Go to bottom of page, type
\begin{axiom} setSimplifyDenomsFlag(true) integrate(sin(x),x) \end{axiom}
Then click the preview button
to send email to supprt group use fricas-devel@googlegroups.com
To download go to https://sourceforge.net/projects/fricas
To installl on Linux Manjaro, type yay -S fricas . Do not use the Manjaro GUI package
manager, it always gives build error for some reason. Make sure to install yay first using GUI
manager.
Make sure when installing Linux on VBox, to add second CPU to configuration of VBox. i.e. do not use ONE CPU (which is default). There is a bug in fricas installation which makes it fail due to use of multi-threading if only one CPU exist. This should be fixed in future, but just in case.
To install directly, see http://fricas.sourceforge.net/doc/INSTALL.txt
To build directly (but I use yay now and not this any more)
#install sbcl #sudo apt-get install sbcl #do not use this. bug sudo apt-get install clisp #This lisp works sudo apt-get install dvipng sudo apt-get install auctex bzip2 -dk fricas-1.3.2-full.tar.bz2 tar -xf fricas-1.3.2-full.tar
Now build it
make clean fricas-1.3.2>./configure --with-lisp=/usr/bin/clisp checking build system type... x86_64-linux-gnu checking host system type... x86_64-linux-gnu checking target system type... x86_64-linux-gnu checking for make... make checking for gcc... gcc checking whether the C compiler works... yes checking for C compiler default output file name... a.out checking for suffix of executables... checking whether we are cross compiling... no checking for suffix of object files... o checking whether we are using the GNU C compiler... yes checking whether gcc accepts -g... yes checking for gcc option to accept ISO C89... none needed checking for a BSD-compatible install... /usr/bin/install -c checking for touch... touch checking for mktemp... mktemp checking for gawk... gawk checking for gtar... no checking for tar... tar checking for ranlib... ranlib checking for ar... ar checking for latex... /usr/local/texlive/2017/bin/x86_64-linux/latex checking for makeindex... makeindex checking PREGENERATED... "/home/me/data/fricas/fricas-1.3.2/pre-generated" checking for sbcl... /usr/bin/sbcl checking Lisp implementation... This is SBCL 1.3.1.debian, an implementation of ANSI Common Lisp. More information about SBCL is available at <http://www.sbcl.org/>. SBCL is free software, provided as is, with absolutely no warranty. It is mostly in the public domain; some portions are provided under BSD-style licenses. See the CREDITS and COPYING files in the distribution for more information. * sbcl checking how to run the C preprocessor... gcc -E checking for grep that handles long lines and -e... /bin/grep checking for egrep... /bin/grep -E checking for ANSI C header files... yes checking for sys/types.h... yes checking for sys/stat.h... yes checking for stdlib.h... yes checking for string.h... yes checking for memory.h... yes checking for strings.h... yes checking for inttypes.h... yes checking for stdint.h... yes checking for unistd.h... yes fasl checking dirent.h usability... yes checking dirent.h presence... yes checking for dirent.h... yes checking whether closedir is declared... yes checking whether opendir is declared... yes checking whether readdir is declared... yes checking whether dirfd is declared... yes checking whether fchdir is declared... yes checking signal.h usability... yes checking signal.h presence... yes checking for signal.h... yes checking whether sigaction is declared... yes checking for sys/stat.h... (cached) yes checking for unistd.h... (cached) yes checking whether getuid is declared... yes checking whether geteuid is declared... yes checking whether getgid is declared... yes checking whether getegid is declared... yes checking whether kill is declared... yes checking sys/socket.h usability... yes checking sys/socket.h presence... yes checking for sys/socket.h... yes checking util.h usability... no checking util.h presence... no checking for util.h... no checking pty.h usability... yes checking pty.h presence... yes checking for pty.h... yes checking whether openpty is declared... yes checking for openpty in -lc... no checking for openpty in -lutil... yes checking sys/wait.h usability... yes checking sys/wait.h presence... yes checking for sys/wait.h... yes checking whether wait is declared... yes checking whether fork is declared... yes checking for X... no configure: The Graphics and HyperDoc components are disabled. configure: WARNING: Aldor interface will not be built. configure: creating ./config.status config.status: creating src/clef/Makefile config.status: creating src/sman/Makefile config.status: creating src/hyper/Makefile config.status: creating src/doc/Makefile config.status: creating Makefile config.status: creating src/Makefile config.status: creating src/lib/Makefile config.status: creating src/lisp/Makefile config.status: creating src/boot/Makefile config.status: creating src/interp/Makefile config.status: creating src/algebra/Makefile config.status: creating src/input/Makefile config.status: creating src/etc/Makefile config.status: creating src/aldor/Makefile config.status: creating src/aldor/Makefile2 config.status: creating src/aldor/Makefile3 config.status: creating contrib/emacs/Makefile config.status: creating config/fricas_c_macros.h extracting list of SPAD type definitions Type 'make' (without quotes) to build FriCAS
And
make
Add these to .bashrc
export PATH=/home/me/data/fricas/fricas-1.3.2/target/x86_64-linux-gnu/bin:$PATH export AXIOM=/home/me/data/fricas/fricas-1.3.2/target/x86_64-linux-gnu export DAASE=/home/me/data/fricas/fricas-1.3.2/target/x86_64-linux-gnu
Example of integral which fails in Fricas
