Mathematica compatibility functions and translator for the
Maxima computer algebra system.
------------------------------------------------------------
VERSION 0.25
Copyright (C) 2008, John Lapeyre All rights reserved.
This program is free software; you can redistribute it
and/or modify it only under the terms of the GNU General
Public License version 2 as published by the Free Software
Foundation.
Mathematica is a registered trademark of Wolfram Research,
Inc. (2008)
------------------------------------------------------------
INTRODUCTION:
This software has three parts:
1) Compatibility functions for Maxima that try to duplicate
Mathematica(tm) (Mma) functions, eg 'Table'. Used alone,
they provide a quasi-Mma environment. Mixima is designed to
extend the maxima environment more or less like any other
package-- not to replace it, as does Mockmma. The
compatibility functions are maxima functions called with
maxima syntax from within maxima.
2) A translator that translates a subset of Mma code to
Maxima code. The compatitiblity functions can be used by
themselves or with this translator. But the translator
produces code that depends on the compatibility functions.
3) A mock Mma mode that allows using Mathematica syntax at
the command line. This is a sort of Mma clone. This is a
modified version of the Fateman Mockmma project. The allowed
syntax and semantics is limited.
There are more READMEs at the top level and some information
can be found in doc/mixima_user_doc Also see the section on
online help at the bottom of this document.
------------------------------------------------------------
INSTALL:
MS Windows and other OSs: If you have maxima installed, this software
should work in principle. It is tested a bit on Win32; the testsuite
passes. For Windows, copy the entire folder .\build\mixima
to your maxima share folder. For instance, copy the
folder to
c:\Program Files\Maxima-5.25.1-gcl\share\maxima\5.25.1\share
Then you should have a folder
c:\Program Files\Maxima-5.25.1-gcl\share\maxima\5.25.1\share\mixima
with all the mixima files in it.
Linux/unix system with perl installed: Edit the
file config_install.pl to suit your preference (the default
should be ok) and type
mkdistcompat.pl
Then, as root (or sudo) type
./install.pl
With default settings, this installs files to the maxima
share directories and some executables to /usr/local/bin.
If this does not work, try copying ./build/mixima to a
location where your maxima installation can see it.
Known problems:
* The mockmma shell does not currently work well with xmaxima nor
wxmaxima. The compatibility functions seem to work ok.
* wxmaxima has a bug that will print an error message involving STRIPDOLLAR.
Mixima can still be used, but the state of maxima is changed and and some things
are broken. To avoid this, remove the line that loads "loadlast.mac" in
the file "mixima.mac". The offending function is Clear().
------------------------------------------------------------
TESTING:
If mixima is installed, give the maxima commands
load("mixima/mixima");
mixtest();
Or in this toplevel directory, start maxima and give the following commands:
load("./tests/mixima_testsuite.mac");
or
load("./tests/mixima_testsuite_slow.mac");
------------------------------------------------------------
QUICK START:
The compatibility functions are functions written in the
Maxima language that emulate the behavior of Mathematica
(Mma) functions. For example:
* Compatibility Functions
> maxima
(%i1) load("mixima/mixima");
(%o1) /usr/share/maxima/5.21.1/share/mixima/mixima.mac
(%i2) Table( i*j, [i,3],[j,3]);
(%o2) [[1, 2, 3], [2, 4, 6], [3, 6, 9]]
(%i3) mixFuncs(); /* lists compatibililty functions */
(%i4) mixDoc(Table); /* prints examples */
* entering the mockmma shell to enter Mma code at the command line
(%i5) tomma();
In[6]:= Array[#1^#2 &,{3,4}]
(%i6) Array(lambda( [[lambda_args]], (lambda_args[1]^lambda_args[2]) ),[3,4])
(%o6) [[1, 1, 1, 1], [2, 4, 8, 16], [3, 9, 27, 81]]
Out[6]:= {{1, 1, 1, 1}, {2, 4, 8, 16}, {3, 9, 27, 81}}
In[7]:= Exit
(%o7) true
(%i8) %o6;
(%o8) [[1, 1, 1, 1], [2, 4, 8, 16], [3, 9, 27, 81]]
tomma() does not work with xmaxima and wxmaxima.
* Evaluating strings of Mma code.
