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SandBox SPAD for Python
  
last edited 17 years ago

Edit detail for SandBox SPAD for Python revision 1 of 1
1
Editor:
Time: 2007/11/18 18:33:52 GMT-8
Note: continued: SandBox SPAD for Python 2 
changed:
-
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":http://docs.python.org/ref/customization.html

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}
\sage{x+y}
\end{equation}

\begin{verbatim}
print x*y
\end{verbatim}

\begin{equation}
\sage{x*y}
\end{equation}

\begin{verbatim}
print x+1.0
\end{verbatim}

\begin{equation}
\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"::Symbol) * (-imag(x))::OutputForm
      else
        real(x)::OutputForm + outputForm("i"::Symbol) * imag(x)::OutputForm
\end{spad}

"Reference":/public/book2.pdf#page=940

\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"::Symbol) * (-imag(x))::OutputForm
      else
        real(x)::OutputForm + outputForm("i"::Symbol) * imag(x)::OutputForm
\end{aldor}

"Reference":http://www.aldor.org/docs/HTML/chap7.html

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]


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) -> <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


;;;     ***       |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) -> <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.
Some or all expressions may not have rendered properly, because Latex returned the following error:
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ogreek, ancientgreek, hungarian, italian, latin, mongolian, norsk, icelandic, i
nterlingua, turkish, coptic, romanian, welsh, serbian, slovenian, estonian, esp
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 Xy-pic version 3.7 <1999/02/16>
 Copyright (c) 1991-1998 by Kristoffer H. Rose <krisrose@ens-lyon.fr>
 Xy-pic is free software: see the User's Guide for details.




Loading kernel: messages; fonts; allocations: state, direction,
utility macros; pictures: \xy, positions, objects, decorations;
kernel objects: directionals, circles, text; options; algorithms: directions,
edges, connections;  Xy-pic loaded))
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l.180     _
           +: (%,%) -> %              ++ __add__    in Python
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l.186 
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l.201 \end{spad}
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l.223 


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l.236 \end{aldor}
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(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.