OpenXM/src/sage/asir.py - diff

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Diff for /OpenXM/src/sage/asir.py between version 1.1 and 1.2

version 1.1, 2018/09/08 05:35:35

version 1.2, 2019/03/06 02:38:33

Line 1

# $OpenXM$

# $OpenXM: OpenXM/src/sage/asir.py,v 1.1 2018/09/08 05:35:35 takayama Exp $

from __future__ import print_function

from __future__ import absolute_import

import os

from .expect import Expect, ExpectElement

from sage.interfaces.expect import Expect, ExpectElement

from sage.misc.misc import verbose

##Ref: @s/2018/09/20180907-sage-asir-proj, Using External Libraries and Interfaces

##Ref: /usr/lib/python2.7/dist-packages/sage/interfaces

##Usage: load("asir.py");

class Asir(Expect):

r"""

Interface to the Asir interpreter.

EXAMPLES::

sage: asir.eval("a = [ 1, 1, 2; 3, 5, 8; 13, 21, 33 ]") # optional - asir

sage: asir.eval("F=fctr(x^10-1)") # optional - asir

'a =\n\n 1 1 2\n 3 5 8\n 13 21 33\n\n's

sage: asir.eval("b = [ 1; 3; 13]") # optional - asir

'b =\n\n 1\n 3\n 13\n\n'

sage: asir.eval("c=a \\ b") # solves linear equation: a*c = b # optional - asir; random output

'c =\n\n 1\n 7.21645e-16\n -7.21645e-16\n\n'

sage: asir.eval("c") # optional - asir; random output

'c =\n\n 1\n 7.21645e-16\n -7.21645e-16\n\n'

"""

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

Line 39 class Asir(Expect):

Line 36 class Asir(Expect):

Expect.__init__(self,

name = 'asir',

# We want the prompt sequence to be unique to avoid confusion with syntax error messages containing >>>

# prompt = 'asir\:\d+> ',

prompt = 'asir>',

# prompt = '',

# We don't want any pagination of output

# command = command + " --no-line-editing --silent --eval 'PS2(PS1());more off' --persist",

command = 'openxm ox_texmacs --view sage --quiet --noCopyright',

# command = "openxm asir -quiet",

maxread = maxread,

server = server,

server_tmpdir = server_tmpdir,

Line 58 class Asir(Expect):

Line 51 class Asir(Expect):

def set_seed(self, seed=None):

"""

Sets the seed for the random number generator

Not implemented. Sets the seed for the random number generator

for this asir interpreter.

EXAMPLES::

sage: o = Asir() # optional - asir

sage: o.set_seed(1) # optional - asir

sage: [o.rand() for i in range(5)] # optional - asir

[ 0.134364, 0.847434, 0.763775, 0.255069, 0.495435]

"""

if seed is None:

return 0

seed = self.rand_seed()

self.eval("rand('state',%d)" % seed)

self._seed = seed

return seed

def __reduce__(self):

"""

Line 90 class Asir(Expect):

Line 71 class Asir(Expect):

sage: filename = tmp_filename()

sage: asir._read_in_file_command(filename)

'source("...");'

'load("...");'

"""

return 'source("%s");'%filename

return 'load("%s");'%filename

def _quit_string(self):

"""

Line 113 class Asir(Expect):

Line 94 class Asir(Expect):

You must get ...

"""

return """

You must get the program "asir" in order to use Asir

You must get the program "asir" and "ox_texmacs" in order to use Asir

from Sage. You can read all about Asir at

http://www.gnu.org/software/asir/

http://www.openxm.org

The command openxm must be in the search path.

LINUX:

Do apt-get install asir as root on your machine (Ubuntu/Debian).

Other Linux systems have asir too.

OS X:

* This website has details on OS X builds of Asir:

http://wiki.asir.org/Asir_for_MacOS_X

* Darwin ports and fink have Asir as well.