(%i1) smmatomax(" a = 1 ");
(%o1) 1
(%i2) a;
(%o2) 1
smmatomax() should work with xmaxima and wxmaxima.
* translating code at the unix shell
mmatomax mma_code.m
------------------------------------------------------------
MORE DETAILS:
Mixima can be used several ways:
** Functions that extend Maxima with functions similar to those in Mma
> maxima
(%i1) load("mixima/mixima");
(%o1) /usr/share/maxima/5.21.1/share/mixima/mixima.mac
(%i2) Table( i*j, [i,3],[j,3]);
(%o2) [[1, 2, 3], [2, 4, 6], [3, 6, 9]]
Note that the syntax used here is Maxima syntax, not Mma. For instance
lists: {} --> []
function call: [] --> ()
assignment: = --> : ,etc.
A list of the compatibility functions is included in the file
'function_list'. Example code can be found in the ./tests folder
and in the ./applications folder. The code in the tests folder contains comments
for some Mma functions concerning how much of those functions are implemented.
As a convenience, the executable 'mixima' loads the mixima code automatically
(but does not currently allow other initialization scripts):
> mixima
...
(%i1) Tuples([0,1],2);
(%o1) [[0, 0], [0, 1], [1, 0], [1, 1]]
** Mixima can use the Mockmma shell. For example,
(%i1) tomma();
...
In[1]:= Table[ i j,{i,3},{j,3}]
Out[1]:= {{1, 2, 3}, {2, 4, 6}, {3, 6, 9}}
In[2]:= NIntegrate[1/Sqrt[x],{x,0,1},PrecisionGoal->12]
Out[2]:= 1.999999999999998
In[3]:= Exit
As a convenience, the executable 'miximamma' starts maxima and
the Mockmma shell with the mixima translator.
Here are commands that can be used to control whether the results are
shown in Maxima or Mma or both.
MmaShowOut[True] (or False) to control Mma output
MmaShowTrans[True] (or False) to control maxima display of translation.
MmaVerbose[True] (or False) to print more stuff during evaluation.
MmaPrintEx[arg] print strings suitable for inserting in rtest files
as tests and examples. If no arg is given , print no function name
in the example. If a string is given, it is used as the function name
for subsequent input. If arg is False, then disable.
** The original Mockmma is included (modified slightly from the Mockmma distribution)
Usually, when we refer to mockmma, we don't mean this original,
but rather the mockmma shell modified to use the compatibility functions.
(%i1) :lisp (mockmma)
...
In[1]:=
As a convenience, the executable 'mockmma' starts maxima and
Mockmma (the version by H.Monroe based on code by Fateman et. al.)
Note that for many inputs, Mockmma and Mixima with the Mockmma shell
give identical output. But in fact there are important difference that
are not explained here.
** Using translator from maxima
** Using stand alone translation scripts
For these, see README.translator
------------------------------------------------------------
COMPATIBILITY FUNCTIONS:
A) Use
Due in part to fundamental differences int the two CAS's,
these compatibility functions reproduce the behavior of the
original functions imperfectly and to varying
degrees. Examples of ways in which they may be useful are
1. They can be used in Maxima projects by people who are already
familiar with the Mma functions.
2. They can be used to more easily translate user Mma code to Maxima.
3. They may provide functionality not currently available in Maxima.
Use of Compatibility functions
Load the functions from the Maxima prompt with
(%i1) load("mixima/mixima");
The other source files will then be loaded automatically.
The files must have been placed in your Maxima search path
for this to work.
Examples of how to use the functions and some notes on limits in functionality
are in the test file rtest_mixima.mac
----------------------
B) Matrices and Sets
* Maxima has a special data type for matrices, while Mma implements matrices
as ordinary lists. This is handled in the compatibility functions by allowing
either a Maxima list or a Maxima matrix as an argument that is to be interpreted
as a matrix. If the function returns a matrix, then, if possible, the output type
is the same as the input type. For instace:
(%i29) Inverse( matrix( [1,2],[3,4]));
(%o29) matrix([-2,1],[3/2,-1/2])
(%i30) Inverse( [ [1,2],[3,4] ]);
(%o30) [[-2,1],[3/2,-1/2]]
* Likewise Mma implements sets as ordinary lists. These are handled by the
compatibility functions in the same way that matrices are. For instance:
(%i34) Union( {1,2}, {3,4});
(%o34) {1,2,3,4}
(%i35) Union( [1,2], [3,4]);
(%o35) [1,2,3,4]
* If the arguments are a both sets and lists, then the return type is the
same as the first argument.
