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 Topics FrontPage FriCAS language FriCAS compiler SandBox SPAD for Python <-- You are here. In Python we might write: \begin{sageblock} class Complex: "Example to demonstrate SPAD equivalent of Python Classes" def __init__(self, realpart, imagpart): self.r = realpart self.i = imagpart def real(self): return self.r def imag(self): return self.i def __str__(self): if self.i<0: return "%g - i %g"%(self.real(),-self.imag()) else: return "%g + i %g"%(self.real(),self.imag()) def __coerce__(self,b): if isinstance(b,Complex): return(self,b) else: return(self,Complex(b,0)) def __add__(self,b): return Complex(self.real()+b.real(), self.imag()+b.imag()) def __mul__(self,b): return Complex(self.real()b.real() - self.imag()b.imag(), self.real()b.imag() + self.imag()b.real()) \end{sageblock} Reference Now we can write: \begin{sageblock} x = Complex(3.0, -4.5) y = Complex(-2.0, 5.4) \end{sageblock} \begin{verbatim} print x+y \end{verbatim} \begin{equation} \label{eq1} \sage{x+y} \end{equation} \begin{verbatim} print x*y \end{verbatim} \begin{equation} \label{eq2} \sage{xy} \end{equation*} \begin{verbatim} print x+1.0 \end{verbatim} \begin{equation} \label{eq3} \sage{x+1.0} \end{equation} In SPAD (the Axiom first generation extension library compiler) we would write: \begin{spad} )abbrev domain CMPLXS ComplexSpad +++ Example of SPAD equivalent of Python Class ComplexSpad(): with new: (Float,Float) -> % ++ __init__ in Python coerce: Float -> % ++ __coerce__ in Python real: % -> Float ++ real in Python imag: % -> Float ++ imag in Python _+: (%,%) -> % ++ __add__ in Python _*: (%,%) -> % ++ __mul__ in Python coerce: % -> OutputForm ++ __str__ in Python == add Rep ==> Record(r:Float,i:Float) import Rep, OutputForm, Symbol new(realpart:Float,imagpart:Float):% == [realpart,imagpart] pretend % coerce(x:Float):% == new(x,0) real(x:%):Float == (x pretend Rep).r imag(x:%):Float == (x pretend Rep).i +(x:%, y:%):% == new(real(x)+real(y), imag(x)+imag(y)) (x:%, y:%):% == new(real(x)real(y) - imag(x)imag(y), real(x)imag(y) + imag(x)*real(y)) coerce(x:%):OutputForm == if imag(x)<0 then real(x)::OutputForm - outputForm(i) * (-imag(x))::OutputForm else real(x)::OutputForm + outputForm(i) * imag(x)::OutputForm \end{spad} Reference \begin{axiom} x := new(3.0, -4.5)$ComplexSpad y := new(-2.0, 5.4)$ComplexSpad x+y x*y x+1.0 \end{axiom} In Aldor we could write: \begin{aldor} #pile #include "axiom.as" ComplexAldor(): with new: (Float,Float) -> % coerce: Float -> % real: % -> Float imag: % -> Float _+: (%,%) -> % _*: (%,%) -> % coerce: % -> OutputForm == add Rep ==> Record(r:Float,i:Float) import from Rep, OutputForm, Symbol new(realpart:Float,imagpart:Float):% == per [realpart,imagpart] coerce(x:Float):% == new(x,0.0) real(x:%):Float == rep(x).r imag(x:%):Float == rep(x).i +(x:%, y:%):% == new(real(x)+real(y), imag(x)+imag(y)) (x:%, y:%):% == new(real(x)real(y) - imag(x)imag(y), real(x)imag(y) + imag(x)*real(y)) coerce(x:%):OutputForm == if imag(x)<0 then real(x)::OutputForm - outputForm(i) * (-imag(x))::OutputForm else real(x)::OutputForm + outputForm(i) * imag(x)::OutputForm \end{aldor} Reference And we get the following result when calling it in Axiom: \begin{axiom} x := new(3.0, -4.5)$ComplexAldor y := new(-2.0, 