Coverage for local/lib/python2.7/site-packages/sage/interfaces/maxima.py: 64%

93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

sage: f = maxima('(x + 3*y + x^2*y)^3')

sage: f.expand()

x^6*y^3+9*x^4*y^3+27*x^2*y^3+27*y^3+3*x^5*y^2+18*x^3*y^2+27*x*y^2+3*x^4*y+9*x^2*y+x^3

sage: f.subst('x=5/z')

(5/z+(25*y)/z^2+3*y)^3

sage: g = f.subst('x=5/z')

sage: h = g.ratsimp(); h

(27*y^3*z^6+135*y^2*z^5+(675*y^3+225*y)*z^4+(2250*y^2+125)*z^3+(5625*y^3+1875*y)*z^2+9375*y^2*z+15625*y^3)/z^6

sage: h.factor()

(3*y*z^2+5*z+25*y)^3/z^6

sage: eqn = maxima(['a+b*c=1', 'b-a*c=0', 'a+b=5'])

sage: s = eqn.solve('[a,b,c]'); s

[[a=-(sqrt(79)*%i-11)/4,b=(sqrt(79)*%i+9)/4,c=(sqrt(79)*%i+1)/10],[a=(sqrt(79)*%i+11)/4,b=-(sqrt(79)*%i-9)/4,c=-(sqrt(79)*%i-1)/10]]

Here is an example of solving an algebraic equation::

sage: maxima('x^2+y^2=1').solve('y')

[y=-sqrt(1-x^2),y=sqrt(1-x^2)]

sage: maxima('x^2 + y^2 = (x^2 - y^2)/sqrt(x^2 + y^2)').solve('y')

[y=-sqrt(((-y^2)-x^2)*sqrt(y^2+x^2)+x^2),y=sqrt(((-y^2)-x^2)*sqrt(y^2+x^2)+x^2)]

You can even nicely typeset the solution in latex::

sage: latex(s)

\left[ \left[ a=-{{\sqrt{79}\,i-11}\over{4}} , b={{\sqrt{79}\,i+9 }\over{4}} , c={{\sqrt{79}\,i+1}\over{10}} \right] , \left[ a={{ \sqrt{79}\,i+11}\over{4}} , b=-{{\sqrt{79}\,i-9}\over{4}} , c=-{{ \sqrt{79}\,i-1}\over{10}} \right] \right]

To have the above appear onscreen via ``xdvi``, type

``view(s)``. (TODO: For OS X should create pdf output

and use preview instead?)

sage: e = maxima('sin(u + v) * cos(u)^3'); e

cos(u)^3*sin(v+u)

sage: f = e.trigexpand(); f

cos(u)^3*(cos(u)*sin(v)+sin(u)*cos(v))

sage: f.trigreduce()

(sin(v+4*u)+sin(v-2*u))/8+(3*sin(v+2*u)+3*sin(v))/8

sage: w = maxima('3 + k*%i')

sage: f = w^2 + maxima('%e')^w

sage: f.realpart()

%e^3*cos(k)-k^2+9

sage: f = maxima('x^3 * %e^(k*x) * sin(w*x)'); f

x^3*%e^(k*x)*sin(w*x)

sage: f.diff('x')

k*x^3*%e^(k*x)*sin(w*x)+3*x^2*%e^(k*x)*sin(w*x)+w*x^3*%e^(k*x)*cos(w*x)

sage: f.integrate('x')

(((k*w^6+3*k^3*w^4+3*k^5*w^2+k^7)*x^3+(3*w^6+3*k^2*w^4-3*k^4*w^2-3*k^6)*x^2+((-18*k*w^4)-12*k^3*w^2+6*k^5)*x-6*w^4+36*k^2*w^2-6*k^4)*%e^(k*x)*sin(w*x)+(((-w^7)-3*k^2*w^5-3*k^4*w^3-k^6*w)*x^3+(6*k*w^5+12*k^3*w^3+6*k^5*w)*x^2+(6*w^5-12*k^2*w^3-18*k^4*w)*x-24*k*w^3+24*k^3*w)*%e^(k*x)*cos(w*x))/(w^8+4*k^2*w^6+6*k^4*w^4+4*k^6*w^2+k^8)

sage: f = maxima('1/x^2')

sage: f.integrate('x', 1, 'inf')

sage: g = maxima('f/sinh(k*x)^4')

sage: g.taylor('x', 0, 3)

f/(k^4*x^4)-(2*f)/((3*k^2)*x^2)+(11*f)/45-((62*k^2*f)*x^2)/945

sage: maxima.taylor('asin(x)','x',0, 10)

x+x^3/6+(3*x^5)/40+(5*x^7)/112+(35*x^9)/1152

Examples involving matrices

---------------------------

We illustrate computing with the matrix whose `i,j` entry

is `i/j`, for `i,j=1,\ldots,4`.

