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|
r"""
Interface to Singular
AUTHORS:
- David Joyner and William Stein (2005): first version
- Martin Albrecht (2006-03-05): code so singular.[tab] and x =
singular(...), x.[tab] includes all singular commands.
- Martin Albrecht (2006-03-06): This patch adds the equality symbol to
singular. Also fix a problem in which " " as prompt means comparison
will break all further communication with Singular.
- Martin Albrecht (2006-03-13): added current_ring() and
current_ring_name()
- William Stein (2006-04-10): Fixed problems with ideal constructor
- Martin Albrecht (2006-05-18): added sage_poly.
- Simon King (2010-11-23): Reduce the overhead caused by waiting for
the Singular prompt by doing garbage collection differently.
- Simon King (2011-06-06): Make conversion from Singular to Sage more flexible.
- Simon King (2015): Extend pickling capabilities.
Introduction
------------
This interface is extremely flexible, since it's exactly like
typing into the Singular interpreter, and anything that works there
should work here.
The Singular interface will only work if Singular is installed on
your computer; this should be the case, since Singular is included
with Sage. The interface offers three pieces of functionality:
#. ``singular_console()`` - A function that dumps you
into an interactive command-line Singular session.
#. ``singular(expr, type='def')`` - Creation of a
Singular object. This provides a Pythonic interface to Singular.
For example, if ``f=singular(10)``, then
``f.factorize()`` returns the factorization of
`10` computed using Singular.
#. ``singular.eval(expr)`` - Evaluation of arbitrary
Singular expressions, with the result returned as a string.
Of course, there are polynomial rings and ideals in Sage as well
(often based on a C-library interface to Singular). One can convert
an object in the Singular interpreter interface to Sage by the
method ``sage()``.
Tutorial
--------
EXAMPLES: First we illustrate multivariate polynomial
factorization::
sage: R1 = singular.ring(0, '(x,y)', 'dp')
sage: R1
polynomial ring, over a field, global ordering
// characteristic : 0
// number of vars : 2
// block 1 : ordering dp
// : names x y
// block 2 : ordering C
sage: f = singular('9x16 - 18x13y2 - 9x12y3 + 9x10y4 - 18x11y2 + 36x8y4 + 18x7y5 - 18x5y6 + 9x6y4 - 18x3y6 - 9x2y7 + 9y8')
sage: f
9*x^16-18*x^13*y^2-9*x^12*y^3+9*x^10*y^4-18*x^11*y^2+36*x^8*y^4+18*x^7*y^5-18*x^5*y^6+9*x^6*y^4-18*x^3*y^6-9*x^2*y^7+9*y^8
sage: f.parent()
Singular
::
sage: F = f.factorize(); F
[1]:
_[1]=9
_[2]=x^6-2*x^3*y^2-x^2*y^3+y^4
_[3]=-x^5+y^2
[2]:
1,1,2
::
sage: F[1]
9,
x^6-2*x^3*y^2-x^2*y^3+y^4,
-x^5+y^2
sage: F[1][2]
x^6-2*x^3*y^2-x^2*y^3+y^4
We can convert `f` and each exponent back to Sage objects
as well.
::
sage: g = f.sage(); g
9*x^16 - 18*x^13*y^2 - 9*x^12*y^3 + 9*x^10*y^4 - 18*x^11*y^2 + 36*x^8*y^4 + 18*x^7*y^5 - 18*x^5*y^6 + 9*x^6*y^4 - 18*x^3*y^6 - 9*x^2*y^7 + 9*y^8
sage: F[1][2].sage()
x^6 - 2*x^3*y^2 - x^2*y^3 + y^4
sage: g.parent()
Multivariate Polynomial Ring in x, y over Rational Field
This example illustrates polynomial GCD's::
sage: R2 = singular.ring(0, '(x,y,z)', 'lp')
sage: a = singular.new('3x2*(x+y)')
sage: b = singular.new('9x*(y2-x2)')
sage: g = a.gcd(b)
sage: g
x^2+x*y
This example illustrates computation of a Groebner basis::
sage: R3 = singular.ring(0, '(a,b,c,d)', 'lp')
sage: I = singular.ideal(['a + b + c + d', 'a*b + a*d + b*c + c*d', 'a*b*c + a*b*d + a*c*d + b*c*d', 'a*b*c*d - 1'])
sage: I2 = I.groebner()
sage: I2
c^2*d^6-c^2*d^2-d^4+1,
c^3*d^2+c^2*d^3-c-d,
b*d^4-b+d^5-d,
b*c-b*d^5+c^2*d^4+c*d-d^6-d^2,
b^2+2*b*d+d^2,
a+b+c+d
The following example is the same as the one in the Singular - Gap
interface documentation::
sage: R = singular.ring(0, '(x0,x1,x2)', 'lp')
sage: I1 = singular.ideal(['x0*x1*x2 -x0^2*x2', 'x0^2*x1*x2-x0*x1^2*x2-x0*x1*x2^2', 'x0*x1-x0*x2-x1*x2'])
sage: I2 = I1.groebner()
sage: I2
x1^2*x2^2,
x0*x2^3-x1^2*x2^2+x1*x2^3,
x0*x1-x0*x2-x1*x2,
x0^2*x2-x0*x2^2-x1*x2^2
sage: I2.sage()
Ideal (x1^2*x2^2, x0*x2^3 - x1^2*x2^2 + x1*x2^3, x0*x1 - x0*x2 - x1*x2, x0^2*x2 - x0*x2^2 - x1*x2^2) of Multivariate Polynomial Ring in x0, x1, x2 over Rational Field
This example illustrates moving a polynomial from one ring to
another. It also illustrates calling a method of an object with an
argument.
::
sage: R = singular.ring(0, '(x,y,z)', 'dp')
sage: f = singular('x3+y3+(x-y)*x2y2+z2')
sage: f
x^3*y^2-x^2*y^3+x^3+y^3+z^2
sage: R1 = singular.ring(0, '(x,y,z)', 'ds')
sage: f = R.fetch(f)
sage: f
z^2+x^3+y^3+x^3*y^2-x^2*y^3
We can calculate the Milnor number of `f`::
sage: _=singular.LIB('sing.lib') # assign to _ to suppress printing
sage: f.milnor()
4
The Jacobian applied twice yields the Hessian matrix of
`f`, with which we can compute.
::
sage: H = f.jacob().jacob()
sage: H
6*x+6*x*y^2-2*y^3,6*x^2*y-6*x*y^2, 0,
6*x^2*y-6*x*y^2, 6*y+2*x^3-6*x^2*y,0,
0, 0, 2
sage: H.sage()
[6*x + 6*x*y^2 - 2*y^3 6*x^2*y - 6*x*y^2 0]
[ 6*x^2*y - 6*x*y^2 6*y + 2*x^3 - 6*x^2*y 0]
[ 0 0 2]
sage: H.det() # This is a polynomial in Singular
72*x*y+24*x^4-72*x^3*y+72*x*y^3-24*y^4-48*x^4*y^2+64*x^3*y^3-48*x^2*y^4
sage: H.det().sage() # This is the corresponding polynomial in Sage
72*x*y + 24*x^4 - 72*x^3*y + 72*x*y^3 - 24*y^4 - 48*x^4*y^2 + 64*x^3*y^3 - 48*x^2*y^4
The 1x1 and 2x2 minors::
sage: H.minor(1)
2,
6*y+2*x^3-6*x^2*y,
6*x^2*y-6*x*y^2,
6*x^2*y-6*x*y^2,
6*x+6*x*y^2-2*y^3
sage: H.minor(2)
12*y+4*x^3-12*x^2*y,
12*x^2*y-12*x*y^2,
12*x^2*y-12*x*y^2,
12*x+12*x*y^2-4*y^3,
-36*x*y-12*x^4+36*x^3*y-36*x*y^3+12*y^4+24*x^4*y^2-32*x^3*y^3+24*x^2*y^4
::
sage: _=singular.eval('option(redSB)')
sage: H.minor(1).groebner()
1
Computing the Genus
-------------------
We compute the projective genus of ideals that define curves over
`\QQ`. It is *very important* to load the
``normal.lib`` library before calling the
``genus`` command, or you'll get an error message.
EXAMPLE::
sage: singular.lib('normal.lib')
sage: R = singular.ring(0,'(x,y)','dp')
sage: i2 = singular.ideal('y9 - x2*(x-1)^9 + x')
sage: i2.genus()
40
Note that the genus can be much smaller than the degree::
sage: i = singular.ideal('y9 - x2*(x-1)^9')
sage: i.genus()
0
An Important Concept
--------------------
AUTHORS:
- Neal Harris
The following illustrates an important concept: how Sage interacts
with the data being used and returned by Singular. Let's compute a
Groebner basis for some ideal, using Singular through Sage.
::
sage: singular.lib('poly.lib')
sage: singular.ring(32003, '(a,b,c,d,e,f)', 'lp')
polynomial ring, over a field, global ordering
// characteristic : 32003
// number of vars : 6
// block 1 : ordering lp
// : names a b c d e f
// block 2 : ordering C
sage: I = singular.ideal('cyclic(6)')
sage: g = singular('groebner(I)')
Traceback (most recent call last):
...
TypeError: Singular error:
...
