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Section 1 - About 1.1: What is FriCAS? 1.2: What is the relation between FriCAS and Axiom? 1.3: What does the FriCAS name mean? Section 2 - Online resources 2.1: Where can I find online information about FriCAS? 2.2: Where should I report bugs? 2.3: Where can I find documentation? Section 3 - 3.1: How can one use FriCAS in a pipe? 3.2: How can one use FriCAS in batch mode? 3.3: How to find where an exported function is implemented? Section 4 - User Interface 4.1: Clef does not work. Is there an alternative? 4.2: Default HyperDoc window is too small. How to enlarge it? 1.1: 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. 1.2: 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. Currently (April 2013) in the src/algebra subdirectory, which hosts mathematical functionality about 25% of code was added after fork. 1.3: 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: Polish word "frykas" (which sounds similar to FriCAS) denotes generally tasty food, French word "fricassee" and German "Frikassee" name a particular food. 2.1: Where can I find online information about FriCAS? The FriCAS home page is hosted at SourceForge: http://fricas.sourceforge.net There is a mailing list (please sign up before posting a message): https://groups.google.com/group/fricas-devel?hl=en This list is intended both for users and developers. 2.2: Where should I report bugs? FriCAS has a bug tracker at SourceForge: http://sourceforge.net/tracker/?atid=972421&group_id=200168 bugs specific to FriCAS should be reported there. There are also Wiki pages collecting information about bugs in all FriCAS derivatives: http://fricas-wiki.math.uni.wroc.pl/IssueTracker This page is obsolete and should not be used for new reports. 2.3: Where can I find documentation? The main source of information about FriCAS is "Axiom book" by Jenks and Sutor. 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 and in .xhtml form at: http://fricas-wiki.math.uni.wroc.pl/JenksSutorInXhtml 3.1: How one can use FriCAS in a pipe? 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 '-nosman' option like: fricas -nosman < tst.input > tst.output Note: Similarly to command line pipe mode requires each function to be defined in a single line. 3.2: How can one use FriCAS in batch mode? Pass ')read file.input' in pipe mode like: echo ')read tst.input' | fricas -nosman > tst.output 3.3: How to find where an exported function is implemented? In Hyperdoc 'Browse' window enter constructor name or abbreviation and click on 'Constructors'. In the resulting form specify all parameters. Then click on 'Operations' and then click on 'Implementations'. If you are interested in a single operation, after clicking on 'Operations' click on an operation name and then click on 'Implementations'. 4.1: Clef does not work. Is there an alternative? It is possible to use 'rlwrap' program (which is readline-based). The main FriCAS executable is designed to be run via line-editing wrapper program. Normally for command line editing FriCAS uses clef. However, it is possible to use different wrapper. To use 'rlwrap' do the following: 1) Make a shell script to change calling convention, like: #!/bin/sh CFILE=$2 shift 3 exec /full/path/to/rlwrap -f$CFILE "$@" 2) Type fricas -clefprog /path/to/wrapper/script 4.2 Default HyperDoc window is too small. How to enlarge it? Put the lines like below in file called ~/.Xresources: FriCAS.hyperdoc.FormGeometry: =1200x700+40+40 FriCAS.hyperdoc.Geometry: =1200x700+40+40 They should take effect the next time you log in (if not you may have to manually run "xrdb ~/.Xresources"). ---------------------------------------------------------------------- ---------------------------------------------------------------------- Below is old Axiom FAQ (slightly adapted to match the new name FriCAS) FAQ 12: The fricas command fails. FAQ 13: How can I create and access Lisp functions from FriCAS? FAQ 15: How can I see what the interpreter is trying to do? FAQ 16: How can I record console output? FAQ 17: Graphics don't work or sman fails to start ? FAQ 19: How can I get equations written on one line? FAQ 24: What is the purpose of the domain HACKPI? FAQ 25: Can I create or edit hypertex pages? FAQ 32: How can I input an equation as a string? FAQ 33: How can I run hypertex standalone? FAQ 35: Why do .fricas.input defined functions fail in fricas? FAQ 38: How can I debug algebra code? FAQ 39: How can I access lisp code from the FriCAS command line? =================================================================== FAQ 12: The fricas command fails. =================================================================== This is likely one of two problems. FriCAS uses clef as its command line editor. This has functionality similar to GNU Readline but was written independently. The fricas command uses: clef -e$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. Next it is possible to run the fricas image, called FRICASsys, directly. Just type FRICASsys. It won't have command recall or command line editing but everything else is there. =================================================================== FAQ 13: 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 with: GENSYM()$Lisp Lisp is the domain, known to the interpreter and compiler, that contains lisp functions and symbols. Notice that FriCAS is case-sensitive and that generally lisp symbols are upper case. You can also create and call lisp functions. For instance: )lisp (defun foo () (print "it works")) Value = FOO FOO()$Lisp "it works" it works Type: SExpression While accessing and writing functions in Lisp is possible it is generally not recommended as FriCAS contains a programming language that should be able to achieve almost everything you need. =================================================================== FAQ 15: 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) =================================================================== FAQ 16: How can I record console output? =================================================================== )spool filename starts sending output to the file called filename )spool )off stops sending output to the file =================================================================== FAQ 17: Graphics don't work or sman fails to start ? =================================================================== First try running sman as : sman -debug -noclef -nonag -noht If graphics still don't work or sman fails to start then look at the error messages. =================================================================== FAQ 19: How can I get equations written on one line? =================================================================== > Dear FriCAS supporters, > 2. I would also like to have the output of kind > > " - (s-1) * (s+1) * (p^4 +(2*e^3 + (24*s^2 - 4)*e)*p^3 * ...) * ... > " > > For example, my DoCon program can read this format ... > > 2.1 It prints these polynomials like for (Z[e])[p]: > " (e^2 + 2e)*p " > How to print it like for Z[p,e]: > " 2*p*e + e^2 " You may wish to use the InputForm domain, where you can find some bizarre functions. In your case, "unparse" may help you, as follows. (1) -> p:=(a+b+y)^2*y+1-(x+y+z)^4 (1) 4 3 2 2 2 - z + (- 4y - 4x)z + (- 6y - 12x y - 6x )z + 3 2 2 3 4 3 2 2 (- 4y - 12x y - 12x y - 4x )z - y + (- 4x + 1)y + (- 6x + 2b + 2a)y + 3 2 2 4 (- 4x + b + 2a b + a )y - x + 1 Type: Polynomial Integer (2) -> pi:=p::InputForm (2) (+ (+ (+ (+ (* - 1 (** z 4)) (* (+ (* - 4 y) (* - 4 x)) (** z 3))) (* (+ (+ (* - 6 (** y 2)) (* (* - 12 x) y)) (* - 6 (** x 2))) (** z 2))) (* (+ (+ (+ (* - 4 (** y 3)) (* (* - 12 x) (** y 2))) (* (* - 12 (** x 2)) y)) (* - 4 (** x 3))) z) ) (+ (+ (+ (+ (* - 1 (** y 4)) (* (+ (* - 4 x) 1) (** y 3))) (* (+ (* - 6 (** x 2)) (+ (* 2 b) (* 2 a))) (** y 2))) (* (+ (* - 4 (** x 3)) (+ (+ (** b 2) (* (* 2 a) b)) (** a 2))) y)) (+ (* - 1 (** x 4)) 1)) ) Type: InputForm (3) -> unparse(pi) (3) "(-z**4)+((-4*y)+(-4*x))*z**3+((-6*y*y)+(-12*x*y)+(-6*x*x))*z*z+((-4*y**3)+(- 12*x*y*y)+(-12*x*x*y)+(-4*x**3))*z+(-y**4)+((-4*x)+1)*y**3+((-6*x*x)+2*b+2*a) *y*y+((-4*x**3)+b*b+2*a*b+a*a)*y+(-x**4)+1" Type: String Alternatively you can get the LaTeX output string: (4) -> )lisp (|parseAndInterpret| "integrate(sin(x),x)::TexFormat::OutputForm") (4) ["$$","-{\cos ","\left(","{x} ","\right)}","$$"] Type: OutputForm Value = ((|OutputForm|) WRAPPED BRACKET (AGGLST "\"$$\"" "\"-{\\cos \"" "\"\\left(\"" "\"{x} \"" "\"\\right)}\"" "\"$$\"")) or the text form: (5) -> )lisp (|parseAndInterpret| "integrate(sin(x),x)::OutputForm") (5) - cos(x) Type: OutputForm Value = ((|OutputForm|) WRAPPED "-" (|cos| |x|)) or the actual string output: FriCAS's algebra gets output to a stream called |$algebraOutputStream| Thus you can get the output you want by: )set message autoload off )lisp (progn ; we need a new output stream that is backed by a string (setq tmpout (make-string-output-stream)) ; we hold on to the regular algebra output stream (setq save |$algebraOutputStream|) ; we capture the algebra output into the string stream (setq |$algebraOutputStream| tmpout) ; we generate output from string input (|parseAndInterpret| "(x+1)^9") ; we save the output into the result variable (setq result (get-output-stream-string |$algebraOutputStream|)) ; we restore the regular algebra output stream (setq |$algebraOutputStream| save) ; and we return the string as our value result) )lisp result result contains the output from fricas that you want. Alternatively you can see the internal representation using |pf2Sex| (parsed function to s-expression) by doing: if you start fricas and type )trace (|pf2Sex|) and then type some expression 1 you'll see the input and output of this function. This function (parsed function to s-expression) is internal to the fricas interpreter. it takes the parsed input line and converts it to a lisp s-expression. so the above '1' input yields 1> (|pf2Sex| ((|Integer| (|posn (0 "1" 1 1 "strings") . 0)) . "1")) 1< (|pf2Sex| 1) the "1>" line tells you the function input. the "1<" line tells you the function output. notice that even a simple input line generates type information. this function is not part of the exposed user interface because there is nothing at the user level that needs this information. =================================================================== FAQ 24: 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 draw(sin x,x=-%pi..