Interface to Maple

AUTHORS:

  • William Stein (2005): maple interface
  • Gregg Musiker (2006-02-02): tutorial
  • William Stein (2006-03-05): added tab completion, e.g., maple.[tab], and help, e.g, maple.sin?.

You must have the optional commercial Maple interpreter installed and available as the command maple in your PATH in order to use this interface. You do not have to install any optional Sage packages.

Type maple.[tab] for a list of all the functions available from your Maple install. Type maple.[tab]? for Maple’s help about a given function. Type maple(...) to create a new Maple object, and maple.eval(...) to run a string using Maple (and get the result back as a string).

EXAMPLES:

sage: maple('3 * 5')                                 # optional - maple
15
sage: maple.eval('ifactor(2005)')                    # optional - maple
'"(5)*"(401)'
sage: maple.ifactor(2005)                            # optional - maple
"(5)*"(401)
sage: maple.fsolve('x^2=cos(x)+4', 'x=0..5')         # optional - maple
1.914020619
sage: maple.factor('x^5 - y^5')                      # optional - maple
(x-y)*(x^4+x^3*y+x^2*y^2+x*y^3+y^4)    

If the string “error” (case insensitive) occurs in the output of anything from Maple, a RuntimeError exception is raised.

Tutorial

AUTHORS:

  • Gregg Musiker (2006-02-02): initial version.

This tutorial is based on the Maple Tutorial for number theory from http://www.math.mun.ca/~drideout/m3370/numtheory.html.

There are several ways to use the Maple Interface in Sage. We will discuss two of those ways in this tutorial.

  1. If you have a maple expression such as

    factor( (x^5-1));
    

    We can write that in sage as

    sage: maple('factor(x^5-1)')                 # optional - maple
    (x-1)*(x^4+x^3+x^2+x+1)
    

    Notice, there is no need to use a semicolon.

  2. Since Sage is written in Python, we can also import maple commands and write our scripts in a Pythonic way. For example, factor() is a maple command, so we can also factor in Sage using

    sage: maple('(x^5-1)').factor()              # optional - maple
    (x-1)*(x^4+x^3+x^2+x+1)
    

    where expression.command() means the same thing as command(expression) in Maple. We will use this second type of syntax whenever possible, resorting to the first when needed.

    sage: maple('(x^12-1)/(x-1)').simplify()     # optional - maple
    x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
    

The normal command will always reduce a rational function to the lowest terms. The factor command will factor a polynomial with rational coefficients into irreducible factors over the ring of integers. So for example,

sage: maple('(x^12-1)').factor( )           # optional - maple
(x-1)*(x+1)*(x^2+x+1)*(x^2-x+1)*(x^2+1)*(x^4-x^2+1)
sage: maple('(x^28-1)').factor( )           # optional - maple
(x-1)*(x^6+x^5+x^4+x^3+x^2+x+1)*(x+1)*(1-x+x^2-x^3+x^4-x^5+x^6)*(x^2+1)*(x^12-x^10+x^8-x^6+x^4-x^2+1)

Another important feature of maple is its online help. We can access this through sage as well. After reading the description of the command, you can press q to immediately get back to your original prompt.

Incidentally you can always get into a maple console by the command

sage: maple.console()          # not tested
sage: !maple                   # not tested

Note that the above two commands are slightly different, and the first is preferred.

For example, for help on the maple command fibonacci, we type

sage: maple.help('fibonacci')  # not tested, since it uses a pager

We see there are two choices. Type

sage: maple.help('combinat, fibonacci')   # not tested, since it uses a pager

We now see how the Maple command fibonacci works under the combinatorics package. Try typing in

sage: maple.fibonacci(10)                # optional - maple
fibonacci(10)

You will get fibonacci(10) as output since Maple has not loaded the combinatorics package yet. To rectify this type

sage: maple('combinat[fibonacci]')(10)     # optional - maple
55

instead.