We restart everything and try again, but correctly.
::
sage: singular.quit()
sage: singular.lib('poly.lib'); R = singular.ring(32003, '(a,b,c,d,e,f)', 'lp')
sage: I = singular.ideal('cyclic(6)')
sage: I.groebner()
f^48-2554*f^42-15674*f^36+12326*f^30-12326*f^18+15674*f^12+2554*f^6-1,
...
It's important to understand why the first attempt at computing a
basis failed. The line where we gave singular the input
'groebner(I)' was useless because Singular has no idea what 'I' is!
Although 'I' is an object that we computed with calls to Singular
functions, it actually lives in Sage. As a consequence, the name
'I' means nothing to Singular. When we called
``I.groebner()``, Sage was able to call the groebner
function on'I' in Singular, since 'I' actually means something to
Sage.
Long Input
----------
The Singular interface reads in even very long input (using files)
in a robust manner, as long as you are creating a new object.
::
sage: t = '"%s"'%10^15000 # 15 thousand character string (note that normal Singular input must be at most 10000)
sage: a = singular.eval(t)
sage: a = singular(t)
TESTS:
We test an automatic coercion::
sage: a = 3*singular('2'); a
6
sage: type(a)
<class 'sage.interfaces.singular.SingularElement'>
sage: a = singular('2')*3; a
6
sage: type(a)
<class 'sage.interfaces.singular.SingularElement'>
Create a ring over GF(9) to check that ``gftables`` has been installed,
see :trac:`11645`::
sage: singular.eval("ring testgf9 = (9,x),(a,b,c,d,e,f),(M((1,2,3,0)),wp(2,3),lp);")
''
"""
#*****************************************************************************
# Copyright (C) 2005 David Joyner and William Stein
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 2 of the License, or
# (at your option) any later version.
# http://www.gnu.org/licenses/
#*****************************************************************************
from __future__ import print_function
from __future__ import absolute_import
import os
import re
import sys
import pexpect
from time import sleep
from .expect import Expect, ExpectElement, FunctionElement, ExpectFunction
from sage.interfaces.tab_completion import ExtraTabCompletion
from sage.structure.sequence import Sequence
from sage.structure.element import RingElement
import sage.rings.integer
from sage.misc.misc import get_verbose
from sage.misc.superseded import deprecation
from six import reraise as raise_
class SingularError(RuntimeError):
"""
Raised if Singular printed an error message
"""
pass
class Singular(ExtraTabCompletion, Expect):
r"""
Interface to the Singular interpreter.
EXAMPLES: A Groebner basis example.
::
sage: R = singular.ring(0, '(x0,x1,x2)', 'lp')
sage: I = singular.ideal([ 'x0*x1*x2 -x0^2*x2', 'x0^2*x1*x2-x0*x1^2*x2-x0*x1*x2^2', 'x0*x1-x0*x2-x1*x2'])
sage: I.groebner()
x1^2*x2^2,
x0*x2^3-x1^2*x2^2+x1*x2^3,
x0*x1-x0*x2-x1*x2,
x0^2*x2-x0*x2^2-x1*x2^2
AUTHORS:
- David Joyner and William Stein
"""
def __init__(self, maxread=None, script_subdirectory=None,
logfile=None, server=None,server_tmpdir=None,
seed=None):
"""
EXAMPLES::
sage: singular == loads(dumps(singular))
True
"""
prompt = '> '
Expect.__init__(self,
terminal_echo=False,
name = 'singular',
prompt = prompt,
# no tty, fine grained cputime()
# and do not display CTRL-C prompt
command = "Singular -t --ticks-per-sec 1000 --cntrlc=a",
server = server,
server_tmpdir = server_tmpdir,
script_subdirectory = script_subdirectory,
restart_on_ctrlc = True,
verbose_start = False,
logfile = logfile,
eval_using_file_cutoff=100 if os.uname()[0]=="SunOS" else 1000)
self.__libs = []
self._prompt_wait = prompt
self.__to_clear = [] # list of variable names that need to be cleared.
self._seed = seed
def set_seed(self,seed=None):
"""
Sets the seed for singular interpeter.
The seed should be an integer at least 1
and not more than 30 bits.
See
http://www.singular.uni-kl.de/Manual/html/sing_19.htm#SEC26
and
http://www.singular.uni-kl.de/Manual/html/sing_283.htm#SEC323
EXAMPLES::
sage: s = Singular()
sage: s.set_seed(1)
1
sage: [s.random(1,10) for i in range(5)]
[8, 10, 4, 9, 1]
"""
if seed is None:
seed = self.rand_seed()
self.eval('system("--random",%d)' % seed)
self._seed = seed
return seed
def _start(self, alt_message=None):
"""
EXAMPLES::
sage: s = Singular()
sage: s.is_running()
False
sage: s._start()
sage: s.is_running()
True
sage: s.quit()
"""
self.__libs = []
Expect._start(self, alt_message)
# Load some standard libraries.
self.lib('general') # assumed loaded by misc/constants.py
# these options are required by the new coefficient rings
# supported by Singular 3-1-0.
self.option("redTail")
self.option("redThrough")
self.option("intStrategy")
self._saved_options = self.option('get')
# set random seed
self.set_seed(self._seed)
def __reduce__(self):
"""
EXAMPLES::
sage: singular.__reduce__()
(<function reduce_load_Singular at 0x...>, ())
"""
return reduce_load_Singular, ()
def _equality_symbol(self):
"""
EXAMPLES::
sage: singular._equality_symbol()
'=='
"""
return '=='
def _true_symbol(self):
"""
EXAMPLES::
sage: singular._true_symbol()
'1'
"""
return '1'
def _false_symbol(self):
"""
EXAMPLES::
sage: singular._false_symbol()
'0'
"""
return '0'
def _quit_string(self):
"""
EXAMPLES::
sage: singular._quit_string()
'quit'
"""
return 'quit'
def _send_interrupt(self):
"""
Send an interrupt to Singular. If needed, additional
semi-colons are sent until we get back at the prompt.
TESTS:
The following works without restarting Singular::
sage: a = singular(1)
sage: _ = singular._expect.sendline('1+') # unfinished input
sage: try:
....: alarm(0.5)
....: singular._expect_expr('>') # interrupt this
....: except KeyboardInterrupt:
....: pass
Control-C pressed. Interrupting Singular. Please wait a few seconds...
We can still access a::
sage: 2*a
2
"""
# Work around for Singular bug
# http://www.singular.uni-kl.de:8002/trac/ticket/727
sleep(0.1)
E = self._expect
E.sendline(chr(3))
for i in range(5):
try:
E.expect_upto(self._prompt, timeout=1.0)
return
except Exception:
pass
E.sendline(";")
def _read_in_file_command(self, filename):
r"""
EXAMPLES::
sage: singular._read_in_file_command('test')
'< "...";'
sage: filename = tmp_filename()
sage: f = open(filename, 'w')
sage: f.write('int x = 2;\n')
sage: f.close()
sage: singular.read(filename)
sage: singular.get('x')
'2'
"""
return '< "%s";'%filename
def eval(self, x, allow_semicolon=True, strip=True, **kwds):
r"""
Send the code x to the Singular interpreter and return the output
as a string.
INPUT:
- ``x`` - string (of code)
- ``allow_semicolon`` - default: False; if False then
raise a TypeError if the input line contains a semicolon.
- ``strip`` - ignored
EXAMPLES::
sage: singular.eval('2 > 1')
'1'
sage: singular.eval('2 + 2')
'4'
if the verbosity level is `> 1` comments are also printed
and not only returned.
::
sage: r = singular.ring(0,'(x,y,z)','dp')
sage: i = singular.ideal(['x^2','y^2','z^2'])
sage: s = i.std()
sage: singular.eval('hilb(%s)'%(s.name()))
'// 1 t^0\n// -3 t^2\n// 3 t^4\n// -1 t^6\n\n// 1 t^0\n//
3 t^1\n// 3 t^2\n// 1 t^3\n// dimension (affine) = 0\n//
degree (affine) = 8'
::
sage: set_verbose(1)
sage: o = singular.eval('hilb(%s)'%(s.name()))
// 1 t^0
// -3 t^2
// 3 t^4
// -1 t^6
// 1 t^0
// 3 t^1
// 3 t^2
// 1 t^3
// dimension (affine) = 0
// degree (affine) = 8
This is mainly useful if this method is called implicitly. Because
then intermediate results, debugging outputs and printed statements
are printed
::
sage: o = s.hilb()
// 1 t^0
// -3 t^2
// 3 t^4
// -1 t^6
// 1 t^0
// 3 t^1
// 3 t^2
// 1 t^3
// dimension (affine) = 0
// degree (affine) = 8
// ** right side is not a datum, assignment ignored
...
rather than ignored
::
sage: set_verbose(0)
sage: o = s.hilb()
"""
# Simon King:
# In previous versions, the interface was first synchronised and then
# unused variables were killed. This created a considerable overhead.
# By trac ticket #10296, killing unused variables is now done inside
# singular.set(). Moreover, it is not done by calling a separate _eval_line.
# In that way, the time spent by waiting for the singular prompt is reduced.
# Before #10296, it was possible that garbage collection occured inside
# of _eval_line. But collection of the garbage would launch another call
# to _eval_line. The result would have been a dead lock, that could only
# be avoided by synchronisation. Since garbage collection is now done
# without an additional call to _eval_line, synchronisation is not
# needed anymore, saving even more waiting time for the prompt.
# Uncomment the print statements below for low-level debugging of
# code that involves the singular interfaces. Everything goes
# through here.
x = str(x).rstrip().rstrip(';')
x = x.replace("> ",">\t") #don't send a prompt (added by Martin Albrecht)
if not allow_semicolon and x.find(";") != -1:
raise TypeError("singular input must not contain any semicolons:\n%s"%x)
if len(x) == 0 or x[len(x) - 1] != ';':
x += ';'
s = Expect.eval(self, x, **kwds)
if s.find("error") != -1 or s.find("Segment fault") != -1:
raise SingularError('Singular error:\n%s'%s)
if get_verbose() > 0:
for line in s.splitlines():
if line.startswith("//"):
print(line)
return s
else:
return s
def set(self, type, name, value):
"""
Set the variable with given name to the given value.