* Use the compatibility function 'Dot' and not the Maxima
'.' if you want the the Mma function 'Dot', which can also
be written in Mma in the '.' form. In other words do not use
the Maxima '.' function for the Mma '.', but rather use
the compatibility Dot. The function Dot does not accept Maxima
matrices (but they can be converted) because the two systems
are not compatible. Read the documentation on matrix multiplication
for both systems to see why.
* Useful functions are
ensuremat(m) . Converts m to a maxima matrix if it is
a list. Returns m unchanged if it is already a matrix
ensurelist(m) makes matrix m to a list if not already a list.
----------------------
C) Online Help
mixFuncs();
lists compatibility functions and operators.
mixFuncs(string);
lists compatibility functions and operators whose
names contain string.
mixDoc(function);
lists examples of a function, where function is a symbol or
a string. ie.
mixDoc("Integrate"); or mixima_doc(Integrate);
mixDoc(Integrate,bad);
list unimplemented or failed examples.
Not all functions have examples.
D) Syntax
@@ can be used for Apply
-> can be used for Rule.
I'm not sure how useful this syntax is. It should probably be made optional.
------------------------------------------------------------
MMA SHELL:
* Here is an example of entering and using the shell.
Note below that the mma shell and maxima shell use the same
line numbers. Use In[3], Out[3] to acess %i3, etc. The Mma parser
can't read %i3 properly.
Note that in the mixima-mockmma shell, the maxima input and output is
printed.
(%i1) a : 1;
(%o1) 1
(%i2) tomma();
In[3]:= a
(%i3) a
(%o3) 1
Out[3]:= 1
In[4]:= b = 2
(%i4) (b:2)
(%o4) 2
Out[4]:= 2
In[5]:= In[1]
(%i5) In(1)
(%o5) a : 1
Out[5]:= MSETQ[a, 1]
In[6]:= Out[1]
(%i6) Out(1)
(%o6) 1
Out[6]:= 1
In[7]:= Exit
(%i7) Exit
(%o7) Exit
(%o7) true
(%i8) %o4;
(%o8) 2
(%i9)
* What happens when you use the shell ? You enter a line of
Mma code. It is parsed as Mma code. This is translated to
maxima code and evaluated by maxima. The resulting maxima
expression is then translated back to Mma and printed.
You can turn off the printing of the intermediate results.
In[10]:= MmaShowTrans[False]
(%i10) MmaShowTrans(False)
Unsetting maxima translation
Out[10]:= False
In[11]:= N[Pi,12]
Out[11]:= 3.1415926535897931
In[12]:= InString[11]
Out[12]:= N(Pi,12)
In this case, using InString[11] gives the desired
result. In[11] ( or %i11 in maxima) give errors because
they stored results passed throught the simplifier,
which are returned in a new context.
You can read Mma expressions from a file with
miximaEvalFile("filename");
or from withing the mockmma shell
miximaEvalFile["./translator/t1.m"]
* Commands related to the mockmma shell
These 'commands' are functions that can be usefully
called from withing the maxima shell as well; eg
In(3) rather than In[3].
InString[n]
The nth (eg 3rd) mma input string from user's input,
returned by the parser, with whitespace and commas
stripped. This is stored as %is3. Recall that the line
numbers and input and output are the same in the two shells.
Thus, if the nth line was entered in the maxima shell, there
will be no corresponding mma string and InString[n] returns
an atom, eg %is3.
mInString[n]
The nth (eg 3rd) maxima input string built by translating the
mma input string. Also available as %ims3, but this is
not valid syntax in the mockmma shell.
In[n]
The nth maxima input expression. Currently only printed
in '2d' form. This expression is created by the parser from
the user's mma input string. This is the correct expression
to use in the mockmma shell. This is the same as %i3, etc.
in the maxima shell. The expressions entered in the mockmma
shell are copied to %i{n} so that they are available
within the maxima shell; also via In(n).
Out[n]
The nth maxima output expression. This is the correct
way to access the output for further calculation
from within the mockmma shell.
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