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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}

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) -> <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</spad> 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 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

$$-{2.0}+{i \ {5.4}} \leqno(2)$$

$${1.0}+{i \ {0.9}} \leqno(3)$$

$${18.3}+{i \ {25.2}} \leqno(4)$$

$${4.0} -{i \ {4.5}} \leqno(5)$$

Type: ComplexSpad (6) -> <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</aldor> 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.

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[2]

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[3] Missing $inserted. <inserted text>$ l.180 _ +: (%,%) -> % ++ __add__ in Python Missing $inserted. <inserted text>$ l.186

Missing $inserted. <inserted text>$ l.191 _ +(x:%, y:%):% == Missing $inserted. <inserted text>$ l.201 \end{spad} \newpage [4]

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