If you want to load the combinatorics package for future calculations, in Sage this can be done as

sage: maple.with_package('combinat')       # optional - maple

or

sage: maple.load('combinat')               # optional - maple

Now if we type maple.fibonacci(10), we get the correct output:

sage: maple.fibonacci(10)                  # optional - maple
55

Some common maple packages include combinat, linalg, and numtheory. To produce the first 19 Fibonacci numbers, use the sequence command.

sage: maple('seq(fibonacci(i),i=1..19)')     # optional - maple
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584,
4181

Two other useful Maple commands are ifactor and isprime. For example

sage: maple.isprime(maple.fibonacci(27))     # optional - maple
false
sage: maple.ifactor(maple.fibonacci(27))     # optional - maple
"(2)*"(17)*"(53)*"(109)

Note that the isprime function that is included with Sage (which uses PARI) is better than the Maple one (it is faster and gives a provably correct answer, whereas Maple is sometimes wrong).

sage: alpha = maple('(1+sqrt(5))/2')         # optional - maple
sage: beta = maple('(1-sqrt(5))/2')          # optional - maple
sage: f19  = alpha^19 - beta^19/maple('sqrt(5)')      # optional - maple
sage: f19                                             # optional - maple
(1/2+1/2*5^(1/2))^19-1/5*(1/2-1/2*5^(1/2))^19*5^(1/2)
sage: f19.simplify()                # somewhat randomly ordered output; optional - maple
6765+5778/5*5^(1/2)

Let’s say we want to write a maple program now that squares a number if it is positive and cubes it if it is negative. In maple, that would look like

mysqcu := proc(x) 
if x > 0 then x^2;
else x^3; fi;
end;

In Sage, we write

sage: mysqcu = maple('proc(x) if x > 0 then x^2 else x^3 fi end')    # optional - maple
sage: mysqcu(5)                                                      # optional - maple
25
sage: mysqcu(-5)                                                     # optional - maple
-125

More complicated programs should be put in a separate file and loaded.

class sage.interfaces.maple.Maple(maxread=100, script_subdirectory='', server=None, server_tmpdir=None, logfile=None)

Interface to the Maple interpreter.

Type maple.[tab] for a list of all the functions available from your Maple install. Type maple.[tab]? for Maple’s help about a given function. Type maple(...) to create a new Maple object, and maple.eval(...) to run a string using Maple (and get the result back as a string).

__init__(maxread=100, script_subdirectory='', server=None, server_tmpdir=None, logfile=None)

Create an instance of the Maple interpreter.

EXAMPLES:

sage: maple == loads(dumps(maple))
True
__reduce__()

EXAMPLES:

sage: maple.__reduce__()
(<function reduce_load_Maple at 0x...>, ())
sage: f, args = _
sage: f(*args)
Maple
_assign_symbol()

Returns the symbol used for assignment in Maple.

EXAMPLES:

sage: maple._assign_symbol()
':='
_commands()

Return list of all commands defined in Maple.

EXAMPLES:

sage: c = maple._commands() # optional - maple
sage: len(c) > 100          # optional - maple
True
sage: 'dilog' in c          # optional - maple
True
_equality_symbol()

Returns the symbol used for equality testing in Maple.

EXAMPLES:

sage: maple._equality_symbol()
'='

sage: maple(2) == maple(2) # optional -- requires maple
True
_eval_line(line, allow_use_file=True, wait_for_prompt=True)

EXAMPLES:

sage: maple._eval_line('2+2')  # optional - maple
'4'
_function_class()

EXAMPLES:

sage: maple._function_class()
<class 'sage.interfaces.maple.MapleFunction'>
sage: type(maple.diff)
<class 'sage.interfaces.maple.MapleFunction'>
_function_element_class()

Returns the MapleFunctionElement class.

EXAMPLES:

sage: maple._function_element_class()
<class 'sage.interfaces.maple.MapleFunctionElement'>
sage: two = maple(2)  # optional - maple
sage: type(two.gcd)   # optional - maple
<class 'sage.interfaces.maple.MapleFunctionElement'>
_help(str)

Returns the Maple help on str.

EXAMPLES:

sage: maple._help('gcd')  # optional - maple
"gcd - greatest common divisor of polynomials...
_install_hints()

Hints for installing Maple on your computer.

AUTHORS:

  • William Stein and Justin Walker (2006-02-12).

EXAMPLES:

sage: print maple._install_hints()
In order...
_keyboard_interrupt()
_object_class()

Returns the class of MapleElements.

EXAMPLES:

sage: maple._object_class()
<class 'sage.interfaces.maple.MapleElement'>
sage: m = maple(2)  # optional - maple
sage: type(m)       # optional - maple
<class 'sage.interfaces.maple.MapleElement'>
_quit_string()

EXAMPLES:

sage: maple._quit_string()
'quit'
sage: m = Maple()
sage: a = m(2)           # optional - maple
sage: m.is_running()     # optional - maple
True
sage: m.quit()           # optional - maple
sage: m.is_running()     # optional - maple
False
_read_in_file_command(filename)

Returns the string used to read filename into Maple.