ii:=integrate(log(1+x)/x/(1+(1+x)^(1/2))^(1/2),x) >> Error detected within library code: integrate: implementation incomplete (constant residues)
For Fricas, use these commands to get 1D plain text output
setSimplifyDenomsFlag(true) )set output algebra on ii:=integrate(1/(x*(3*x^2 - 6*x + 4)^(1/3)),x); unparse(ii::InputForm)
Otherwise the output will go to console in 2D. To get Latex output do
setSimplifyDenomsFlag(true) )set message prompt plain )set output algebra off )set output tex on s:=asin(sqrt(1-x^2))/sqrt(1-x^2); ii:=integrate(s,x)
To record console session to file, use (from https://github.com/daly/axiom/blob/master/faq)
)spool filename starts sending output to the file called filename )spool )off stops sending output to the file
Like this
)spool /home/me/data/output.txt )set message prompt plain )set output algebra off )set output tex on ii:=integrate(sin(x), x) )set output tex off )set output algebra on unparse(ii::InputForm) )spool )off
To send Latex output to file do
)set output tex on )set output tex filename
To turn off, just do )set output tex off. Make sure to tex on first. To send back to
console, do )set output tex console
To read an input file into Axiom, use the )read system command. read For example, you can read a file in a particular directory by issuing
)read /spad/src/input/matrix.input
To make record
)clear prop r r: Record(a: String,b:Integer) r:=["hello",10]
Some hints below thanks to Waldek Hebisch http://mathforum.org/kb/message.jspa?messageID=9791385
copied here so easy for me to get to:
1. How to measure CPU time used from the int call? (3) -> )set messages time on (3) -> integrate(x^(3/2)/sqrt(1 + x^5), x) Type: Union(Expression(Integer),...) Time: 0.06 (EV) + 0.00 (OT) = 0.06 sec
There is command ')set messages time on' tell FriCAS to print time needed to execute
following command. The (EV) part means actual computation (OT) printing and at the end
there is total
2. How to measure leaf count/size of result? (Maple and Mathematica have build in function to do this)
That is a bit tricky. FriCAS (like Axiom) has quite different representation of expressions tham Maple or Mathematica. In FriCAS expression is a quotient of two polnomials, with variables beeing kernels:
(13) -> f := exp(x^3 + 1/x) + 1 (14) -> numer(f) 4 x + 1 ------ x (15) -> denom(f) (16) -> variables(numer(f)) 4 x + 1 ------ x (16) [%e ] Type: List(Kernel(Expression(Integer))) Time: 0.00 (OT) = 0.00 sec
From FriCAS point of view natural measure of size is number of monomials in numerator and denominator:
(17) -> numberOfMonomials(numer(f)) (17) 2 (18) -> numberOfMonomials(denom(f)) (18) 1
but this may underestimate size because kernels may be big. Also internally given kernel is stored only once, but in printed output it may appear several times.
It is possible to traverse expression is somewhat tree like manner, so it is possible to give better approximation to say Maple result, but that would require investigating what Maple is doing. I personally never used Maple node count so I do not know it this is simple or if there are some traps.
3. How to check if int passed or failed? Aborted? nil result? etc..
integrate may produce an error (in particular it will do so if it can not decide if integral is elementary). Or may produce unevaluated integral. Or normal result. At programistic level it is possible to catch errors, but a bit tricky, If you look at printed output, than errors are reasonably easy to match via a regex:
(22) -> integrate(1/sqrt(exp(x) - x + 1), x) integrate: implementation incomplete (constant residues)
the '>> Error' part indicates error. Unevaluated integrals always have integral sign at top
level. FriCAS never returns partial results, so text match is relatively easy. Or you may use
code like:
test_int(f) == res : Union(Expression Integer, LE) res := integrate(f, 'x) res0 : List Expression Integer := res case Expression Integer => [res::(Expression Integer)]@(List Expression Integer) res case List Expression Integer => res::(List Expression Integer) error "test_int: impossible 1" for ri in res0 repeat #(kernels ri) > 0 and is?(operator first kernels ri, 'integral) => print("Unevaluated integral"::OutputForm)
Note1: this is part extracted from bigger test script, I did not test it alone.
Note2: FriCAS may either return list of results or a single result. Middle part converts this to have always a list (typically of length 1). The last part is a loop so that all solutions can be examined. It you only want to know if result is evaluated, than loop is not needed: more than one result means that integral is evaluated.
Note3: In FriCAS testsuite I use a bit different test for evaluated integrals. Namely, FriCAS can do useful computations on unevaluated integrals and in particular unevaluated integrals may appear in the argument to integrate. Such unevaluated integrals of course may propagate form input to the output. The test above may misclasify such integral as unevaluated, while better test checks that unevaluated integral came from the input.
4. And most importantly, how to export the result (if it passed) to a plain text file in
_Latex_ format?
(24) -> )set output tex on (24) -> integrate(exp(x)*exp(1/(exp(x)+1)-x), x)
Here one have to decide what to do with errors. Without error trapping error will abort currently executing function and propagate to top level (up to command line).
After doing:
)set break resume
after error FriCAS will continue executing file from next command (but still abort current command). If you need real loop then I can provide error catcher, but it is a bit more complicated than snippets above. Waldek Hebisch
To get type of value in fricas do typeOf(r)
To clear everything do
)clear all )clear completely