sage: f = maxima.eval('f[i,j] := i/j')

sage: A = maxima('genmatrix(f,4,4)'); A

matrix([1,1/2,1/3,1/4],[2,1,2/3,1/2],[3,3/2,1,3/4],[4,2,4/3,1])

sage: A.determinant()

sage: A.echelon()

matrix([1,1/2,1/3,1/4],[0,0,0,0],[0,0,0,0],[0,0,0,0])

sage: A.eigenvalues()

[[0,4],[3,1]]

sage: A.eigenvectors()

[[[0,4],[3,1]],[[[1,0,0,-4],[0,1,0,-2],[0,0,1,-4/3]],[[1,2,3,4]]]]

We can also compute the echelon form in Sage::

sage: B = matrix(QQ, A)

sage: B.echelon_form()

[ 1 1/2 1/3 1/4]

[ 0 0 0 0]

sage: B.charpoly('x').factor()

(x - 4) * x^3

Laplace Transforms

------------------

We illustrate Laplace transforms::

sage: _ = maxima.eval("f(t) := t*sin(t)")

sage: maxima("laplace(f(t),t,s)")

(2*s)/(s^2+1)^2

sage: maxima("laplace(delta(t-3),t,s)") #Dirac delta function

%e^-(3*s)

sage: _ = maxima.eval("f(t) := exp(t)*sin(t)")

sage: maxima("laplace(f(t),t,s)")

1/(s^2-2*s+2)

sage: _ = maxima.eval("f(t) := t^5*exp(t)*sin(t)")

sage: maxima("laplace(f(t),t,s)")

(360*(2*s-2))/(s^2-2*s+2)^4-(480*(2*s-2)^3)/(s^2-2*s+2)^5+(120*(2*s-2)^5)/(s^2-2*s+2)^6

sage: print(maxima("laplace(f(t),t,s)"))

3 5

360 (2 s - 2) 480 (2 s - 2) 120 (2 s - 2)

--------------- - --------------- + ---------------

2 4 2 5 2 6

(s - 2 s + 2) (s - 2 s + 2) (s - 2 s + 2)

sage: maxima("laplace(diff(x(t),t),t,s)")

s*'laplace(x(t),t,s)-x(0)

sage: maxima("laplace(diff(x(t),t,2),t,s)")

(-%at('diff(x(t),t,1),t=0))+s^2*'laplace(x(t),t,s)-x(0)*s

It is difficult to read some of these without the 2d

representation::

sage: print(maxima("laplace(diff(x(t),t,2),t,s)"))

d ! 2

(- -- (x(t))! ) + s laplace(x(t), t, s) - x(0) s

dt !

!t = 0

Even better, use

``view(maxima("laplace(diff(x(t),t,2),t,s)"))`` to see

a typeset version.

Continued Fractions

-------------------

A continued fraction `a + 1/(b + 1/(c + \cdots))` is

represented in maxima by the list `[a, b, c, \ldots]`.

sage: maxima("cf((1 + sqrt(5))/2)")

[1,1,1,1,2]

sage: maxima("cf ((1 + sqrt(341))/2)")

[9,1,2,1,2,1,17,1,2,1,2,1,17,1,2,1,2,1,17,2]

Special examples

----------------

In this section we illustrate calculations that would be awkward to

do (as far as I know) in non-symbolic computer algebra systems like

MAGMA or GAP.