REMARK:
If a variable in the Singular interface was previously marked for
deletion, the actual deletion is done here, before the new variable
is created in Singular.
EXAMPLES::
sage: singular.set('int', 'x', '2')
sage: singular.get('x')
'2'
We test that an unused variable is only actually deleted if this method
is called::
sage: a = singular(3)
sage: n = a.name()
sage: del a
sage: singular.eval(n)
'3'
sage: singular.set('int', 'y', '5')
sage: singular.eval('defined(%s)'%n)
'0'
"""
cmd = ''.join('if(defined(%s)){kill %s;};'%(v,v) for v in self.__to_clear)
cmd += '%s %s=%s;'%(type, name, value)
self.__to_clear = []
self.eval(cmd)
def get(self, var):
"""
Get string representation of variable named var.
EXAMPLES::
sage: singular.set('int', 'x', '2')
sage: singular.get('x')
'2'
"""
return self.eval('print(%s);'%var)
def clear(self, var):
"""
Clear the variable named ``var``.
EXAMPLES::
sage: singular.set('int', 'x', '2')
sage: singular.get('x')
'2'
sage: singular.clear('x')
"Clearing the variable" means to allow to free the memory
that it uses in the Singular sub-process. However, the
actual deletion of the variable is only committed when
the next element in the Singular interface is created::
sage: singular.get('x')
'2'
sage: a = singular(3)
sage: singular.get('x')
'`x`'
"""
# We add the variable to the list of vars to clear when we do an eval.
# We queue up all the clears and do them at once to avoid synchronizing
# the interface at the same time we do garbage collection, which can
# lead to subtle problems. This was Willem Jan's ideas, implemented
# by William Stein.
self.__to_clear.append(var)
def _create(self, value, type='def'):
"""
Creates a new variable in the Singular session and returns the name
of that variable.
EXAMPLES::
sage: singular._create('2', type='int')
'sage...'
sage: singular.get(_)
'2'
"""
name = self._next_var_name()
self.set(type, name, value)
return name
def __call__(self, x, type='def'):
"""
Create a singular object X with given type determined by the string
x. This returns var, where var is built using the Singular
statement type var = ... x ... Note that the actual name of var
could be anything, and can be recovered using X.name().
The object X returned can be used like any Sage object, and wraps
an object in self. The standard arithmetic operators work. Moreover
if foo is a function then X.foo(y,z,...) calls foo(X, y, z, ...)
and returns the corresponding object.
EXAMPLES::
sage: R = singular.ring(0, '(x0,x1,x2)', 'lp')
sage: I = singular.ideal([ 'x0*x1*x2 -x0^2*x2', 'x0^2*x1*x2-x0*x1^2*x2-x0*x1*x2^2', 'x0*x1-x0*x2-x1*x2'])
sage: I
-x0^2*x2+x0*x1*x2,
x0^2*x1*x2-x0*x1^2*x2-x0*x1*x2^2,
x0*x1-x0*x2-x1*x2
sage: type(I)
<class 'sage.interfaces.singular.SingularElement'>
sage: I.parent()
Singular
"""
if isinstance(x, SingularElement) and x.parent() is self:
return x
elif isinstance(x, ExpectElement):
return self(x.sage())
elif not isinstance(x, ExpectElement) and hasattr(x, '_singular_'):
return x._singular_(self)
# some convenient conversions
if type in ("module","list") and isinstance(x,(list,tuple,Sequence)):
x = str(x)[1:-1]
return SingularElement(self, type, x, False)
def _coerce_map_from_(self, S):
"""
Return ``True`` if ``S`` admits a coercion map into the
Singular interface.
EXAMPLES::
sage: singular._coerce_map_from_(ZZ)
True
sage: singular.coerce_map_from(ZZ)
Call morphism:
From: Integer Ring
To: Singular
sage: singular.coerce_map_from(float)
"""
# we want to implement this without coercing, since singular has state.
if hasattr(S, 'an_element'):
if hasattr(S.an_element(), '_singular_'):
return True
try:
self._coerce_(S.an_element())
return True
except TypeError:
pass
elif S is int or S is long:
return True
return None
def cputime(self, t=None):
r"""
Returns the amount of CPU time that the Singular session has used.
If ``t`` is not None, then it returns the difference
between the current CPU time and ``t``.
EXAMPLES::
sage: t = singular.cputime()
sage: R = singular.ring(0, '(x0,x1,x2)', 'lp')
sage: I = singular.ideal([ 'x0*x1*x2 -x0^2*x2', 'x0^2*x1*x2-x0*x1^2*x2-x0*x1*x2^2', 'x0*x1-x0*x2-x1*x2'])
sage: gb = I.groebner()
sage: singular.cputime(t) #random
0.02
"""
if t:
return float(self.eval('timer-(%d)'%(int(1000*t))))/1000.0
else:
return float(self.eval('timer'))/1000.0
###################################################################
# Singular libraries
###################################################################
def lib(self, lib, reload=False):
"""
Load the Singular library named lib.
Note that if the library was already loaded during this session it
is not reloaded unless the optional reload argument is True (the
default is False).
EXAMPLES::
sage: singular.lib('sing.lib')
sage: singular.lib('sing.lib', reload=True)
"""
if lib[-4:] != ".lib":
lib += ".lib"
if not reload and lib in self.__libs:
return
self.eval('LIB "%s"'%lib)
self.__libs.append(lib)
LIB = lib
load = lib
###################################################################
# constructors
###################################################################
def ideal(self, *gens):
"""
Return the ideal generated by gens.
INPUT:
- ``gens`` - list or tuple of Singular objects (or
objects that can be made into Singular objects via evaluation)
OUTPUT: the Singular ideal generated by the given list of gens
EXAMPLES: A Groebner basis example done in a different way.
::
sage: _ = singular.eval("ring R=0,(x0,x1,x2),lp")
sage: i1 = singular.ideal([ 'x0*x1*x2 -x0^2*x2', 'x0^2*x1*x2-x0*x1^2*x2-x0*x1*x2^2', 'x0*x1-x0*x2-x1*x2'])
sage: i1
-x0^2*x2+x0*x1*x2,
x0^2*x1*x2-x0*x1^2*x2-x0*x1*x2^2,
x0*x1-x0*x2-x1*x2
::
sage: i2 = singular.ideal('groebner(%s);'%i1.name())
sage: i2
x1^2*x2^2,
x0*x2^3-x1^2*x2^2+x1*x2^3,
x0*x1-x0*x2-x1*x2,
x0^2*x2-x0*x2^2-x1*x2^2
"""
if isinstance(gens, str):
gens = self(gens)
if isinstance(gens, SingularElement):
return self(gens.name(), 'ideal')
if not isinstance(gens, (list, tuple)):
raise TypeError("gens (=%s) must be a list, tuple, string, or Singular element"%gens)
if len(gens) == 1 and isinstance(gens[0], (list, tuple)):
gens = gens[0]
gens2 = []
for g in gens:
if not isinstance(g, SingularElement):
gens2.append(self.new(g))
else:
gens2.append(g)
return self(",".join([g.name() for g in gens2]), 'ideal')
def list(self, x):
r"""
Creates a list in Singular from a Sage list ``x``.
EXAMPLES::
sage: singular.list([1,2])
[1]:
1
[2]:
2
"""
return self(x, 'list')
def matrix(self, nrows, ncols, entries=None):
"""
EXAMPLES::
sage: singular.lib("matrix")
sage: R = singular.ring(0, '(x,y,z)', 'dp')
sage: A = singular.matrix(3,2,'1,2,3,4,5,6')
sage: A
1,2,
3,4,
5,6
sage: A.gauss_col()
2,-1,
1,0,
0,1
AUTHORS:
- Martin Albrecht (2006-01-14)
"""
name = self._next_var_name()
if entries is None:
self.eval('matrix %s[%s][%s]'%(name, nrows, ncols))
else:
self.eval('matrix %s[%s][%s] = %s'%(name, nrows, ncols, entries))
return SingularElement(self, None, name, True)
def ring(self, char=0, vars='(x)', order='lp', check=True):
r"""
Create a Singular ring and makes it the current ring.
INPUT:
- ``char`` - characteristic of the base ring (see
examples below), which must be either 0, prime (!), or one of
several special codes (see examples below).