EXAMPLES:

sage: maple._read_in_file_command('test')
'read "test"'
sage: filename = tmp_filename()
sage: f = open(filename, 'w')
sage: f.write('xx := 22;\n')
sage: f.close()
sage: maple.read(filename)    # optional - maple
sage: maple.get('xx').strip() # optional - maple
'22'
_source(s)

Tries to return the source code of a Maple function str as a string.

EXAMPLES:

sage: print maple._source('curry').strip()  # optional - maple
p -> subs('_X' = args[2 .. nargs], () -> p(_X, args))
sage: maple._source('ZZZ')                  # optional - maple
...
Exception: no source code could be found
_true_symbol()

Returns the symbol used for truth in Maple.

EXAMPLES:

sage: maple._true_symbol()
'true'
sage: maple(2) == maple(2) # optional - maple
True
clear(var)

Clear the variable named var.

Unfortunately, Maple does not have a clear command. The next best thing is to set equal to the constant 0, so that memory will be freed.

EXAMPLES:

sage: maple.set('xx', '2')  # optional - maple
sage: maple.get('xx')       # optional - maple
'2'
sage: maple.clear('xx')     # optional - maple
sage: maple.get('xx')       # optional - maple
'0'
completions(s)

Return all commands that complete the command starting with the string s. This is like typing s[Ctrl-T] in the maple interpreter.

EXAMPLES:

sage: c = maple.completions('di')  # optional - maple
sage: 'divide' in c                # optional - maple
True
console()

Spawn a new Maple command-line session.

EXAMPLES:

sage: maple.console() # not tested
    |^/|     Maple 11 (IBM INTEL LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
>
cputime(t=None)

Returns the amount of CPU time that the Maple session has used. If t is not None, then it returns the difference between the current CPU time and t.

EXAMPLES:

sage: t = maple.cputime() # optional - maple
sage: t                   # random; optional - maple
0.02
sage: x = maple('x')      # optional - maple
sage: maple.diff(x^2, x)  # optional - maple
2*x
sage: maple.cputime(t)    # random; optional - maple
0.0
expect()

Returns the pexpect object for this Maple session.

EXAMPLES:

sage: m = Maple()
sage: m.expect() is None
True
sage: m._start()           # optional - maple
sage: m.expect()           # optional - maple
<pexpect.spawn instance at 0x...>
sage: m.quit()             # optional - maple
get(var)

Get the value of the variable var.

EXAMPLES:

sage: maple.set('xx', '2') # optional - maple
sage: maple.get('xx')      # optional - maple
'2'
help(str)

Display Maple help about str. This is the same as typing “?str” in the Maple console.

INPUT:

  • str - a string to search for in the maple help system

EXAMPLES:

sage: maple.help('digamma') #not tested
Psi - the Digamma and Polygamma functions
...
load(package)

Make a package of Maple procedures available in the interpreter.

INPUT:

  • package - string

EXAMPLES: Some functions are unknown to Maple until you use with to include the appropriate package.

sage: maple.quit()   # optional -- to reset maple.
sage: maple('partition(10)')              # optional -- requires maple
partition(10)
sage: maple('bell(10)')                   # optional -- requires maple
bell(10)
sage: maple.with_package('combinat')      # optional -- requires maple
sage: maple('partition(10)')              # optional -- requires maple
[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 2, 2, 2], [1, 1, 2, 2, 2, 2], [2, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1, 2, 3], [1, 1, 1, 2, 2, 3], [1, 2, 2, 2, 3], [1, 1, 1, 1, 3, 3], [1, 1, 2, 3, 3], [2, 2, 3, 3], [1, 3, 3, 3], [1, 1, 1, 1, 1, 1, 4], [1, 1, 1, 1, 2, 4], [1, 1, 2, 2, 4], [2, 2, 2, 4], [1, 1, 1, 3, 4], [1, 2, 3, 4], [3, 3, 4], [1, 1, 4, 4], [2, 4, 4], [1, 1, 1, 1, 1, 5], [1, 1, 1, 2, 5], [1, 2, 2, 5], [1, 1, 3, 5], [2, 3, 5], [1, 4, 5], [5, 5], [1, 1, 1, 1, 6], [1, 1, 2, 6], [2, 2, 6], [1, 3, 6], [4, 6], [1, 1, 1, 7], [1, 2, 7], [3, 7], [1, 1, 8], [2, 8], [1, 9], [10]]
sage: maple('bell(10)')                   # optional -- requires maple
115975
sage: maple('fibonacci(10)')              # optional -- requires maple
55
set(var, value)

Set the variable var to the given value.