"""

def _eval_line(self, line, reformat=True, allow_use_file=False,

Line 133 class Asir(Expect):

Line 106 class Asir(Expect):

EXAMPLES::

sage: print(asir._eval_line('2+2')) #optional - asir

ans = 4

'4'

"""

from pexpect.exceptions import EOF

if not wait_for_prompt:

Line 169 class Asir(Expect):

Line 142 class Asir(Expect):

return ''

def _keyboard_interrupt(self):

print("CntrlC: Interrupting %s..."%self)

print("Ctrl-C: Interrupting %s..."%self)

if self._restart_on_ctrlc:

try:

self._expect.close(force=1)

Line 252 class Asir(Expect):

Line 225 class Asir(Expect):

EXAMPLES::

sage: asir.set('x', '2') # optional - asir

sage: asir.set('X', '2') # optional - asir

sage: asir.get('x') # optional - asir

sage: asir.get('X') # optional - asir

' 2'

"""

cmd = '%s=%s;'%(var,value)

Line 267 class Asir(Expect):

Line 240 class Asir(Expect):

EXAMPLES::

sage: asir.set('x', '2') # optional - asir

sage: asir.set('X', '2') # optional - asir

sage: asir.get('x') # optional - asir

sage: asir.get('X') # optional - asir

' 2'

"""

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

i = s.find('=')

return s[i+1:]

def clear(self, var):

"""

Clear the variable named var.

EXAMPLES::

sage: asir.set('x', '2') # optional - asir

sage: asir.clear('x') # optional - asir

sage: asir.get('x') # optional - asir

"error: 'x' undefined near line ... column 1"

"""

self.eval('clear %s'%var)

def console(self):

"""

Spawn a new Asir command-line session.

Line 297 class Asir(Expect):

Line 257 class Asir(Expect):

EXAMPLES::

sage: asir_console() # not tested

sage: asir_console()

GNU Asir, version 2.1.73 (i386-apple-darwin8.5.3).

This is Risa/Asir, ....

...

asir:1> 2+3

[nnnn] 2+3;

ans = 5

asir:2> [ctl-d]

[nnnn] quit();

Pressing ctrl-d exits the asir console and returns you to Sage.

quit(); exits the asir console and returns you to Sage.

asir, like Sage, remembers its history from one session to

another.

"""

asir_console()

def version(self):

"""

Return the version of Asir.

bug: it returns error because sage tries to set sage0=version();

insread of Sage0=version();

OUTPUT: string

EXAMPLES::

Line 323 class Asir(Expect):

Line 281 class Asir(Expect):

sage: v # optional - asir; random

'2.13.7'

sage: import re

sage: assert re.match("\d+\.\d+\.\d+", v) is not None # optional - asir

"""

return str(self("version()")).strip()

def solve_linear_system(self, A, b):

r"""

Use asir to compute a solution x to A\*x = b, as a list.

INPUT:

- ``A`` -- mxn matrix A with entries in `\QQ` or `\RR`

- ``b`` -- m-vector b entries in `\QQ` or `\RR` (resp)

OUTPUT: A list x (if it exists) which solves M\*x = b

EXAMPLES::

sage: M33 = MatrixSpace(QQ,3,3)

sage: A = M33([1,2,3,4,5,6,7,8,0])

sage: V3 = VectorSpace(QQ,3)

sage: b = V3([1,2,3])

sage: asir.solve_linear_system(A,b) # optional - asir (and output is slightly random in low order bits)

[-0.33333299999999999, 0.66666700000000001, -3.5236600000000002e-18]

AUTHORS:

- David Joyner and William Stein

"""

m = A.nrows()

if m != len(b):

raise ValueError("dimensions of A and b must be compatible")

from sage.matrix.all import MatrixSpace

from sage.rings.all import QQ

MS = MatrixSpace(QQ,m,1)

b = MS(list(b)) # converted b to a "column vector"

sA = self.sage2asir_matrix_string(A)

sb = self.sage2asir_matrix_string(b)

self.eval("a = " + sA )

self.eval("b = " + sb )

soln = asir.eval("c = a \\ b")

soln = soln.replace("\n\n ","[")

soln = soln.replace("\n\n","]")

soln = soln.replace("\n",",")

sol = soln[3:]

return eval(sol)

def sage2asir_matrix_string(self, A):

"""

Return an asir matrix from a Sage matrix.