5.4)$ComplexAldor x+y x*y x+1.0 \end{axiom} [SandBox SPAD for Python 2] Some or all expressions may not have rendered properly, because Axiom returned the following error:Error: export AXIOM=/usr/local/lib/fricas/target/x86_64-unknown-linux; export ALDORROOT=/usr/local/aldor/linux/1.1.0; export PATH=$ALDORROOT/bin:$PATH; export HOME=/var/zope2/var/LatexWiki; ulimit -t 600; export LD_LIBRARY_PATH=/usr/local/lib/fricas/target/x86_64-unknown-linux/lib; LANG=en_US.UTF-8 $AXIOM/bin/AXIOMsys < /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/4574157217867657312-25px.axm ; file: /var/aw/var/LatexWiki/CMPLXS.NRLIB/CMPLXS.lsp ; in: SDEFUN |CMPLXS;new;2F$;1| ; (BOOT::SDEFUN BOOT::|CMPLXS;new;2F$;1| ; ((BOOT::|realpart| BOOT::|Float|) ; (BOOT::|imagpart| BOOT::|Float|) (BOOT::$ BOOT::$)) ; (CONS BOOT::|realpart| BOOT::|imagpart|)) ; --> DEFUN PROGN EVAL-WHEN ; ==> ; (SB-IMPL::%DEFUN 'BOOT::|CMPLXS;new;2F$;1| ; (SB-INT:NAMED-LAMBDA BOOT::|CMPLXS;new;2F$;1| ; (BOOT::|realpart| BOOT::|imagpart| BOOT::$) ; (BLOCK BOOT::|CMPLXS;new;2F$;1| ; (CONS BOOT::|realpart| BOOT::|imagpart|))) ; NIL 'NIL (SB-C:SOURCE-LOCATION)) ; ; caught STYLE-WARNING: ; The variable$ is defined but never used. ; in: SDEFUN |CMPLXS;real;$F;3| ; (BOOT::SDEFUN BOOT::|CMPLXS;real;$F;3| ; ((BOOT::|x| BOOT::$) (BOOT::$ BOOT::|Float|)) ; (BOOT::QCAR BOOT::|x|)) ; --> DEFUN PROGN EVAL-WHEN ; ==> ; (SB-IMPL::%DEFUN 'BOOT::|CMPLXS;real;$F;3| ; (SB-INT:NAMED-LAMBDA BOOT::|CMPLXS;real;$F;3| ; (BOOT::|x| BOOT::$) ; (BLOCK BOOT::|CMPLXS;real;$F;3| (BOOT::QCAR BOOT::|x|))) ; NIL 'NIL (SB-C:SOURCE-LOCATION)) ; ; caught STYLE-WARNING: ; The variable $is defined but never used. ; in: SDEFUN |CMPLXS;imag;$F;4| ; (BOOT::SDEFUN BOOT::|CMPLXS;imag;$F;4| ; ((BOOT::|x| BOOT::$) (BOOT::$BOOT::|Float|)) ; (BOOT::QCDR BOOT::|x|)) ; --> DEFUN PROGN EVAL-WHEN ; ==> ; (SB-IMPL::%DEFUN 'BOOT::|CMPLXS;imag;$F;4| ; (SB-INT:NAMED-LAMBDA BOOT::|CMPLXS;imag;$F;4| ; (BOOT::|x| BOOT::$) ; (BLOCK BOOT::|CMPLXS;imag;$F;4| (BOOT::QCDR BOOT::|x|))) ; NIL 'NIL (SB-C:SOURCE-LOCATION)) ; ; caught STYLE-WARNING: ; The variable$ is defined but never used. ; ; compilation unit finished ; caught 3 STYLE-WARNING conditions Killed Checking for foreign routines AXIOM="/usr/local/lib/fricas/target/x86_64-unknown-linux" spad-lib="/usr/local/lib/fricas/target/x86_64-unknown-linux/lib/libspad.so" foreign routines found openServer result -2 FriCAS Computer Algebra System Version: FriCAS 1.2.2 Timestamp: Mon Sep 30 18:53:32 UTC 2013 ----------------------------------------------------------------------------- Issue )copyright to view copyright notices. Issue )summary for a summary of useful system commands. Issue )quit to leave FriCAS and return to shell. ----------------------------------------------------------------------------- (1) -> (1) -> (1) -> (1) -> (1) -> )abbrev domain CMPLXS ComplexSpad +++ Example of SPAD equivalent of Python Class ComplexSpad(): with new: (Float,Float) -> % ++ __init__ in Python coerce: Float -> % ++ __coerce__ in Python real: % -> Float ++ real in Python imag: % -> Float ++ imag in Python _+: (%,%) -> % ++ __add__ in Python _*: (%,%) -> % ++ __mul__ in Python coerce: % -> OutputForm ++ __str__ in Python == add Rep ==> Record(r:Float,i:Float) import Rep, OutputForm, Symbol