EXAMPLES:

sage: maple.set('xx', '2') # optional - maple
sage: maple.get('xx')      # optional - maple
'2'
source(s)

Display the Maple source (if possible) about s. This is the same as returning the output produced by the following Maple commands:

interface(verboseproc=2): print(s)

INPUT:

  • s - a string representing the function whose source code you want

EXAMPLES:

sage: maple.source('curry')  #not tested
p -> subs('_X' = args[2 .. nargs], () -> p(_X, args))
trait_names(verbose=True, use_disk_cache=True)

Returns a list of all the commands defined in Maple and optionally (per default) store them to disk.

EXAMPLES:

sage: c = maple.trait_names(use_disk_cache=False, verbose=False) # optional - maple
sage: len(c) > 100  # optional - maple
True
sage: 'dilog' in c  # optional - maple
True
with_package(package)

Make a package of Maple procedures available in the interpreter.

INPUT:

  • package - string

EXAMPLES: Some functions are unknown to Maple until you use with to include the appropriate package.

sage: maple.quit()   # optional -- to reset maple.
sage: maple('partition(10)')              # optional -- requires maple
partition(10)
sage: maple('bell(10)')                   # optional -- requires maple
bell(10)
sage: maple.with_package('combinat')      # optional -- requires maple
sage: maple('partition(10)')              # optional -- requires maple
[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 2, 2, 2], [1, 1, 2, 2, 2, 2], [2, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1, 2, 3], [1, 1, 1, 2, 2, 3], [1, 2, 2, 2, 3], [1, 1, 1, 1, 3, 3], [1, 1, 2, 3, 3], [2, 2, 3, 3], [1, 3, 3, 3], [1, 1, 1, 1, 1, 1, 4], [1, 1, 1, 1, 2, 4], [1, 1, 2, 2, 4], [2, 2, 2, 4], [1, 1, 1, 3, 4], [1, 2, 3, 4], [3, 3, 4], [1, 1, 4, 4], [2, 4, 4], [1, 1, 1, 1, 1, 5], [1, 1, 1, 2, 5], [1, 2, 2, 5], [1, 1, 3, 5], [2, 3, 5], [1, 4, 5], [5, 5], [1, 1, 1, 1, 6], [1, 1, 2, 6], [2, 2, 6], [1, 3, 6], [4, 6], [1, 1, 1, 7], [1, 2, 7], [3, 7], [1, 1, 8], [2, 8], [1, 9], [10]]
sage: maple('bell(10)')                   # optional -- requires maple
115975
sage: maple('fibonacci(10)')              # optional -- requires maple
55
class sage.interfaces.maple.MapleElement(parent, value, is_name=False, name=None)
__cmp__(other)

Compare equality between self and other, using maple.

These examples are optional, and require Maple to be installed. You don’t need to install any Sage packages for this.

EXAMPLES:

sage: a = maple(5)                             # optional - maple
sage: b = maple(5)                             # optional - maple
sage: a == b                                   # optional - maple
True
sage: a == 5                                   # optional - maple
True
sage: c = maple(3)                             # optional - maple
sage: a == c                                   # optional - maple
False
sage: a < c                                    # optional - maple
False
sage: a < 6                                    # optional - maple
True
sage: c <= a                                   # optional - maple
True
sage: M = matrix(ZZ, 2, range(1,5))            # optional - maple
sage: Mm = maple(M)                            # optional - maple
sage: Mm == Mm                                 # optional - maple
True
sage: Mm < 5                                   # optional - maple
True
sage: (Mm < 5) == (M < 5)                      # optional - maple
True
sage: 5 < Mm                                   # optional - maple
False

TESTS:

sage: x = var('x')
sage: t = maple((x+1)^2)                       # optional -- requires maple
sage: u = maple(x^2+2*x+1)                     # optional -- requires maple
sage: u == t # todo: not implemented
True         # returns False, should use 'testeq' in maple
sage: maple.eval('testeq(%s = %s)'%(t.name(),u.name()))    # optional - maple
'true'
__float__()

Returns a floating point version of self.

EXAMPLES:

sage: float(maple(1/2))  # optional - maple
0.5
sage: type(_)            # optional - maple
<type 'float'>
__hash__()

Returns a 64-bit integer representing the hash of self. Since Python uses 32-bit hashes, it will automatically convert the result of this to a 32-bit hash.