INPUT: A Sage matrix with entries in the rationals or reals.

OUTPUT: A string that evaluates to an Asir matrix.

EXAMPLES::

sage: M33 = MatrixSpace(QQ,3,3)

sage: A = M33([1,2,3,4,5,6,7,8,0])

sage: asir.sage2asir_matrix_string(A) # optional - asir

'[1, 2, 3; 4, 5, 6; 7, 8, 0]'

AUTHORS:

- David Joyner and William Stein

"""

return str(A.rows()).replace('), (', '; ').replace('(', '').replace(')','')

def de_system_plot(self, f, ics, trange):

r"""

Plots (using asir's interface to gnuplot) the solution to a

`2\times 2` system of differential equations.

INPUT:

- ``f`` - a pair of strings representing the

differential equations; The independent variable must be called x

and the dependent variable must be called y.

- ``ics`` - a pair [x0,y0] such that x(t0) = x0, y(t0)

= y0

- ``trange`` - a pair [t0,t1]

OUTPUT: a gnuplot window appears

EXAMPLES::

sage: asir.de_system_plot(['x+y','x-y'], [1,-1], [0,2]) # not tested -- does this actually work (on OS X it fails for me -- William Stein, 2007-10)

This should yield the two plots `(t,x(t)), (t,y(t))` on the

same graph (the `t`-axis is the horizontal axis) of the

system of ODEs

.. math::

x' = x+y, x(0) = 1;\qquad y' = x-y, y(0) = -1, \quad\text{for}\quad 0 < t < 2.

"""

eqn1 = f[0].replace('x','x(1)').replace('y','x(2)')

eqn2 = f[1].replace('x','x(1)').replace('y','x(2)')

fcn = "function xdot = f(x,t) xdot(1) = %s; xdot(2) = %s; endfunction"%(eqn1, eqn2)

self.eval(fcn)

x0_eqn = "x0 = [%s; %s]"%(ics[0], ics[1])

self.eval(x0_eqn)

t_eqn = "t = linspace(%s, %s, 200)'"%(trange[0], trange[1])

self.eval(t_eqn)

x_eqn = 'x = lsode("f",x0,t);'

self.eval(x_eqn)

self.eval("plot(t,x)")

def _object_class(self):

"""

EXAMPLES::

Line 449 class Asir(Expect):

Line 296 class Asir(Expect):

asir_functions = set()

def to_complex(asir_string, R):

#Todo, the following class has not yet been implemented.

r"""

# These are sample interface with octave.

Helper function to convert asir complex number

TESTS::

sage: from sage.interfaces.asir import to_complex

sage: to_complex('(0,1)', CDF)

1.0*I

sage: to_complex('(1.3231,-0.2)', CDF)

1.3231 - 0.2*I

"""

real, imag = asir_string.strip('() ').split(',')

return R(float(real), float(imag))

class AsirElement(ExpectElement):

def _get_sage_ring(self):

r"""

Line 680 def asir_console():

Line 514 def asir_console():

EXAMPLES::

sage: asir_console() # not tested

GNU Asir, version 2.1.73 (i386-apple-darwin8.5.3).

This is Risa/Asir ....

...

asir:1> 2+3

[nnnn] 2+3;

ans = 5

asir:2> [ctl-d]

[nnnn] quit();

Pressing ctrl-d exits the asir console and returns you to Sage.

quit(); exits the asir console and returns you to Sage.

asir, like Sage, remembers its history from one session to

another.

"""

from sage.repl.rich_output.display_manager import get_display_manager

if not get_display_manager().is_in_terminal():

raise RuntimeError('Can use the console only in the terminal. Try %%asir magics instead.')

os.system('openxm asir') # with asir prompt

os.system('openxm fep asir') # with asir prompt

# os.system('openxm asir -quiet')

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