r"""
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.
#. 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.
#. 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.
"""
from __future__ import with_statement
import os
from expect import Expect, ExpectElement, ExpectFunction, FunctionElement, gc_disabled
import pexpect
from sage.misc.misc import verbose, DOT_SAGE
from sage.misc.pager import pager
COMMANDS_CACHE = '%s/maple_commandlist_cache.sobj'%DOT_SAGE
class Maple(Expect):
"""
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).
"""
def __init__(self, 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
"""
Expect.__init__(self,
name = 'maple',
prompt = '#-->',
command = "maple -t",
maxread = maxread,
script_subdirectory = script_subdirectory,
restart_on_ctrlc = False,
server = server,
server_tmpdir = server_tmpdir,
verbose_start = False,
logfile = logfile,
eval_using_file_cutoff=1)
def _function_class(self):
"""
EXAMPLES::
sage: maple._function_class()
<class 'sage.interfaces.maple.MapleFunction'>
::
sage: type(maple.diff)
<class 'sage.interfaces.maple.MapleFunction'>
"""
return MapleFunction
def _keyboard_interrupt(self):
print "Interrupting %s..."%self
self._expect.sendline(chr(3))
self._expect.expect(self._prompt)
self._expect.expect(self._prompt)
raise RuntimeError, "Ctrl-c pressed while running %s"%self
def __reduce__(self):
"""
EXAMPLES::
sage: maple.__reduce__()
(<function reduce_load_Maple at 0x...>, ())
sage: f, args = _
sage: f(*args)
Maple
"""
return reduce_load_Maple, tuple([])
def _read_in_file_command(self, filename):
r"""
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'
"""
return 'read "%s"'%filename
def _quit_string(self):
"""
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
"""
return 'quit'
def _install_hints(self):
"""
Hints for installing Maple on your computer.
AUTHORS:
- William Stein and Justin Walker (2006-02-12).
EXAMPLES::
sage: print maple._install_hints()
In order...
"""
return """
In order to use the Maple interface you need to have Maple installed
and have a script in your PATH called "maple" that runs the
command-line version of Maple. Alternatively, you could use a remote
connection to a server running Maple; for hints, type
print maple._install_hints_ssh()
(1) You might have to buy Maple (http://webstore.maplesoft.com/).
(2) * LINUX: The maple script comes standard with your Maple install.
* APPLE OS X:
(a) create a file called maple (in your PATH), with the following contents:
#!/bin/sh
/Library/Frameworks/Maple.framework/Versions/Current/bin/maple $@
(b) Save the file.
(c) Make the file executable.
chmod +x maple
* WINDOWS:
You must install Maple-for-Linux into the VMware machine (sorry, that's
the only way at present).
"""
def expect(self):
"""
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
"""
return self._expect
def console(self):
"""
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.
>
"""
maple_console()
def completions(self, 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
"""
bs = chr(8)*len(s)
if self._expect is None:
self._start()
E = self._expect
E.sendline('%s%s%s'%(s,chr(20),bs))
t = E.timeout
E.timeout=0.3
try:
E.expect('----')
except pexpect.TIMEOUT:
E.timeout = t
return []
E.timeout = t
v = E.before
E.expect(self._prompt)
E.expect(self._prompt)
return v.split()[2:]
def _commands(self):
"""
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
"""
try:
v = sum([self.completions(chr(65+n)) for n in range(26)], []) + \
sum([self.completions(chr(97+n)) for n in range(26)], [])
except RuntimeError:
print "\n"*3
print "*"*70
print "WARNING: You do not have a working version of Maple installed!"
print "*"*70
v = []
v.sort()
return v
def trait_names(self, 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
"""
try:
return self.__trait_names
except AttributeError:
import sage.misc.persist
if use_disk_cache:
try:
self.__trait_names = sage.misc.persist.load(COMMANDS_CACHE)
return self.__trait_names
except IOError:
pass
if verbose:
print "\nBuilding Maple command completion list (this takes"
print "a few seconds only the first time you do it)."
print "To force rebuild later, delete %s."%COMMANDS_CACHE
v = self._commands()
self.__trait_names = v
if len(v) > 200:
sage.misc.persist.save(v, COMMANDS_CACHE)
return v
def _eval_line(self, line, allow_use_file=True, wait_for_prompt=True, restart_if_needed=False):
"""
EXAMPLES::
sage: maple._eval_line('2+2') # optional - maple
'4'
"""
line += ';'
with gc_disabled():
z = Expect._eval_line(self, line, allow_use_file=allow_use_file,
wait_for_prompt=wait_for_prompt).replace('\\\n','').strip()
if z.lower().find("error") != -1:
e = self.expect()
e.sendline('%s__sage__;'%(chr(8)*len(line)))
e.expect('__sage__;')
e.expect(self._prompt)
raise RuntimeError, "An error occurred running a Maple command:\nINPUT:\n%s\nOUTPUT:\n%s"%(line, z)
return z
def cputime(self, t=None):
r"""
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
"""
if t is None:
return float(self('time()'))
else:
return float(self('time() - %s'%float(t)))
def set(self, 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'
"""
cmd = '%s:=%s:'%(var,value)
out = self.eval(cmd)
if out.find("error") != -1:
raise TypeError, "Error executing code in Maple\nCODE:\n\t%s\nMaple ERROR:\n\t%s"%(cmd, out)
def get(self, var):
"""
Get the value of the variable var.
EXAMPLES::
sage: maple.set('xx', '2') # optional - maple
sage: maple.get('xx') # optional - maple
'2'
"""
s = self.eval('printf("%%q",%s)'%var)
return s
def _object_class(self):
"""
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'>
"""
return MapleElement
def _function_element_class(self):
"""
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'>
"""
return MapleFunctionElement
def _equality_symbol(self):
"""
Returns the symbol used for equality testing in Maple.