We compute the gcd of `2x^{n+4} - x^{n+2}` and

`4x^{n+1} + 3x^n` for arbitrary `n`.

sage: f = maxima('2*x^(n+4) - x^(n+2)')

sage: g = maxima('4*x^(n+1) + 3*x^n')

sage: f.gcd(g)

x^n

You can plot 3d graphs (via gnuplot)::

sage: maxima('plot3d(x^2-y^2, [x,-2,2], [y,-2,2], [grid,12,12])') # not tested

[displays a 3 dimensional graph]

You can formally evaluate sums (note the ``nusum``

command)::

sage: S = maxima('nusum(exp(1+2*i/n),i,1,n)')

sage: print(S)

2/n + 3 2/n + 1

%e %e

----------------------- - -----------------------

1/n 1/n 1/n 1/n

(%e - 1) (%e + 1) (%e - 1) (%e + 1)

We formally compute the limit as `n\to\infty` of

`2S/n` as follows::

sage: T = S*maxima('2/n')

sage: T.tlimit('n','inf')

%e^3-%e

Miscellaneous

-------------

Obtaining digits of `\pi`::

sage: maxima.eval('fpprec : 100')

'100'

sage: maxima(pi).bfloat()

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068b0

Defining functions in maxima::

sage: maxima.eval('fun[a] := a^2')

'fun[a]:=a^2'

sage: maxima('fun[10]')

100

Interactivity

-------------

Unfortunately maxima doesn't seem to have a non-interactive mode,

which is needed for the Sage interface. If any Sage call leads to

maxima interactively answering questions, then the questions can't be

answered and the maxima session may hang. See the discussion at

http://www.ma.utexas.edu/pipermail/maxima/2005/011061.html for some

ideas about how to fix this problem. An example that illustrates this

problem is ``maxima.eval('integrate (exp(a*x), x, 0, inf)')``.

Latex Output

------------

To TeX a maxima object do this::

sage: latex(maxima('sin(u) + sinh(v^2)'))

\sinh v^2+\sin u

Here's another example::

sage: g = maxima('exp(3*%i*x)/(6*%i) + exp(%i*x)/(2*%i) + c')

sage: latex(g)

-{{i\,e^{3\,i\,x}}\over{6}}-{{i\,e^{i\,x}}\over{2}}+c

Long Input

----------

The MAXIMA interface reads in even very long input (using files) in

a robust manner, as long as you are creating a new object.

.. note::

Using ``maxima.eval`` for long input is much less robust, and is

not recommended.

sage: t = '"%s"'%10^10000 # ten thousand character string.

sage: a = maxima(t)

TESTS:

This working tests that a subtle bug has been fixed::

sage: f = maxima.function('x','gamma(x)')

sage: g = f(1/7)

sage: g

gamma(1/7)

sage: del f

sage: maxima(sin(x))

sin(_SAGE_VAR_x)

This tests to make sure we handle the case where Maxima asks if an

expression is positive or zero.

sage: var('Ax,Bx,By')

(Ax, Bx, By)

sage: t = -Ax*sin(sqrt(Ax^2)/2)/(sqrt(Ax^2)*sqrt(By^2 + Bx^2))

sage: t.limit(Ax=0, dir='+')

A long complicated input expression::

sage: maxima._eval_line('((((((((((0) + ((1) / ((n0) ^ (0)))) + ((1) / ((n1) ^ (1)))) + ((1) / ((n2) ^ (2)))) + ((1) / ((n3) ^ (3)))) + ((1) / ((n4) ^ (4)))) + ((1) / ((n5) ^ (5)))) + ((1) / ((n6) ^ (6)))) + ((1) / ((n7) ^ (7)))) + ((1) / ((n8) ^ (8)))) + ((1) / ((n9) ^ (9)));')

'1/n9^9+1/n8^8+1/n7^7+1/n6^6+1/n5^5+1/n4^4+1/n3^3+1/n2^2+1/n1+1'

Test that Maxima gracefully handles this syntax error (:trac:`17667`)::

sage: maxima.eval("1 == 1;")

Traceback (most recent call last):

...

TypeError: ...incorrect syntax: = is not a prefix operator...

"""

#*****************************************************************************

# Distributed under the terms of the GNU General Public License (GPL)

# This code is distributed in the hope that it will be useful,

# but WITHOUT ANY WARRANTY; without even the implied warranty of

# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU

# General Public License for more details.

# The full text of the GPL is available at:

# http://www.gnu.org/licenses/

#*****************************************************************************

from __future__ import print_function, absolute_import

from six import string_types

import os

import re

import pexpect

from random import randrange

from sage.env import DOT_SAGE, SAGE_LOCAL

from sage.misc.misc import ECL_TMP

from .expect import (Expect, ExpectElement, FunctionElement,

ExpectFunction, gc_disabled)

from .maxima_abstract import (MaximaAbstract, MaximaAbstractFunction,

MaximaAbstractElement,

MaximaAbstractFunctionElement,

MaximaAbstractElementFunction)

from sage.docs.instancedoc import instancedoc

# Thanks to the MRO for multiple inheritance used by the Sage's Python,

# this should work as expected

class Maxima(MaximaAbstract, Expect):

"""

Interface to the Maxima interpreter.