%pi) ] or when the exact symbolic value is meant. The interpreter defaults a typeless %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. =================================================================== FAQ 25: Can I create or edit hypertex pages? =================================================================== The hypertex is intended to be edited by users. We are looking to build special purpose pages around courses such as linear algebra. Assume HERE=$FRICAS/doc/hypertex/pages The text can be found in$HERE/foo.ht or $HERE/foo.pht The macros are tex-like and live in$HERE/util.ht To change a page you need to: cd $HERE edit the page rm *~ (to delete backup copies) htadd * hypertex the htadd command takes arguments: htadd [-s|-l|-f db-directory] [-d|-n] filenames but, I'm sorry to say, these have not been fully documented. The htadd function will maintain the file called$HERE/ht.db which is a database of absolute byte indexes into files. Forgetting to run htadd will still work, sort-of, until you hit a bad byte index and then it will fail. Hypertex can also be directed elsewhere by using the HTPATH shell variable. =================================================================== FAQ 32: How can I input an equation as a string? =================================================================== There is an embedded command server within FRICASsys. Look at: http://daly.axiom-developer.org/TimothyDaly_files/lisptalk/pages/lisp35.html In particular, see the function parseAndInterpret stringBuf (which is boot language code. So in lisp I have to tack on the | | onto the function name and then I can call it like this: (1) -> )lisp (|parseAndInterpret| "integrate(sin x,x)") (1) - cos(x) Type: Union(Expression Integer,...) Value = ((|Union| (|Expression| (|Integer|)) (|List| (|Expression| (|Integer|))) ) WRAPPED 0 (1 # (1 0 . -1)) 0 . 1) (2) -> and sure enough! FriCAS parses and interprets the string. The result appears as stdout and the value returned seems to contain the type information. The "WRAPPED" information is the lisp data structure. > The string output function mentioned in FAQ 19 is a linear > form of the output. However FriCAS's native output machinery > is called CHARYBDIS which was a research project from the > 60s with the goal of printing mathematics on typewriters. > FriCAS still uses that code. =================================================================== FAQ 33: How do I run hypertex standalone? =================================================================== export FRICAS=/whatever/mnt/linux export HTPATH=$FRICAS/doc/hypertex/pages export PATH=$FRICAS/bin:$PATH hypertex =================================================================== FAQ 35: Why do .fricas.input defined functions fail in fricas? =================================================================== You write this in your .fricas.input file: 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. The .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. The "fricas" command does several things that FRICASsys does not. In particular the fricas shell script starts up the 'sman' process which starts FRICASsys (which reads the .fricas.input 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: FRICASsys mrandom(3,3,3) -- compiles and runs the function )quit Now do: 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 hardcopy book on page 579). =================================================================== FAQ 38: 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 ')trace'. 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:: )trace To untrace everything that is traced, issue:: )trace )off 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:: )trace f 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:: )trace _/D_,1 To trace all domains or packages that are or will be created from a particular constructor, give the constructor name or abbreviation after ')trace':: )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 'Matrix(Integer)' and 'Matrix(Float)'), they will be automatically traced. The second command traces 'List(Integer)'. The following are the general options for the ')trace' command. ')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 )break before. ')count' -- causes the system to keep a count of the number of times the traced function is entered. The total can be displayed with:: )trace )stats 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 untraced. ')depth n' -- causes trace information to be shown for only n levels of recursion of the traced function. The command:: )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 is traced. ')nt' -- This suppresses all normal trace information. This option is useful if the ')count' or ')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:: )trace )restore ')only listOfDataToDisplay' -- causes only specific trace information to be shown. ')restore' -- causes the last untraced functions to be retraced. If additional options are present, they are added to those previously in effect. ')stats' -- causes the display of statistics collected by the use of the ')count' and ')timer' options. ')stats reset' -- resets to 0 the statistics collected by the use of the ')count' and ')timer' options. ')timer' -- causes the system to keep a count of execution times for the traced function. The total can be displayed with ')trace )stats' and cleared with ')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 traced function. ')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 ')vartrace' 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 is running. 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. The command:: )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. Also See: ')boot', ')lisp' , and ')ltrace'. Please refer to the FriCAS Book section "FriCAS System Commands" for more detailed information. =================================================================== FAQ 39: 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 $dalymode says: If the first character is a '(' then it is lisp else it is fricas to disable it do: --> (setq$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: BOOT>(restart)