- ``vars`` - a tuple or string that defines the
variable names
- ``order`` - string - the monomial order (default:
'lp')
- ``check`` - if True, check primality of the
characteristic if it is an integer.
OUTPUT: a Singular ring
.. note::
This function is *not* identical to calling the Singular
``ring`` function. In particular, it also attempts to
"kill" the variable names, so they can actually be used
without getting errors, and it sets printing of elements
for this range to short (i.e., with \*'s and carets).
EXAMPLES: We first declare `\QQ[x,y,z]` with degree reverse
lexicographic ordering.
::
sage: R = singular.ring(0, '(x,y,z)', 'dp')
sage: R
polynomial ring, over a field, global ordering
// characteristic : 0
// number of vars : 3
// block 1 : ordering dp
// : names x y z
// block 2 : ordering C
::
sage: R1 = singular.ring(32003, '(x,y,z)', 'dp')
sage: R2 = singular.ring(32003, '(a,b,c,d)', 'lp')
This is a ring in variables named x(1) through x(10) over the
finite field of order `7`::
sage: R3 = singular.ring(7, '(x(1..10))', 'ds')
This is a polynomial ring over the transcendental extension
`\QQ(a)` of `\QQ`::
sage: R4 = singular.ring('(0,a)', '(mu,nu)', 'lp')
This is a ring over the field of single-precision floats::
sage: R5 = singular.ring('real', '(a,b)', 'lp')
This is over 50-digit floats::
sage: R6 = singular.ring('(real,50)', '(a,b)', 'lp')
sage: R7 = singular.ring('(complex,50,i)', '(a,b)', 'lp')
To use a ring that you've defined, use the set_ring() method on
the ring. This sets the ring to be the "current ring". For
example,
::
sage: R = singular.ring(7, '(a,b)', 'ds')
sage: S = singular.ring('real', '(a,b)', 'lp')
sage: singular.new('10*a')
(1.000e+01)*a
sage: R.set_ring()
sage: singular.new('10*a')
3*a
"""
if len(vars) > 2:
s = '; '.join(['if(defined(%s)>0){kill %s;};'%(x,x)
for x in vars[1:-1].split(',')])
self.eval(s)
if check and isinstance(char, (int, long, sage.rings.integer.Integer)):
if char != 0:
n = sage.rings.integer.Integer(char)
if not n.is_prime():
raise ValueError("the characteristic must be 0 or prime")
R = self('%s,%s,%s'%(char, vars, order), 'ring')
self.eval('short=0') # make output include *'s for multiplication for *THIS* ring.
return R
def string(self, x):
"""
Creates a Singular string from a Sage string. Note that the Sage
string has to be "double-quoted".
EXAMPLES::
sage: singular.string('"Sage"')
Sage
"""
return self(x, 'string')
def set_ring(self, R):
"""
Sets the current Singular ring to R.
EXAMPLES::
sage: R = singular.ring(7, '(a,b)', 'ds')
sage: S = singular.ring('real', '(a,b)', 'lp')
sage: singular.current_ring()
polynomial ring, over a field, global ordering
// characteristic : 0 (real)
// number of vars : 2
// block 1 : ordering lp
// : names a b
// block 2 : ordering C
sage: singular.set_ring(R)
sage: singular.current_ring()
polynomial ring, over a field, local/mixed ordering
// characteristic : 7
// number of vars : 2
// block 1 : ordering ds
// : names a b
// block 2 : ordering C
"""
if not isinstance(R, SingularElement):
raise TypeError("R must be a singular ring")
self.eval("setring %s; short=0"%R.name(), allow_semicolon=True)
setring = set_ring
def current_ring_name(self):
"""
Returns the Singular name of the currently active ring in
Singular.
OUTPUT: currently active ring's name
EXAMPLES::
sage: r = PolynomialRing(GF(127),3,'xyz')
sage: r._singular_().name() == singular.current_ring_name()
True
"""
ringlist = self.eval("listvar(ring)").splitlines()
p = re.compile("// ([a-zA-Z0-9_]*).*\[.*\].*\*.*") #do this in constructor?
for line in ringlist:
m = p.match(line)
if m:
return m.group(int(1))
return None
def current_ring(self):
"""
Returns the current ring of the running Singular session.
EXAMPLES::
sage: r = PolynomialRing(GF(127),3,'xyz', order='invlex')
sage: r._singular_()
polynomial ring, over a field, global ordering
// characteristic : 127
// number of vars : 3
// block 1 : ordering rp
// : names x y z
// block 2 : ordering C
sage: singular.current_ring()
polynomial ring, over a field, global ordering
// characteristic : 127
// number of vars : 3
// block 1 : ordering rp
// : names x y z
// block 2 : ordering C
"""
name = self.current_ring_name()
if name:
return self(name)
else:
return None
def _tab_completion(self):
"""
Return a list of all Singular commands.
EXAMPLES::
sage: singular._tab_completion()
['exteriorPower',
...
'stdfglm']
"""
p = re.compile("// *([a-z0-9A-Z_]*).*") #compiles regular expression
proclist = self.eval("listvar(proc)").splitlines()
return [p.match(line).group(int(1)) for line in proclist]
def console(self):
"""
EXAMPLES::
sage: singular_console() #not tested
SINGULAR / Development
A Computer Algebra System for Polynomial Computations / version 3-0-4
0<
by: G.-M. Greuel, G. Pfister, H. Schoenemann \ Nov 2007
FB Mathematik der Universitaet, D-67653 Kaiserslautern \
"""
singular_console()
def version(self):
"""
EXAMPLES:
"""
return singular_version()
def _function_class(self):
"""
EXAMPLES::
sage: singular._function_class()
<class 'sage.interfaces.singular.SingularFunction'>
"""
return SingularFunction
def _function_element_class(self):
"""
EXAMPLES::
sage: singular._function_element_class()
<class 'sage.interfaces.singular.SingularFunctionElement'>
"""
return SingularFunctionElement
def option(self, cmd=None, val=None):
"""
Access to Singular's options as follows:
Syntax: option() Returns a string of all defined options.
Syntax: option( 'option_name' ) Sets an option. Note to disable an
option, use the prefix no.
Syntax: option( 'get' ) Returns an intvec of the state of all
options.
Syntax: option( 'set', intvec_expression ) Restores the state of
all options from an intvec (produced by option('get')).
EXAMPLES::
sage: singular.option()
//options: redefine loadLib usage prompt
sage: singular.option('get')
0,
10321
sage: old_options = _
sage: singular.option('noredefine')
sage: singular.option()
//options: loadLib usage prompt
sage: singular.option('set', old_options)
sage: singular.option('get')
0,
10321
"""
if cmd is None:
return SingularFunction(self,"option")()
elif cmd == "get":
#return SingularFunction(self,"option")("\"get\"")
return self(self.eval("option(get)"),"intvec")
elif cmd == "set":
if not isinstance(val,SingularElement):
raise TypeError("singular.option('set') needs SingularElement as second parameter")
#SingularFunction(self,"option")("\"set\"",val)
self.eval("option(set,%s)"%val.name())
else:
SingularFunction(self,"option")("\""+str(cmd)+"\"")
def _keyboard_interrupt(self):
print("Interrupting %s..." % self)
try:
self._expect.sendline(chr(4))
except pexpect.ExceptionPexpect as msg:
raise pexpect.ExceptionPexpect("THIS IS A BUG -- PLEASE REPORT. This should never happen.\n" + msg)
self._start()
raise KeyboardInterrupt("Restarting %s (WARNING: all variables defined in previous session are now invalid)" % self)
class SingularElement(ExtraTabCompletion, ExpectElement):
def __init__(self, parent, type, value, is_name=False):
"""
EXAMPLES::
sage: a = singular(2)
sage: loads(dumps(a))
2
"""
RingElement.__init__(self, parent)
if parent is None: return
if not is_name:
try:
self._name = parent._create( value, type)
# Convert SingularError to TypeError for
# coercion to work properly.
except SingularError as x:
self._session_number = -1
raise_(TypeError, x, sys.exc_info()[2])
except BaseException:
self._session_number = -1
raise
else:
self._name = value
self._session_number = parent._session_number
def __repr__(self):
r"""
Return string representation of ``self``.
EXAMPLE::
sage: r = singular.ring(0,'(x,y)','dp')
sage: singular(0)
0
sage: singular('x') # indirect doctest
x
sage: singular.matrix(2,2)
0,0,
0,0
sage: singular.matrix(2,2,"(25/47*x^2*y^4 + 63/127*x + 27)^3,y,0,1")
15625/103823*x^6*y.., y,
0, 1
Note that the output is truncated
::
sage: M= singular.matrix(2,2,"(25/47*x^2*y^4 + 63/127*x + 27)^3,y,0,1")
sage: M.rename('T')
sage: M
T[1,1],y,
0, 1
if ``self`` has a custom name, it is used to print the
matrix, rather than abbreviating its contents
"""
try:
self._check_valid()
except ValueError:
return '(invalid object -- defined in terms of closed session)'
try:
if self._get_using_file:
s = self.parent().get_using_file(self._name)
except AttributeError:
s = self.parent().get(self._name)
if self._name in s:
if hasattr(self, '__custom_name'):
s = s.replace(self._name, self.__dict__['__custom_name'])
elif self.type() == 'matrix':
s = self.parent().eval('pmat(%s,20)'%(self.name()))
return s
def __copy__(self):
r"""
Returns a copy of ``self``.