EXAMPLES::

sage: m = Maxima()

sage: m == maxima

False

"""

def __init__(self, script_subdirectory=None, logfile=None, server=None,

init_code=None):

"""

Create an instance of the Maxima interpreter.

TESTS::

sage: Maxima == loads(dumps(Maxima))

True

sage: maxima == loads(dumps(maxima))

True

Unpickling a Maxima Pexpect interface gives the default interface::

sage: m = Maxima()

sage: maxima == loads(dumps(m))

True

We make sure labels are turned off (see :trac:`6816`)::

sage: 'nolabels : true' in maxima._Expect__init_code

True

"""

# TODO: Input and output prompts in maxima can be changed by

# setting inchar and outchar..

eval_using_file_cutoff = 256

self.__eval_using_file_cutoff = eval_using_file_cutoff

STARTUP = os.path.join(SAGE_LOCAL,'bin','sage-maxima.lisp')

# We set maxima's configuration directory to $DOT_SAGE/maxima

# This avoids that sage's maxima inadvertently loads

# ~/.maxima/maxima-init.mac

# If you absolutely want maxima instances that are started by

# this interface to preload commands, put them in

# $DOT_SAGE/maxima/maxima-init.mac

# (we use the "--userdir" option in maxima for this)

SAGE_MAXIMA_DIR = os.path.join(DOT_SAGE,"maxima")

if not os.path.exists(STARTUP):

raise RuntimeError('You must get the file local/bin/sage-maxima.lisp')

#self.__init_code = init_code

if init_code is None:

# display2d -- no ascii art output

# keepfloat -- don't automatically convert floats to rationals

init_code = ['display2d : false', 'keepfloat : true']

# Turn off the prompt labels, since computing them *very

# dramatically* slows down the maxima interpret after a while.

# See the function makelabel in suprv1.lisp.

# Many thanks to andrej.vodopivec@gmail.com and also

# Robert Dodier for figuring this out!

# See trac # 6818.

init_code.append('nolabels : true')

MaximaAbstract.__init__(self,"maxima")

Expect.__init__(self,

name = 'maxima',

prompt = '$\%i[0-9]+$ ',

command = 'maxima --userdir="%s" -p "%s"'%(SAGE_MAXIMA_DIR,STARTUP),

env = {'TMPDIR': str(ECL_TMP)},

script_subdirectory = script_subdirectory,

restart_on_ctrlc = False,

verbose_start = False,

init_code = init_code,

logfile = logfile,

eval_using_file_cutoff=eval_using_file_cutoff)

# Must match what is in the file local/bin/sage-maxima.lisp

self._display_prompt = '<sage-display>'

# See #15440 for the importance of the trailing space

self._output_prompt_re = re.compile('$\%o[0-9]+$ ')

self._ask = ['zero or nonzero\\?', 'an integer\\?',

'positive, negative or zero\\?', 'positive or negative\\?',

'positive or zero\\?', 'equal to .*\\?']

self._prompt_wait = [self._prompt] + [re.compile(x) for x in self._ask] + \

['Break [0-9]+'] #note that you might need to change _expect_expr if you

#change this

self._error_re = re.compile('(Principal Value|debugmode|incorrect syntax|Maxima encountered a Lisp error)')

self._display2d = False

def set_seed(self, seed=None):

"""

http://maxima.sourceforge.net/docs/manual/maxima_10.html

make_random_state (n) returns a new random state object created from an

integer seed value equal to n modulo 2^32. n may be negative.

EXAMPLES::

sage: m = Maxima()

sage: m.set_seed(1)

sage: [m.random(100) for i in range(5)]

[45, 39, 24, 68, 63]

"""

if seed is None:

seed = self.rand_seed()

self.set_random_state(self.make_random_state(seed))

self._seed = seed

return seed

def _start(self):

"""

Starts the Maxima interpreter.