EXAMPLES::
sage: maple._equality_symbol()
'='
sage: maple(2) == maple(2) # optional -- requires maple
True
"""
return '='
def _true_symbol(self):
"""
Returns the symbol used for truth in Maple.
EXAMPLES::
sage: maple._true_symbol()
'true'
::
sage: maple(2) == maple(2) # optional - maple
True
"""
return 'true'
def _assign_symbol(self):
"""
Returns the symbol used for assignment in Maple.
EXAMPLES::
sage: maple._assign_symbol()
':='
"""
return ":="
def _source(self, 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
Traceback (most recent call last):
...
Exception: no source code could be found
"""
cmd = 'echo "interface(verboseproc=2): print(%s);" | maple -q'%s
src = os.popen(cmd).read()
if src.strip() == s:
raise Exception, "no source code could be found"
else:
return src
def source(self, 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))
"""
try:
pager()(self._source(s))
except Exception:
pager()('No source code could be found.')
def _help(self, str):
r"""
Returns the Maple help on ``str``.
EXAMPLES::
sage: maple._help('gcd') # optional - maple
"gcd - greatest common divisor of polynomials...
"""
return os.popen('echo "?%s" | maple -q'%str).read()
def help(self, 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
...
"""
pager()(self._help(str))
def with_package(self, 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
"""
self.eval('with(%s)'%package)
load = with_package
def clear(self, 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'
"""
self.set(var, '0')
class MapleFunction(ExpectFunction):
def _sage_doc_(self):
"""
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...
"""
M = self._parent
return M._help(self._name)
def _sage_src_(self):
"""
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
Traceback (most recent call last):
...
Exception: no source code could be found
"""
M = self._parent
return M._source(self._name)
class MapleFunctionElement(FunctionElement):
def _sage_doc_(self):
"""
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...
"""
return self._obj.parent()._help(self._name)
def _sage_src_(self):
"""
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
Traceback (most recent call last):
...
Exception: no source code could be found
"""
return self._obj.parent()._source(self._name)
class MapleElement(ExpectElement):
def __float__(self):
"""
Returns a floating point version of self.
EXAMPLES::
sage: float(maple(1/2)) # optional - maple
0.5
sage: type(_) # optional - maple
<type 'float'>
"""
M = self.parent()
return float(maple.eval('evalf(%s)'%self.name()))
def __hash__(self):
"""
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
"""
return int(maple.eval('StringTools:-Hash(convert(%s, string));'%self.name())[1:-1],16)
def __cmp__(self, 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'
"""
P = self.parent()
if P.eval("evalb(%s %s %s)"%(self.name(), P._equality_symbol(),
other.name())) == P._true_symbol():
return 0
try:
if P.eval("evalb(%s %s %s)"%(self.name(), P._lessthan_symbol(), other.name())) == P._true_symbol():
return -1
except RuntimeError, e:
msg = str(e)
if 'is not valid' in msg and 'to < or <=' in msg:
if (hash(str(self)) < hash(str(other))):
return -1
else:
return 1
else:
raise RuntimeError, e
if P.eval("evalb(%s %s %s)"%(self.name(), P._greaterthan_symbol(), other.name())) == P._true_symbol():
return 1
if (hash(self) < hash(other)):
return -1
else:
return 1
def _mul_(self, 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]])
"""
P = self._check_valid()
try:
return P.new('%s . %s'%(self._name, right._name))
except Exception, msg:
raise TypeError,msg
def trait_names(self):
"""
EXAMPLES::
sage: a = maple(2) # optional - maple
sage: 'sin' in a.trait_names() # optional - maple
True
"""
return self.parent().trait_names()
def __repr__(self):
"""
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]])
"""
self._check_valid()
return self.parent().get(self._name)
def _latex_(self):
r"""
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.
"""
return self.parent().eval('latex(%s)'%self.name())
def _sage_(self):
r"""
Convert a maple expression back to a Sage expression.
This currently does not implement a parser for the Maple output language,
therefore only very simple expressions will convert successfully.
EXAMPLE::
sage: m = maple('x^2 + 5*y') # optional - requires maple
sage: m.sage() # optional - requires maple
x^2 + 5*y
::
sage: m = maple('sin(sqrt(1-x^2)) * (1 - cos(1/x))^2') # optional - requires maple
sage: m.sage() # optional - requires maple
(cos(1/x) - 1)^2*sin(sqrt(-x^2 + 1))
"""
result = repr(self)
result = result.replace("Pi", "pi")
try:
from sage.symbolic.all import SR
return SR(result)
except:
raise NotImplementedError, "Unable to parse Maple output: %s" % result
maple = Maple(script_subdirectory='user')
def 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
"""
return maple
import os
def 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.
>
"""
os.system('maple')
def __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
"""
import sage.interfaces.quit
sage.interfaces.quit.expect_quitall()
"""
The following only works in Maple >= 9, I guess, but could
be useful.
From Jaap Spies: In addition Maple has a nice feature the function
> FunctionAdvisor();
> FunctionAdvisor(topics, quiet);
[DE, analytic_extension, asymptotic_expansion, branch_cuts,
branch_points, calling_sequence, class_members,
classify_function, definition, describe, differentiation_rule,
function_classes, identities, integral_form,
known_functions, relate, series, singularities, special_values,
specialize, sum_form, synonyms]
> FunctionAdvisor(syntax, hypergeom);
hypergeom([a, b], [c], z)
Eventually this could be used to do an intelligent command
completion.
"""