EXAMPLES::
sage: R=singular.ring(0,'(x,y)','dp')
sage: M=singular.matrix(3,3,'0,0,-x, 0,y,0, x*y,0,0')
sage: N=copy(M)
sage: N[1,1]=singular('x+y')
sage: N
x+y,0,-x,
0, y,0,
x*y,0,0
sage: M
0, 0,-x,
0, y,0,
x*y,0,0
sage: L=R.ringlist()
sage: L[4]=singular.ideal('x**2-5')
sage: Q=L.ring()
sage: otherR=singular.ring(5,'(x)','dp')
sage: cpQ=copy(Q)
sage: cpQ.set_ring()
sage: cpQ
polynomial ring, over a field, global ordering
// characteristic : 0
// number of vars : 2
// block 1 : ordering dp
// : names x y
// block 2 : ordering C
// quotient ring from ideal
_[1]=x^2-5
sage: R.fetch(M)
0, 0,-x,
0, y,0,
x*y,0,0
"""
if (self.type()=='ring') or (self.type()=='qring'):
# Problem: singular has no clean method to produce
# a copy of a ring/qring. We use ringlist, but this
# is only possible if we make self the active ring,
# use ringlist, and switch back to the previous
# base ring.
br=self.parent().current_ring()
self.set_ring()
OUT = (self.ringlist()).ring()
br.set_ring()
return OUT
else:
return self.parent()(self.name())
def __len__(self):
"""
Returns the size of this Singular element.
EXAMPLES::
sage: R = singular.ring(0, '(x,y,z)', 'dp')
sage: A = singular.matrix(2,2)
sage: len(A)
4
"""
return int(self.size())
def __setitem__(self, n, value):
"""
Set the n-th element of self to x.
INPUT:
- ``n`` - an integer *or* a 2-tuple (for setting
matrix elements)
- ``value`` - anything (is coerced to a Singular
object if it is not one already)
OUTPUT: Changes elements of self.
EXAMPLES::
sage: R = singular.ring(0, '(x,y,z)', 'dp')
sage: A = singular.matrix(2,2)
sage: A
0,0,
0,0
sage: A[1,1] = 5
sage: A
5,0,
0,0
sage: A[1,2] = '5*x + y + z3'
sage: A
5,z^3+5*x+y,
0,0
"""
P = self.parent()
if not isinstance(value, SingularElement):
value = P(value)
if isinstance(n, tuple):
if len(n) != 2:
raise ValueError("If n (=%s) is a tuple, it must be a 2-tuple"%n)
x, y = n
P.eval('%s[%s,%s] = %s'%(self.name(), x, y, value.name()))
else:
P.eval('%s[%s] = %s'%(self.name(), n, value.name()))
def __nonzero__(self):
"""
Returns True if this Singular element is not zero.
EXAMPLES::
sage: singular(0).__nonzero__()
False
sage: singular(1).__nonzero__()
True
"""
P = self.parent()
return P.eval('%s == 0'%self.name()) == '0'
def sage_polystring(self):
r"""
If this Singular element is a polynomial, return a string
representation of this polynomial that is suitable for evaluation
in Python. Thus \* is used for multiplication and \*\* for
exponentiation. This function is primarily used internally.
The short=0 option *must* be set for the parent ring or this
function will not work as expected. This option is set by default
for rings created using ``singular.ring`` or set using
``ring_name.set_ring()``.
EXAMPLES::
sage: R = singular.ring(0,'(x,y)')
sage: f = singular('x^3 + 3*y^11 + 5')
sage: f
x^3+3*y^11+5
sage: f.sage_polystring()
'x**3+3*y**11+5'
"""
return str(self).replace('^','**')
def sage_global_ring(self):
"""
Return the current basering in Singular as a polynomial ring or quotient ring.
EXAMPLE::
sage: singular.eval('ring r1 = (9,x),(a,b,c,d,e,f),(M((1,2,3,0)),wp(2,3),lp)')
''
sage: R = singular('r1').sage_global_ring()
sage: R
Multivariate Polynomial Ring in a, b, c, d, e, f over Finite Field in x of size 3^2
sage: R.term_order()
Block term order with blocks:
(Matrix term order with matrix
[1 2]
[3 0],
Weighted degree reverse lexicographic term order with weights (2, 3),
Lexicographic term order of length 2)
::
sage: singular.eval('ring r2 = (0,x),(a,b,c),dp')
''
sage: singular('r2').sage_global_ring()
Multivariate Polynomial Ring in a, b, c over Fraction Field of Univariate Polynomial Ring in x over Rational Field
::
sage: singular.eval('ring r3 = (3,z),(a,b,c),dp')
''
sage: singular.eval('minpoly = 1+z+z2+z3+z4')
''
sage: singular('r3').sage_global_ring()
Multivariate Polynomial Ring in a, b, c over Finite Field in z of size 3^4
Real and complex fields in both Singular and Sage are defined with a precision.
The precision in Singular is given in terms of digits, but in Sage it is given
in terms of bits. So, the digit precision is internally converted to a reasonable
bit precision::
sage: singular.eval('ring r4 = (real,20),(a,b,c),dp')
''
sage: singular('r4').sage_global_ring()
Multivariate Polynomial Ring in a, b, c over Real Field with 70 bits of precision
The case of complex coefficients is not fully supported, yet, since
the generator of a complex field in Sage is always called "I"::
sage: singular.eval('ring r5 = (complex,15,j),(a,b,c),dp')
''
sage: R = singular('r5').sage_global_ring(); R
Multivariate Polynomial Ring in a, b, c over Complex Field with 54 bits of precision
sage: R.base_ring()('j')
Traceback (most recent call last):
...
NameError: name 'j' is not defined
sage: R.base_ring()('I')
1.00000000000000*I
An example where the base ring is a polynomial ring over an extension of the rational field::
sage: singular.eval('ring r7 = (0,a), (x,y), dp')
''
sage: singular.eval('minpoly = a2 + 1')
''
sage: singular('r7').sage_global_ring()
Multivariate Polynomial Ring in x, y over Number Field in a with defining polynomial a^2 + 1
In our last example, the base ring is a quotient ring::
sage: singular.eval('ring r6 = (9,a), (x,y,z),lp')
''
sage: Q = singular('std(ideal(x^2,x+y^2+z^3))', type='qring')
sage: Q.sage_global_ring()
Quotient of Multivariate Polynomial Ring in x, y, z over Finite Field in a of size 3^2 by the ideal (y^4 - y^2*z^3 + z^6, x + y^2 + z^3)
AUTHOR:
- Simon King (2011-06-06)
"""
# extract the ring of coefficients
singular = self.parent()
charstr = singular.eval('charstr(basering)').split(',',1)
from sage.all import ZZ
is_extension = len(charstr)==2
if charstr[0]=='integer':
br = ZZ
is_extension = False
elif charstr[0]=='0':
from sage.all import QQ
br = QQ
elif charstr[0]=='real':
from sage.all import RealField, ceil, log
prec = singular.eval('ringlist(basering)[1][2][1]')
br = RealField(ceil((ZZ(prec)+1)/log(2,10)))
is_extension = False
elif charstr[0]=='complex':
from sage.all import ComplexField, ceil, log
prec = singular.eval('ringlist(basering)[1][2][1]')
br = ComplexField(ceil((ZZ(prec)+1)/log(2,10)))
is_extension = False
else:
# it ought to be a finite field
q = ZZ(charstr[0])
from sage.all import GF
if q.is_prime():
br = GF(q)
else:
br = GF(q,charstr[1])
# Singular has no extension of a non-prime field
is_extension = False
# We have the base ring of the base ring. But is it
# an extension?
if is_extension:
minpoly = singular.eval('minpoly')
if minpoly == '0':
from sage.all import Frac
BR = Frac(br[charstr[1]])
else:
is_short = singular.eval('short')
if is_short != '0':
singular.eval('short=0')
minpoly = ZZ[charstr[1]](singular.eval('minpoly'))
singular.eval('short=%s'%is_short)
else:
minpoly = ZZ[charstr[1]](minpoly)
BR = br.extension(minpoly,names=charstr[1])
else:
BR = br
# Now, we form the polynomial ring over BR with the given variables,
# using Singular's term order
from sage.rings.polynomial.term_order import termorder_from_singular
from sage.all import PolynomialRing
# Meanwhile Singulars quotient rings are also of 'ring' type, not 'qring' as it was in the past.
# To find out if a singular ring is a quotient ring or not checking for ring type does not help
# and instead of that we we check if the quotient ring is zero or not:
if (singular.eval('ideal(basering)==0')=='1'):
return PolynomialRing(BR, names=singular.eval('varstr(basering)'), order=termorder_from_singular(singular))
P = PolynomialRing(BR, names=singular.eval('varstr(basering)'), order=termorder_from_singular(singular))
return P.quotient(singular('ringlist(basering)[4]')._sage_(P), names=singular.eval('varstr(basering)'))
def sage_poly(self, R=None, kcache=None):
"""
Returns a Sage polynomial in the ring r matching the provided poly
which is a singular polynomial.