EXAMPLES::

sage: m = Maxima()

sage: m.is_running()

False

sage: m._start()

sage: m.is_running()

True

Test that we can use more than 256MB RAM (see :trac:`6772`)::

sage: a = maxima(10)^(10^5)

sage: b = a^600 # long time -- about 10-15 seconds

"""

Expect._start(self)

self._sendline(r":lisp (defun tex-derivative (x l r) (tex (if $derivabbrev (tex-dabbrev x) (tex-d x '\\partial)) l r lop rop ))")

# Don't use ! for factorials (#11539)

self._sendline(":lisp (remprop 'mfactorial 'grind)")

# Remove limit on the max heapsize (since otherwise it defaults

# to 256MB with ECL).

self._sendline(":lisp (ext:set-limit 'ext:heap-size 0)")

self._eval_line('0;')

# set random seed

self.set_seed(self._seed)

def __reduce__(self):

"""

Implementation of __reduce__ for ``Maxima``.

EXAMPLES::

sage: maxima.__reduce__()

(<function reduce_load_Maxima at 0x...>, ())

"""

return reduce_load_Maxima, tuple([]) #(self.__init_code,)

def _sendline(self, string):

"""

Send a string followed by a newline character.

EXAMPLES::

sage: maxima._sendline('t : 9;')

sage: maxima.get('t')

'9'

"""

self._sendstr(string)

os.write(self._expect.child_fd, os.linesep)

def _expect_expr(self, expr=None, timeout=None):

"""

Wait for a given expression expr (which could be a regular

expression or list of regular expressions) to appear in the output

for at most timeout seconds.

See `sage.interfaces.expect.Expect._expect_expr` for full details

on its use and functionality.

TESTS:

These tests indirectly show that the interface is working

and catching certain errors::

sage: maxima('2+2')

sage: maxima('integrate(1/(x^3*(a+b*x)^(1/3)),x)')

Traceback (most recent call last):

...

TypeError: Computation failed since Maxima requested additional

constraints (try the command "maxima.assume('a>0')"

before integral or limit evaluation, for example):

Is a positive or negative?

sage: maxima.assume('a>0')

[a>0]

sage: maxima('integrate(1/(x^3*(a+b*x)^(1/3)),x)')

(-(b^2*log((b*x+a)^(2/3)+a^(1/3)*(b*x+a)^(1/3)+a^(2/3)))/(9*a^(7/3)))+(2*b^2*atan((2*(b*x+a)^(1/3)+a^(1/3))/(sqrt(3)*a^(1/3))))/(3^(3/2)*a^(7/3))+(2*b^2*log((b*x+a)^(1/3)-a^(1/3)))/(9*a^(7/3))+(4*b^2*(b*x+a)^(5/3)-7*a*b^2*(b*x+a)^(2/3))/(6*a^2*(b*x+a)^2-12*a^3*(b*x+a)+6*a^4)

sage: maxima('integrate(x^n,x)')

Traceback (most recent call last):

...

TypeError: Computation failed since Maxima requested additional

constraints (try the command "maxima.assume('n>0')" before

integral or limit evaluation, for example):

Is n equal to -1?

sage: maxima.assume('n+1>0')

[n>-1]

sage: maxima('integrate(x^n,x)')

x^(n+1)/(n+1)

sage: maxima.forget([fact for fact in maxima.facts()])

[[a>0,n>-1]]

sage: maxima.facts()

[]

sage: var('a')

sage: maxima('limit(x^a,x,0)')

Traceback (most recent call last):

...

TypeError: Computation failed since Maxima requested additional

constraints (try the command "maxima.assume('a>0')" before

integral or limit evaluation, for example):

Is a positive, negative or zero?

"""

if expr is None:

expr = self._prompt_wait

if self._expect is None:

self._start()

try:

if timeout:

i = self._expect.expect(expr,timeout=timeout)

else:

i = self._expect.expect(expr)

if i > 0:

v = self._expect.before

#We check to see if there is a "serious" error in Maxima.

#Note that this depends on the order of self._prompt_wait

if expr is self._prompt_wait and i > len(self._ask):

self.quit()

raise ValueError("%s\nComputation failed due to a bug in Maxima -- NOTE: Maxima had to be restarted."%v)

j = v.find('Is ')

v = v[j:]

k = v.find(' ', 3)

msg = """Computation failed since Maxima requested additional constraints (try the command "maxima.assume('""" + v[3:k] + """>0')" before integral or limit evaluation, for example):\n""" + v + self._expect.after

self._sendline(";")

self._expect_expr()

raise ValueError(msg)

except KeyboardInterrupt as msg:

i = 0

while True:

try:

print("Control-C pressed. Interrupting Maxima. Please wait a few seconds...")

self._sendstr('quit;\n'+chr(3))

self.interrupt()

except KeyboardInterrupt:

i += 1

if i > 10:

break

pass

else:

break

raise KeyboardInterrupt(msg)

def _eval_line(self, line, allow_use_file=False,

wait_for_prompt=True, reformat=True, error_check=True, restart_if_needed=False):

"""

Return result of line evaluation.