These examples are optional, and require Maple to be installed. You don’t need to install any Sage packages for this.

EXAMPLES:

sage: m = maple('x^2+y^2')                      # optional - maple
sage: m.__hash__()                              # optional - maple
188724254834261060184983038723355865733L
sage: hash(m)                                   # optional - maple
5035731711831192733
sage: m = maple('x^2+y^3')                      # optional - maple
sage: m.__hash__()                              # optional - maple
264835029579301191531663246434344770556L
sage: hash(m)                                   # optional - maple
-2187277978252104690
__repr__()

Return a string representation of self.

These examples are optional, and require Maple to be installed. You don’t need to install any Sage packages for this.

EXAMPLES:

sage: x = var('x')
sage: maple(x)                      # optional - maple
x
sage: maple(5)                      # optional - maple
5
sage: M = matrix(QQ,2,range(4))
sage: maple(M)                      # optional - maple
Matrix(2, 2, [[0,1],[2,3]])
_latex_()

You can output Maple expressions in latex.

EXAMPLES:

sage: print latex(maple('(x^4 - y)/(y^2-3*x)'))      # optional -- requires maple
{\frac {{x}^{4}-y}{{y}^{2}-3\,x}}
sage: print latex(maple(pi - e^3))                   # optional -- requires maple
\pi - \left( {e^{1}} \right) ^{3}

Note

Some expressions might require the Maple style file maple2e.sty in order to latex correctly.

_mul_(right)

These examples are optional, and require Maple to be installed. You don’t need to install any Sage packages for this.

EXAMPLES:

sage: t = maple(5); u = maple(3)                # optional - maple
sage: t*u                                       # optional - maple
15
sage: M = matrix(ZZ,2,range(4))                 # optional - maple
sage: Mm = maple(M)                             # optional - maple
sage: Mm*Mm                                     # optional - maple
Matrix(2, 2, [[2,3],[6,11]])
sage: v = vector(ZZ,2,[2,3])               
sage: vm = maple(v)                             # optional - maple
sage: vm*Mm                                     # optional - maple
Vector[row](2, [6,11])
sage: t*Mm                                      # optional - maple
Matrix(2, 2, [[0,5],[10,15]])    
trait_names()

EXAMPLES:

sage: a = maple(2) # optional - maple
sage: 'sin' in a.trait_names() # optional - maple
True
class sage.interfaces.maple.MapleFunction(parent, name)
_sage_doc_()

Returns the Maple help for this function. This gets called when doing “?” on self.

EXAMPLES:

sage: maple.gcd._sage_doc_()  # optional - maple
"gcd - greatest common divisor of polynomials...
_sage_src_()

Returns the source code of self. This is the function that eventually gets called when doing maple.gcd?? for example.

EXAMPLES:

sage: print maple.curry._sage_src_().strip() # optional - maple
p -> subs('_X' = args[2 .. nargs], () -> p(_X, args))
sage: maple.ZZZ._sage_src_()                 # optional - maple
...
Exception: no source code could be found
class sage.interfaces.maple.MapleFunctionElement(obj, name)
_sage_doc_()

Returns the Maple help for this function. This gets called when doing “?” on self.

EXAMPLES:

sage: two = maple(2)  # optional - maple
sage: two.gcd._sage_doc_() # optional - maple
"gcd - greatest common divisor of polynomials...
_sage_src_()

Returns the source code of self.

EXAMPLES:

sage: g = maple('gcd')                   # optional - maple
sage: print g.curry._sage_src_().strip() # optional - maple 
p -> subs('_X' = args[2 .. nargs], () -> p(_X, args))
sage: m = maple('2')                     # optional - maple 
sage: m.ZZZ._sage_src_()                 # optional - maple 
...
Exception: no source code could be found
sage.interfaces.maple.__doctest_cleanup()

EXAMPLES:

sage: from sage.interfaces.maple import __doctest_cleanup
sage: m = maple(2)         # optional - maple
sage: maple.is_running()   # optional - maple
True
sage: __doctest_cleanup()
sage: maple.is_running()
False
sage.interfaces.maple.maple_console()

Spawn a new Maple command-line session.

EXAMPLES:

sage: maple_console() #not tested
    |^/|     Maple 11 (IBM INTEL LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
>
sage.interfaces.maple.reduce_load_Maple()

Returns the maple object created in sage.interfaces.maple.

EXAMPLES:

sage: from sage.interfaces.maple import reduce_load_Maple
sage: reduce_load_Maple()
Maple

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