INPUT:
- ``R`` - (default: None); an optional polynomial ring.
If it is provided, then you have to make sure that it
matches the current singular ring as, e.g., returned by
singular.current_ring(). By default, the output of
:meth:`sage_global_ring` is used.
- ``kcache`` - (default: None); an optional dictionary
for faster finite field lookups, this is mainly useful for finite
extension fields
OUTPUT: MPolynomial
EXAMPLES::
sage: R = PolynomialRing(GF(2^8,'a'),2,'xy')
sage: f=R('a^20*x^2*y+a^10+x')
sage: f._singular_().sage_poly(R)==f
True
sage: R = PolynomialRing(GF(2^8,'a'),1,'x')
sage: f=R('a^20*x^3+x^2+a^10')
sage: f._singular_().sage_poly(R)==f
True
::
sage: P.<x,y> = PolynomialRing(QQ, 2)
sage: f = x*y**3 - 1/9 * x + 1; f
x*y^3 - 1/9*x + 1
sage: singular(f)
x*y^3-1/9*x+1
sage: P(singular(f))
x*y^3 - 1/9*x + 1
TESTS::
sage: singular.eval('ring r = (3,z),(a,b,c),dp')
''
sage: singular.eval('minpoly = 1+z+z2+z3+z4')
''
sage: p = singular('z^4*a^3+z^2*a*b*c')
sage: p.sage_poly()
(-z^3 - z^2 - z - 1)*a^3 + (z^2)*a*b*c
sage: singular('z^4')
(-z3-z2-z-1)
AUTHORS:
- Martin Albrecht (2006-05-18)
- Simon King (2011-06-06): Deal with Singular's short polynomial representation,
automatic construction of a polynomial ring, if it is not explicitly given.
.. note::
For very simple polynomials
``eval(SingularElement.sage_polystring())`` is faster than
SingularElement.sage_poly(R), maybe we should detect the
crossover point (in dependence of the string length) and
choose an appropriate conversion strategy
"""
# TODO: Refactor imports to move this to the top
from sage.rings.polynomial.multi_polynomial_ring import MPolynomialRing_polydict
from sage.rings.polynomial.multi_polynomial_libsingular import MPolynomialRing_libsingular
from sage.rings.polynomial.multi_polynomial_element import MPolynomial_polydict
from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
from sage.rings.polynomial.polydict import PolyDict,ETuple
from sage.rings.polynomial.polynomial_singular_interface import can_convert_to_singular
from sage.rings.quotient_ring import QuotientRing_generic
from sage.rings.quotient_ring_element import QuotientRingElement
ring_is_fine = False
if R is None:
ring_is_fine = True
R = self.sage_global_ring()
sage_repr = {}
k = R.base_ring()
variable_str = "*".join(R.variable_names())
# This returns a string which looks like a list where the first
# half of the list is filled with monomials occurring in the
# Singular polynomial and the second half filled with the matching
# coefficients.
#
# Our strategy is to split the monomials at "*" to get the powers
# in the single variables and then to split the result to get
# actual exponent.
#
# So e.g. ['x^3*y^3','a'] get's split to
# [[['x','3'],['y','3']],'a']. We may do this quickly,
# as we know what to expect.
is_short = self.parent().eval('short')
if is_short!='0':
self.parent().eval('short=0')
if isinstance(R, MPolynomialRing_libsingular):
out = R(self)
self.parent().eval('short=%s'%is_short)
return out
singular_poly_list = self.parent().eval("string(coef(%s,%s))"%(\
self.name(),variable_str)).split(",")
self.parent().eval('short=%s'%is_short)
else:
if isinstance(R, MPolynomialRing_libsingular):
return R(self)
singular_poly_list = self.parent().eval("string(coef(%s,%s))"%(\
self.name(),variable_str)).split(",")
# Directly treat constants
if singular_poly_list[0] in ['1', '(1.000e+00)']:
return R(singular_poly_list[1])
coeff_start = len(singular_poly_list) // 2
# Singular 4 puts parentheses around floats and sign outside them
charstr = self.parent().eval('charstr(basering)').split(',',1)
if charstr[0] in ['real', 'complex']:
for i in range(coeff_start, 2*coeff_start):
singular_poly_list[i] = singular_poly_list[i].replace('(','').replace(')','')
if isinstance(R,(MPolynomialRing_polydict,QuotientRing_generic)) and (ring_is_fine or can_convert_to_singular(R)):
# we need to lookup the index of a given variable represented
# through a string
var_dict = dict(zip(R.variable_names(),range(R.ngens())))
ngens = R.ngens()
for i in range(coeff_start):
exp = dict()
monomial = singular_poly_list[i]
if monomial!="1":
variables = [var.split("^") for var in monomial.split("*") ]
for e in variables:
var = e[0]
if len(e)==int(2):
power = int(e[1])
else:
power=1
exp[var_dict[var]]=power
if kcache is None:
sage_repr[ETuple(exp,ngens)]=k(singular_poly_list[coeff_start+i])
else:
elem = singular_poly_list[coeff_start+i]
if elem not in kcache:
kcache[elem] = k( elem )
sage_repr[ETuple(exp,ngens)]= kcache[elem]
p = MPolynomial_polydict(R,PolyDict(sage_repr,force_int_exponents=False,force_etuples=False))
if isinstance(R, MPolynomialRing_polydict):
return p
else:
return QuotientRingElement(R,p,reduce=False)
elif is_PolynomialRing(R) and (ring_is_fine or can_convert_to_singular(R)):
sage_repr = [0]*int(self.deg()+1)
for i in range(coeff_start):
monomial = singular_poly_list[i]
exp = int(0)
if monomial!="1":
term = monomial.split("^")
if len(term)==int(2):
exp = int(term[1])
else:
exp = int(1)
if kcache is None:
sage_repr[exp] = k(singular_poly_list[coeff_start+i])
else:
elem = singular_poly_list[coeff_start+i]
if elem not in kcache:
kcache[elem] = k( elem )
sage_repr[ exp ]= kcache[elem]
return R(sage_repr)
else:
raise TypeError("Cannot coerce %s into %s"%(self,R))
def sage_matrix(self, R, sparse=True):
"""
Returns Sage matrix for self
INPUT:
- ``R`` - (default: None); an optional ring, over which
the resulting matrix is going to be defined.
By default, the output of :meth:`sage_global_ring` is used.
- ``sparse`` - (default: True); determines whether the
resulting matrix is sparse or not.
EXAMPLES::
sage: R = singular.ring(0, '(x,y,z)', 'dp')
sage: A = singular.matrix(2,2)
sage: A.sage_matrix(ZZ)
[0 0]
[0 0]
sage: A.sage_matrix(RDF)
[0.0 0.0]
[0.0 0.0]
"""
from sage.matrix.constructor import Matrix
nrows, ncols = int(self.nrows()),int(self.ncols())
if R is None:
R = self.sage_global_ring()
A = Matrix(R, nrows, ncols, sparse=sparse)
#this is slow
for x in range(nrows):
for y in range(ncols):
A[x,y]=self[x+1,y+1].sage_poly(R)
return A
A = Matrix(R, nrows, ncols, sparse=sparse)
#this is slow
for x in range(nrows):
for y in range(ncols):
A[x,y]=R(self[x+1,y+1])
return A
def _sage_(self, R=None):
r"""
Convert self to Sage.