EXAMPLES:

We check that errors are correctly checked::

sage: maxima._eval_line('1+1;')

'2'

sage: maxima._eval_line('sage0: x == x;')

Traceback (most recent call last):

...

TypeError: Error executing code in Maxima...

"""

if len(line) == 0:

return ''

line = line.rstrip()

if line[-1] != '$' and line[-1] != ';':

line += ';'

self._synchronize()

if len(line) > self.__eval_using_file_cutoff:

# This implicitly uses the set method, then displays

# the result of the thing that was set.

# This only works when the input line is an expression.

# But this is our only choice, since

# batchmode doesn't display expressions to screen.

a = self(line)

return repr(a)

else:

self._sendline(line)

line_echo = self._expect.readline()

if not wait_for_prompt:

return

# line_echo sometimes has randomly inserted terminal echo in front #15811

assert line_echo.strip().endswith(line.strip()), 'mismatch:\n' + line_echo + line

self._expect_expr(self._display_prompt)

out = self._before() # input echo + output prompt + output

if error_check:

self._error_check(line, out)

if not reformat:

return out

self._expect_expr()

assert len(self._before())==0, 'Maxima expect interface is confused!'

r = self._output_prompt_re

m = r.search(out)

if m is not None:

out = out[m.end():]

return re.sub('\s+', '', out)

def _synchronize(self):

"""

Synchronize pexpect interface.

This put a random integer (plus one!) into the output stream, then

waits for it, thus resynchronizing the stream. If the random

integer doesn't appear within 1 second, maxima is sent interrupt

signals.

This way, even if you somehow left maxima in a busy state

computing, calling _synchronize gets everything fixed.

EXAMPLES: This makes Maxima start a calculation::

sage: maxima._sendstr('1/1'*500)

When you type this command, this synchronize command is implicitly

called, and the above running calculation is interrupted::

sage: maxima('2+2')

"""

marker = '__SAGE_SYNCHRO_MARKER_'

if self._expect is None: return

r = randrange(2147483647)

s = marker + str(r+1)

# The 0; *is* necessary... it comes up in certain rare cases

# that are revealed by extensive testing.

# Don't delete it. -- william stein

cmd = '''0;sconcat("%s",(%s+1));\n'''%(marker,r)

self._sendstr(cmd)

try:

self._expect_expr(timeout=0.5)

if not s in self._before():

self._expect_expr(s,timeout=0.5)

self._expect_expr(timeout=0.5)

except pexpect.TIMEOUT:

# Don't call self._interrupt() here, as that might send multiple

# interrupts. On OS X 10.4, maxima takes a long time to

# process one interrupt (7.5 seconds on an idle system, but up

# to a minute on a loaded system) and gets confused by multiple

# interrupts. Instead, send just one interrupt and wait.

# See Trac #9361.

self._sendstr(chr(3))

self._expect_expr(timeout=120)

except pexpect.EOF:

self._crash_msg()

self.quit()

def _batch(self, s, batchload=True):

"""

Call Maxima's batch or batchload command with a file

containing the given string as argument.

EXAMPLES::

sage: maxima._batch('10003;')

'...batchload...'

sage: maxima._batch('10003;',batchload=False)

'...batch...10003...'

"""

filename = '%s-%s'%(self._local_tmpfile(),randrange(2147483647))

F = open(filename, 'w')

F.write(s)

F.close()

if self.is_remote():

self._send_tmpfile_to_server(local_file=filename)

tmp_to_use = self._remote_tmpfile()

tmp_to_use = filename

if batchload:

cmd = 'batchload("%s");'%tmp_to_use

else:

cmd = 'batch("%s");'%tmp_to_use

r = randrange(2147483647)

s = str(r+1)

cmd = "%s1+%s;\n"%(cmd,r)

self._sendline(cmd)

self._expect_expr(s)

out = self._before()

self._error_check(cmd, out)

os.unlink(filename)

return out

def _quit_string(self):

"""

Return string representation of quit command.

EXAMPLES::

sage: maxima._quit_string()

'quit();'

"""

return 'quit();'

def _crash_msg(self):

"""

Return string representation of crash message.