new(realpart:Float,imagpart:Float):% == [realpart,imagpart] pretend % coerce(x:Float):% == new(x,0) real(x:%):Float == (x pretend Rep).r imag(x:%):Float == (x pretend Rep).i +(x:%, y:%):% == new(real(x)+real(y), imag(x)+imag(y)) (x:%, y:%):% == new(real(x)real(y) - imag(x)imag(y), real(x)imag(y) + imag(x)*real(y)) coerce(x:%):OutputForm == if imag(x)<0 then real(x)::OutputForm - outputForm(i) * (-imag(x))::OutputForm else real(x)::OutputForm + outputForm(i) * imag(x)::OutputForm Compiling FriCAS source code from file /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5264130288122953016-25px001.spad using old system compiler. CMPLXS abbreviates domain ComplexSpad ------------------------------------------------------------------------ initializing NRLIB CMPLXS for ComplexSpad compiling into NRLIB CMPLXS processing macro definition Rep ==> Record(r: Float,i: Float) importing Record(r: Float,i: Float) importing OutputForm importing Symbol compiling exported new : (Float,Float) -> $CMPLXS;new;2F$;1 is replaced by CONS Time: 0 SEC. compiling exported coerce : Float -> $Time: 0 SEC. compiling exported real :$ -> Float CMPLXS;real;$F;3 is replaced by QCAR Time: 0 SEC. compiling exported imag :$ -> Float CMPLXS;imag;$F;4 is replaced by QCDR Time: 0 SEC. compiling exported + : ($,$) ->$ Time: 0 SEC. compiling exported * : ($,$) -> $Time: 0 SEC. compiling exported coerce :$ -> OutputForm Time: 0 SEC. (time taken in buildFunctor: 0) ;;; *** |ComplexSpad| REDEFINED ;;; *** |ComplexSpad| REDEFINED Time: 0 SEC. Cumulative Statistics for Constructor ComplexSpad Time: 0 seconds finalizing NRLIB CMPLXS Processing ComplexSpad for Browser database: --------constructor--------- --------(new (% (Float) (Float)))--------- --->-->ComplexSpad((new (% (Float) (Float)))): Improper first word in comments: "__init__ in Python" --------(coerce (% (Float)))--------- --->-->ComplexSpad((coerce (% (Float)))): Improper first word in comments: "__coerce__ in Python" --------(real ((Float) %))--------- --------(imag ((Float) %))--------- --------(+ (% % %))--------- --->-->ComplexSpad((+ (% % %))): Improper first word in comments: "__add__ in Python" --------( (% % %))--------- --->-->ComplexSpad(( (% % %))): Improper first word in comments: "__mul__ in Python" --------(coerce ((OutputForm) %))--------- --->-->ComplexSpad((coerce ((OutputForm) %))): Improper first word in comments: "__str__ in Python" ; compiling file "/var/aw/var/LatexWiki/CMPLXS.NRLIB/CMPLXS.lsp" (written 23 FEB 2014 06:23:18 AM): ; /var/aw/var/LatexWiki/CMPLXS.NRLIB/CMPLXS.fasl written ; compilation finished in 0:00:00.039 ------------------------------------------------------------------------ ComplexSpad is now explicitly exposed in frame initial ComplexSpad will be automatically loaded when needed from /var/aw/var/LatexWiki/CMPLXS.NRLIB/CMPLXS (1) -> x := new(3.0, -4.5)$ComplexSpad $${3.0} -{i \ {4.5}} \leqno(1)$$ Type: ComplexSpad y := new(-2.0, 5.4)$ComplexSpad $$-{2.0}+{i \ {5.4}} \leqno(2)$$ Type: ComplexSpad x+y $${1.0}+{i \ {0.9}} \leqno(3)$$ Type: ComplexSpad x*y $${18.3}+{i \ {25.2}} \leqno(4)$$ Type: ComplexSpad x+1.0 $${4.0} -{i \ {4.5}} \leqno(5)$$ Type: ComplexSpad (6) -> #pile #include "axiom.as" ComplexAldor(): with new: (Float,Float) -> % coerce: Float -> % real: % -> Float imag: % -> Float _+: (%,%) -> % _*: (%,%) -> % coerce: % -> OutputForm == add Rep ==> Record(r:Float,i:Float) import from Rep, OutputForm, Symbol new(realpart:Float,imagpart:Float):% == per [realpart,imagpart] coerce(x:Float):% == new(x,0.0) real(x:%):Float == rep(x).r imag(x:%):Float == rep(x).i +(x:%, y:%):% == new(real(x)+real(y), imag(x)+imag(y)) (x:%, y:%):% == new(real(x)real(y) - imag(x)imag(y), real(x)imag(y) + imag(x)*real(y)) coerce(x:%):OutputForm == if imag(x)<0 then real(x)::OutputForm - outputForm(i) * (-imag(x))::OutputForm else real(x)::OutputForm + outputForm(i) * imag(x)::OutputForm Compiling FriCAS source code from file /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/4438001028188480131-25px003.as using AXIOM-XL compiler and options -O -Fasy -Fao -Flsp -laxiom -Mno-ALDOR_W_WillObsolete -DAxiom -Y $AXIOM/algebra -I$AXIOM/algebra Use the system command )set compiler args to change these options.  Some or all expressions may not have rendered properly, because Latex returned the following error:This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) \write18 enabled. %&-line parsing enabled. entering extended mode (./8890045446626885534-16.0px.tex LaTeX2e <2005/12/01> Babel and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, farsi, croatian, ukrainian, russian, bulgarian, czech, slov ak, danish, dutch, finnish, basque, french, german, ngerman, ibycus, greek, mon ogreek, ancientgreek, hungarian, italian, latin, mongolian, norsk, icelandic, i nterlingua, turkish, coptic, romanian, welsh, serbian, slovenian, estonian, esp eranto, uppersorbian, indonesian, polish, portuguese, spanish, catalan, galicia n, swedish, ukenglish, pinyin, loaded. 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LaTeX Warning: Characters dropped after \end{sageblock}' on input line 150. LaTeX Warning: Characters dropped after \end{verbatim}' on input line 153. (/usr/share/texmf-texlive/tex/latex/jknapltx/ursfs.fd) (/usr/share/texmf-texlive/tex/latex/amsfonts/umsa.fd) (/usr/share/texmf-texlive/tex/latex/amsfonts/umsb.fd) (/usr/share/texmf-texlive/tex/latex/base/ulasy.fd) [1] LaTeX Warning: Characters dropped after \end{verbatim}' on input line 160. [2] LaTeX Warning: Characters dropped after \end{verbatim}' on input line 167. [3] Missing $inserted.$ l.180 _ +: (%,%) -> % ++ __add__ in Python Missing $inserted.$ l.186 Missing $inserted.$ l.191 _ +(x:%, y:%):% == Missing $inserted.$ l.201 \end{spad} \newpage [4] LaTeX Warning: Characters dropped after \end{axiom}' on input line 208. You can't use macro parameter character #' in vertical mode. l.210 # pile You can't use macro parameter character #' in horizontal mode. l.211 # include "axiom.as" Missing $inserted.$ l.217 _ +: (%,%) -> % Missing $inserted.$ l.223 Missing $inserted.$ l.228 _ +(x:%, y:%):% == new(real(x)+real(y), imag(x)+imag(y)) Missing $inserted.$ l.236 \end{aldor} \newpage [5] LaTeX Warning: Characters dropped after \end{axiom}' on input line 243. [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] (./8890045446626885534-16.0px.aux) ) (see the transcript file for additional information) Output written on 8890045446626885534-16.0px.dvi (17 pages, 6272 bytes). Transcript written on 8890045446626885534-16.0px.log. 

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