EXAMPLES::
sage: R = singular.ring(0, '(x,y,z)', 'dp')
sage: A = singular.matrix(2,2)
sage: A.sage(ZZ) # indirect doctest
[0 0]
[0 0]
sage: A = random_matrix(ZZ,3,3); A
[ -8 2 0]
[ 0 1 -1]
[ 2 1 -95]
sage: As = singular(A); As
-8 2 0
0 1 -1
2 1 -95
sage: As.sage()
[ -8 2 0]
[ 0 1 -1]
[ 2 1 -95]
::
sage: singular.eval('ring R = integer, (x,y,z),lp')
'// ** redefining R (ring R = integer, (x,y,z),lp;)'
sage: I = singular.ideal(['x^2','y*z','z+x'])
sage: I.sage()
Ideal (x^2, y*z, x + z) of Multivariate Polynomial Ring in x, y, z over Integer Ring
::
sage: singular('ringlist(basering)').sage()
[['integer'], ['x', 'y', 'z'], [['lp', (1, 1, 1)], ['C', (0)]], Ideal (0) of Multivariate Polynomial Ring in x, y, z over Integer Ring]
::
sage: singular.eval('ring r10 = (9,a), (x,y,z),lp')
''
sage: singular.eval('setring R')
''
sage: singular('r10').sage()
Multivariate Polynomial Ring in x, y, z over Finite Field in a of size 3^2
Note that the current base ring has not been changed by asking for another ring::
sage: singular('basering')
polynomial ring, over a domain, global ordering
// coeff. ring is : integer
// number of vars : 3
// block 1 : ordering lp
// : names x y z
// block 2 : ordering C
::
sage: singular.eval('setring r10')
''
sage: Q = singular('std(ideal(x^2,x+y^2+z^3))', type='qring')
sage: Q.sage()
Quotient of Multivariate Polynomial Ring in x, y, z over Finite Field in a of size 3^2 by the ideal (y^4 - y^2*z^3 + z^6, x + y^2 + z^3)
sage: singular('x^2+y').sage()
x^2 + y
sage: singular('x^2+y').sage().parent()
Quotient of Multivariate Polynomial Ring in x, y, z over Finite Field in a of size 3^2 by the ideal (y^4 - y^2*z^3 + z^6, x + y^2 + z^3)
Test that :trac:`18848` is fixed::
sage: singular(5).sage()
5
sage: type(singular(int(5)).sage())
<type 'sage.rings.integer.Integer'>
"""
typ = self.type()
if typ=='poly':
return self.sage_poly(R)
elif typ=='int':
return sage.rings.integer.Integer(repr(self))
elif typ == 'module':
return self.sage_matrix(R,sparse=True)
elif typ == 'matrix':
return self.sage_matrix(R,sparse=False)
elif typ == 'list':
return [ f._sage_(R) for f in self ]
elif typ == 'intvec':
from sage.modules.free_module_element import vector
return vector([sage.rings.integer.Integer(str(e)) for e in self])
elif typ == 'intmat':
from sage.matrix.constructor import matrix
from sage.rings.integer_ring import ZZ
A = matrix(ZZ, int(self.nrows()), int(self.ncols()))
for i in xrange(A.nrows()):
for j in xrange(A.ncols()):
A[i,j] = sage.rings.integer.Integer(str(self[i+1,j+1]))
return A
elif typ == 'string':
return repr(self)
elif typ == 'ideal':
R = R or self.sage_global_ring()
return R.ideal([p.sage_poly(R) for p in self])
elif typ in ['ring', 'qring']:
br = singular('basering')
self.set_ring()
R = self.sage_global_ring()
br.set_ring()
return R
raise NotImplementedError("Coercion of this datatype not implemented yet")
def is_string(self):
"""
Tell whether this element is a string.
EXAMPLES::
sage: singular('"abc"').is_string()
True
sage: singular('1').is_string()
False
"""
return self.type() == 'string'
def set_ring(self):
"""
Sets the current ring in Singular to be self.
EXAMPLES::
sage: R = singular.ring(7, '(a,b)', 'ds')
sage: S = singular.ring('real', '(a,b)', 'lp')
sage: singular.current_ring()
polynomial ring, over a field, global ordering
// characteristic : 0 (real)
// number of vars : 2
// block 1 : ordering lp
// : names a b
// block 2 : ordering C
sage: R.set_ring()
sage: singular.current_ring()
polynomial ring, over a field, local/mixed ordering
// characteristic : 7
// number of vars : 2
// block 1 : ordering ds
// : names a b
// block 2 : ordering C
"""
self.parent().set_ring(self)
def sage_flattened_str_list(self):
"""
EXAMPLES::
sage: R=singular.ring(0,'(x,y)','dp')
sage: RL = R.ringlist()
sage: RL.sage_flattened_str_list()
['0', 'x', 'y', 'dp', '1,1', 'C', '0', '_[1]=0']
"""
s = str(self)
c = '\[[0-9]*\]:'
r = re.compile(c)
s = r.sub('',s).strip()
return s.split()
def sage_structured_str_list(self):
r"""
If self is a Singular list of lists of Singular elements, returns
corresponding Sage list of lists of strings.
EXAMPLES::
sage: R=singular.ring(0,'(x,y)','dp')
sage: RL=R.ringlist()
sage: RL
[1]:
0
[2]:
[1]:
x
[2]:
y
[3]:
[1]:
[1]:
dp
[2]:
1,1
[2]:
[1]:
C
[2]:
0
[4]:
_[1]=0
sage: RL.sage_structured_str_list()
['0', ['x', 'y'], [['dp', '1,\n1 '], ['C', '0 ']], '0']
"""
if not (self.type()=='list'):
return str(self)
return [X.sage_structured_str_list() for X in self]
def _tab_completion(self):
"""
Returns the possible tab-completions for self. In this case, we
just return all the tab completions for the Singular object.
EXAMPLES::
sage: R = singular.ring(0,'(x,y)','dp')
sage: R._tab_completion()
['exteriorPower',
...
'stdfglm']
"""
return self.parent()._tab_completion()
def type(self):
"""
Returns the internal type of this element.
EXAMPLES::
sage: R = PolynomialRing(GF(2^8,'a'),2,'x')
sage: R._singular_().type()
'ring'
sage: fs = singular('x0^2','poly')
sage: fs.type()
'poly'
"""
# singular reports // $varname $type $stuff
p = re.compile("// [\w]+ (\w+) [\w]*")
m = p.match(self.parent().eval("type(%s)"%self.name()))
return m.group(1)
def __iter__(self):
"""
EXAMPLES::
sage: R = singular.ring(0, '(x,y,z)', 'dp')
sage: A = singular.matrix(2,2)
sage: list(iter(A))
[[0], [0]]
sage: A[1,1] = 1; A[1,2] = 2
sage: A[2,1] = 3; A[2,2] = 4
sage: list(iter(A))
[[1,3], [2,4]]
"""
if self.type()=='matrix':
l = self.ncols()
else:
l = len(self)
for i in range(1, l+1):
yield self[i]
def _singular_(self):
"""
EXAMPLES::
sage: R = singular.ring(0, '(x,y,z)', 'dp')
sage: A = singular.matrix(2,2)
sage: A._singular_() is A
True
"""
return self
def attrib(self, name, value=None):
"""
Get and set attributes for self.
INPUT:
- ``name`` - string to choose the attribute
- ``value`` - boolean value or None for reading,
(default:None)
VALUES: isSB - the standard basis property is set by all commands
computing a standard basis like groebner, std, stdhilb etc.; used
by lift, dim, degree, mult, hilb, vdim, kbase isHomog - the weight
vector for homogeneous or quasihomogeneous ideals/modules isCI -
complete intersection property isCM - Cohen-Macaulay property rank
- set the rank of a module (see nrows) withSB - value of type
ideal, resp. module, is std withHilb - value of type intvec is
hilb(_,1) (see hilb) withRes - value of type list is a free
resolution withDim - value of type int is the dimension (see dim)
withMult - value of type int is the multiplicity (see mult)
EXAMPLE::
sage: P.<x,y,z> = PolynomialRing(QQ)
sage: I = Ideal([z^2, y*z, y^2, x*z, x*y, x^2])
sage: Ibar = I._singular_()
sage: Ibar.attrib('isSB')
0
sage: singular.eval('vdim(%s)'%Ibar.name()) # sage7 name is random
// ** sage7 is no standard basis
4
sage: Ibar.attrib('isSB',1)
sage: singular.eval('vdim(%s)'%Ibar.name())
'4'
"""
if value is None:
return int(self.parent().eval('attrib(%s,"%s")'%(self.name(),name)))
else:
self.parent().eval('attrib(%s,"%s",%d)'%(self.name(),name,value))
class SingularFunction(ExpectFunction):
def _sage_doc_(self):
"""
EXAMPLES::
sage: 'groebner' in singular.groebner._sage_doc_()
True
"""
if not nodes:
generate_docstring_dictionary()
prefix = \
"""
This function is an automatically generated pexpect wrapper around the Singular
function '%s'.
EXAMPLE::
sage: groebner = singular.groebner
sage: P.<x, y> = PolynomialRing(QQ)
sage: I = P.ideal(x^2-y, y+x)
sage: groebner(singular(I))
x+y,
y^2-y
"""%(self._name,)
prefix2 = \
"""
The Singular documentation for '%s' is given below.
"""%(self._name,)
try:
return prefix + prefix2 + nodes[node_names[self._name]]
except KeyError:
return prefix
class SingularFunctionElement(FunctionElement):
def _sage_doc_(self):
r"""
EXAMPLES::
sage: R = singular.ring(0, '(x,y,z)', 'dp')
sage: A = singular.matrix(2,2)
sage: 'matrix_expression' in A.nrows._sage_doc_()
True
"""
if not nodes:
generate_docstring_dictionary()
try:
return nodes[node_names[self._name]]
except KeyError:
return ""
def is_SingularElement(x):
r"""
Returns True is x is of type ``SingularElement``.
EXAMPLES::
sage: from sage.interfaces.singular import is_SingularElement
sage: is_SingularElement(singular(2))
True
sage: is_SingularElement(2)
False
"""
return isinstance(x, SingularElement)
# This is only for backwards compatibility, in order to be able
# to unpickle the invalid objects that are in the pickle jar.
def reduce_load():
"""
This is for backwards compatibility only.
To be precise, it only serves at unpickling the invalid
singular elements that are stored in the pickle jar.
EXAMPLES::
sage: from sage.interfaces.singular import reduce_load
sage: reduce_load()
doctest:...: DeprecationWarning: This function is only used to unpickle invalid objects
See http://trac.sagemath.org/18848 for details.
(invalid object -- defined in terms of closed session)
By :trac:`18848`, pickling actually often works::
sage: loads(dumps(singular.ring()))
polynomial ring, over a field, global ordering
// characteristic : 0
// number of vars : 1
// block 1 : ordering lp
// : names x
// block 2 : ordering C
"""
deprecation(18848, "This function is only used to unpickle invalid objects")
return SingularElement(None, None, None)
nodes = {}
node_names = {}
def generate_docstring_dictionary():
"""
Generate global dictionaries which hold the docstrings for
Singular functions.