EXAMPLES::

sage: maxima._crash_msg()

Maxima crashed -- automatically restarting.

"""

print("Maxima crashed -- automatically restarting.")

def _error_check(self, cmd, out):

"""

Check string for errors.

EXAMPLES::

sage: maxima._error_check("1+1;","Principal Value")

Traceback (most recent call last):

...

TypeError: Error executing code in Maxima

CODE:

1+1;

Maxima ERROR:

Principal Value

"""

r = self._error_re

m = r.search(out)

if not m is None:

self._error_msg(cmd, out)

def _error_msg(self, cmd, out):

"""

Raise error with formatted description.

EXAMPLES::

sage: maxima._error_msg("1+1;","Principal Value")

Traceback (most recent call last):

...

TypeError: Error executing code in Maxima

CODE:

1+1;

Maxima ERROR:

Principal Value

"""

raise TypeError("Error executing code in Maxima\nCODE:\n\t%s\nMaxima ERROR:\n\t%s"%(cmd, out.replace('-- an error. To debug this try debugmode(true);','')))

###########################################

# Direct access to underlying lisp interpreter.

###########################################

def lisp(self, cmd):

"""

Send a lisp command to Maxima.

.. note::

The output of this command is very raw - not pretty.

EXAMPLES::

sage: maxima.lisp("(+ 2 17)") # random formatted output

:lisp (+ 2 17)

(

"""

self._eval_line(':lisp %s\n""'%cmd, allow_use_file=False,

wait_for_prompt=False, reformat=False, error_check=False)

self._expect_expr('(%i)')

return self._before()

#####

def set(self, var, value):

"""

Set the variable var to the given value.

INPUT:

- ``var`` - string

- ``value`` - string

EXAMPLES::

sage: maxima.set('xxxxx', '2')

sage: maxima.get('xxxxx')

'2'

"""

if not isinstance(value, string_types):

raise TypeError

cmd = '%s : %s$'%(var, value.rstrip(';'))

if len(cmd) > self.__eval_using_file_cutoff:

self._batch(cmd, batchload=True)

else:

self._eval_line(cmd)

#self._sendline(cmd)

#self._expect_expr()

#out = self._before()

#self._error_check(cmd, out)

def clear(self, var):

"""

Clear the variable named var.

EXAMPLES::

sage: maxima.set('xxxxx', '2')

sage: maxima.get('xxxxx')

'2'

sage: maxima.clear('xxxxx')

sage: maxima.get('xxxxx')

'xxxxx'

"""

try:

self._expect.send('kill(%s)$'%var)

except (TypeError, AttributeError):

pass

def get(self, var):

"""

Get the string value of the variable var.

EXAMPLES::

sage: maxima.set('xxxxx', '2')

sage: maxima.get('xxxxx')

'2'

"""

s = self._eval_line('%s;'%var)

return s

def _function_class(self):

"""

Return the Python class of Maxima functions.

EXAMPLES::

sage: maxima._function_class()

"""

return MaximaFunction

def _object_class(self):

"""

Return the Python class of Maxima elements.

EXAMPLES::

sage: maxima._object_class()

"""

return MaximaElement

def _function_element_class(self):

"""

Return the Python class of Maxima functions of elements.

EXAMPLES::

sage: maxima._function_element_class()

"""

return MaximaFunctionElement

def _object_function_class(self):

"""

Return the Python class of Maxima user-defined functions.

EXAMPLES::

sage: maxima._object_function_class()

"""

return MaximaElementFunction

## some old helper functions to wrap the calculus use

## of the Maxima interface. these routines expect arguments

## living in the symbolic ring and return something

## that is hopefully coercible into the symbolic ring again.

## def sr_integral(self,*args):

## return args[0]._maxima_().integrate(*args[1:])

## def sr_sum(self,expression,v,a,b):

## sum = "'sum(%s, %s, %s, %s)" % tuple([repr(expr._maxima_()) for expr in (expression, v, a, b)])

## result = self.simplify_sum(sum)

## result = result.ratsimp()

## return expression.parent()(result)

## def sr_limit(self,ex,*args):

## return ex._maxima_().limit(*args)

## def sr_tlimit(self,ex,*args):

## return ex._maxima_().tlimit(*args)

def is_MaximaElement(x):

"""

Returns True if x is of type MaximaElement.

EXAMPLES::

sage: from sage.interfaces.maxima import is_MaximaElement

sage: m = maxima(1)

sage: is_MaximaElement(m)

True

sage: is_MaximaElement(1)

False

"""

return isinstance(x, MaximaElement)

@instancedoc

class MaximaElement(MaximaAbstractElement, ExpectElement):

"""

Element of Maxima through Pexpect interface.

EXAMPLES:

Elements of this class should not be created directly.

The targeted parent should be used instead::

sage: maxima(3)

sage: maxima(cos(x)+e^234)

cos(_SAGE_VAR_x)+%e^234

"""

def __init__(self, parent, value, is_name=False, name=None):

"""

Create a Maxima element.

See ``MaximaElement`` for full documentation.

EXAMPLES::

sage: maxima(zeta(7))

zeta(7)

TESTS::

sage: from sage.interfaces.maxima import MaximaElement

sage: loads(dumps(MaximaElement))==MaximaElement

True

sage: a = maxima(5)

sage: type(a)

sage: loads(dumps(a))==a

True

"""

ExpectElement.__init__(self, parent, value, is_name=False, name=None)

def display2d(self, onscreen=True):

"""

Return the 2d string representation of this Maxima object.

EXAMPLES::

sage: F = maxima('x^5 - y^5').factor()

sage: F.display2d()

4 3 2 2 3 4

- (y - x) (y + x y + x y + x y + x )

"""

self._check_valid()

P = self.parent()

with gc_disabled():

P._eval_line('display2d : true$')

s = P._eval_line('disp(%s)$'%self.name(), reformat=False)

P._eval_line('display2d : false$')

s = s.strip('\r\n')

# if ever want to dedent, see

# http://mail.python.org/pipermail/python-list/2006-December/420033.html

if onscreen:

print(s)

else:

return s

MaximaFunctionElement = MaximaAbstractFunctionElement

MaximaFunction = MaximaAbstractFunction

@instancedoc

class MaximaElementFunction(MaximaElement, MaximaAbstractElementFunction):

"""

Maxima user-defined functions.

EXAMPLES:

Elements of this class should not be created directly.

The method ``function`` of the targeted parent should be used instead::

sage: maxima.function('x,y','h(x)*y')

h(x)*y

"""

def __init__(self, parent, name, defn, args, latex):

"""

Create a Maxima function.

See ``MaximaElementFunction`` for full documentation.

EXAMPLES::

sage: maxima.function('x,y','cos(x)+y')

cos(x)+y

TESTS::

sage: f = maxima.function('x,y','x+y^9')

sage: f == loads(dumps(f))

True

Unpickling a Maxima Pexpect interface gives the default interface::

sage: m = Maxima()

sage: g = m.function('x,y','x+y^9')

sage: h = loads(dumps(g))

sage: g.parent() == h.parent()

False

"""

MaximaElement.__init__(self, parent, name, is_name=True)

MaximaAbstractElementFunction.__init__(self, parent,

name, defn, args, latex)

# An instance

maxima = Maxima(init_code = ['display2d : false',

'domain : complex', 'keepfloat : true'],

script_subdirectory=None)

def reduce_load_Maxima(): #(init_code=None):

"""

Unpickle a Maxima Pexpect interface.

EXAMPLES::

sage: from sage.interfaces.maxima import reduce_load_Maxima

sage: reduce_load_Maxima()

Maxima

"""

return maxima #Maxima(init_code=init_code)

# This is defined for compatibility with the old Maxima interface.

def reduce_load_Maxima_function(parent, defn, args, latex):

"""

Unpickle a Maxima function.

EXAMPLES::

sage: from sage.interfaces.maxima import reduce_load_Maxima_function

sage: f = maxima.function('x,y','sin(x+y)')

sage: _,args = f.__reduce__()

sage: g = reduce_load_Maxima_function(*args)

sage: g == f

True

"""

return parent.function(args, defn, defn, latex)

def __doctest_cleanup():

"""

Kill all Pexpect interfaces.

EXAMPLES::

sage: from sage.interfaces.maxima import __doctest_cleanup

sage: maxima(1)

sage: maxima.is_running()

True

sage: __doctest_cleanup()

sage: maxima.is_running()

False

"""

import sage.interfaces.quit

sage.interfaces.quit.expect_quitall()

Coverage for local/lib/python2.7/site-packages/sage/interfaces/maxima.py : 64%

223 statements 143 run 80 missing 0 excluded