EXAMPLE::
sage: from sage.interfaces.singular import generate_docstring_dictionary
sage: generate_docstring_dictionary()
"""
from sage.env import SAGE_LOCAL
global nodes
global node_names
nodes.clear()
node_names.clear()
singular_docdir = "/usr/share/doc/singular-doc/"
new_node = re.compile("File: singular\.hlp, Node: ([^,]*),.*")
new_lookup = re.compile("\* ([^:]*):*([^.]*)\..*")
L, in_node, curr_node = [], False, None
for line in open(singular_docdir + "singular.hlp"):
m = re.match(new_node,line)
if m:
# a new node starts
in_node = True
nodes[curr_node] = "".join(L)
L = []
curr_node, = m.groups()
elif in_node: # we are in a node
L.append(line)
else:
m = re.match(new_lookup, line)
if m:
a,b = m.groups()
node_names[a] = b.strip()
if line == "6 Index\n":
in_node = False
nodes[curr_node] = "".join(L) # last node
def get_docstring(name):
"""
Return the docstring for the function ``name``.
INPUT:
- ``name`` - a Singular function name
EXAMPLE::
sage: from sage.interfaces.singular import get_docstring
sage: 'groebner' in get_docstring('groebner')
True
sage: 'standard.lib' in get_docstring('groebner')
True
"""
if not nodes:
generate_docstring_dictionary()
try:
return nodes[node_names[name]]
except KeyError:
return ""
##################################
singular = Singular()
def reduce_load_Singular():
"""
EXAMPLES::
sage: from sage.interfaces.singular import reduce_load_Singular
sage: reduce_load_Singular()
Singular
"""
return singular
def singular_console():
"""
Spawn a new Singular command-line session.
EXAMPLES::
sage: singular_console() #not tested
SINGULAR / Development
A Computer Algebra System for Polynomial Computations / version 3-0-4
0<
by: G.-M. Greuel, G. Pfister, H. Schoenemann \ Nov 2007
FB Mathematik der Universitaet, D-67653 Kaiserslautern \
"""
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 %%singular magics instead.')
os.system('Singular')
def singular_version():
"""
Returns the version of Singular being used.
EXAMPLES:
"""
return singular.eval('system("--version");')
class SingularGBLogPrettyPrinter:
"""
A device which prints Singular Groebner basis computation logs
more verbatim.
"""
rng_chng = re.compile("\[\d+:\d+\]")# [m:n] internal ring change to
# poly representation with
# exponent bound m and n words in
# exponent vector
new_elem = re.compile("s") # found a new element of the standard basis
red_zero = re.compile("-") # reduced a pair/S-polynomial to 0
red_post = re.compile("\.") # postponed a reduction of a pair/S-polynomial
cri_hilb = re.compile("h") # used Hilbert series criterion
hig_corn = re.compile("H\(\d+\)") # found a 'highest corner' of degree d, no need to consider higher degrees
num_crit = re.compile("\(\d+\)") # n critical pairs are still to be reduced
red_num = re.compile("\(S:\d+\)") # doing complete reduction of n elements
deg_lead = re.compile("\d+") # the degree of the leading terms is currently d
# SlimGB
red_para = re.compile("M\[(\d+),(\d+)\]") # parallel reduction of n elements with m non-zero output elements
red_betr = re.compile("b") # exchange of a reductor by a 'better' one
non_mini = re.compile("e") # a new reductor with non-minimal leading term
crt_lne1 = re.compile("product criterion:(\d+) chain criterion:(\d+)")
crt_lne2 = re.compile("NF:(\d+) product criterion:(\d+), ext_product criterion:(\d+)")
pat_sync = re.compile("1\+(\d+);")
global_pattern = re.compile("(\[\d+:\d+\]|s|-|\.|h|H\(\d+\)|\(\d+\)|\(S:\d+\)|\d+|M\[\d+,[b,e]*\d+\]|b|e).*")
def __init__(self, verbosity=1):
"""
Construct a new Singular Groebner Basis log pretty printer.
INPUT:
- ``verbosity`` - how much information should be printed
(between 0 and 3)
EXAMPLE::
sage: from sage.interfaces.singular import SingularGBLogPrettyPrinter
sage: s0 = SingularGBLogPrettyPrinter(verbosity=0)
sage: s1 = SingularGBLogPrettyPrinter(verbosity=1)
sage: s0.write("[1:2]12")
sage: s1.write("[1:2]12")
Leading term degree: 12.
"""
self.verbosity = verbosity
self.curr_deg = 0 # current degree
self.max_deg = 0 # maximal degree in total
self.nf = 0 # number of normal forms computed (SlimGB only)
self.prod = 0 # number of S-polynomials discarded using product criterion
self.ext_prod = 0 # number of S-polynomials discarded using extended product criterion
self.chain = 0 # number of S-polynomials discarded using chain criterion
self.storage = "" # stores incomplete strings
self.sync = None # should we expect a sync integer?
def write(self, s):
"""
EXAMPLE::
sage: from sage.interfaces.singular import SingularGBLogPrettyPrinter
sage: s3 = SingularGBLogPrettyPrinter(verbosity=3)
sage: s3.write("(S:1337)")
Performing complete reduction of 1337 elements.
sage: s3.write("M[389,12]")
Parallel reduction of 389 elements with 12 non-zero output elements.
"""
verbosity = self.verbosity
if self.storage:
s = self.storage + s
self.storage = ""
for line in s.splitlines():
# deal with the Sage <-> Singular syncing code
match = re.match(SingularGBLogPrettyPrinter.pat_sync,line)
if match:
self.sync = int(match.groups()[0])
continue
if self.sync and line == "%d"%(self.sync+1):
self.sync = None
continue
if line.endswith(";"):
continue
if line.startswith(">"):
continue
if line.startswith("std") or line.startswith("slimgb"):
continue
# collect stats returned about avoided reductions to zero
match = re.match(SingularGBLogPrettyPrinter.crt_lne1,line)
if match:
self.prod,self.chain = map(int,re.match(SingularGBLogPrettyPrinter.crt_lne1,line).groups())
self.storage = ""
continue
match = re.match(SingularGBLogPrettyPrinter.crt_lne2,line)
if match:
self.nf,self.prod,self.ext_prod = map(int,re.match(SingularGBLogPrettyPrinter.crt_lne2,line).groups())
self.storage = ""
continue
while line:
match = re.match(SingularGBLogPrettyPrinter.global_pattern, line)
if not match:
self.storage = line
line = None
continue
token, = match.groups()
line = line[len(token):]
if re.match(SingularGBLogPrettyPrinter.rng_chng,token):
continue
elif re.match(SingularGBLogPrettyPrinter.new_elem,token) and verbosity >= 3:
print("New element found.")
elif re.match(SingularGBLogPrettyPrinter.red_zero,token) and verbosity >= 2:
print("Reduction to zero.")
elif re.match(SingularGBLogPrettyPrinter.red_post, token) and verbosity >= 2:
print("Reduction postponed.")
elif re.match(SingularGBLogPrettyPrinter.cri_hilb, token) and verbosity >= 2:
print("Hilber series criterion applied.")
elif re.match(SingularGBLogPrettyPrinter.hig_corn, token) and verbosity >= 1:
print("Maximal degree found: %s" % token)
elif re.match(SingularGBLogPrettyPrinter.num_crit, token) and verbosity >= 1:
print("Leading term degree: %2d. Critical pairs: %s."%(self.curr_deg,token[1:-1]))
elif re.match(SingularGBLogPrettyPrinter.red_num, token) and verbosity >= 3:
print("Performing complete reduction of %s elements."%token[3:-1])
elif re.match(SingularGBLogPrettyPrinter.deg_lead, token):
if verbosity >= 1:
print("Leading term degree: %2d." % int(token))
self.curr_deg = int(token)
if self.max_deg < self.curr_deg:
self.max_deg = self.curr_deg
elif re.match(SingularGBLogPrettyPrinter.red_para, token) and verbosity >= 3:
m,n = re.match(SingularGBLogPrettyPrinter.red_para,token).groups()
print("Parallel reduction of %s elements with %s non-zero output elements." % (m, n))
elif re.match(SingularGBLogPrettyPrinter.red_betr, token) and verbosity >= 3:
print("Replaced reductor by 'better' one.")
elif re.match(SingularGBLogPrettyPrinter.non_mini, token) and verbosity >= 2:
print("New reductor with non-minimal leading term found.")
def flush(self):
"""
EXAMPLE::
sage: from sage.interfaces.singular import SingularGBLogPrettyPrinter
sage: s3 = SingularGBLogPrettyPrinter(verbosity=3)
sage: s3.flush()
"""
sys.stdout.flush()
class SingularGBDefaultContext:
"""
Within this context all Singular Groebner basis calculations are
reduced automatically.
AUTHORS:
- Martin Albrecht
- Simon King
"""
def __init__(self, singular=None):
"""
Within this context all Singular Groebner basis calculations
are reduced automatically.
INPUT:
- ``singular`` - Singular instance (default: default instance)
EXAMPLE::
sage: from sage.interfaces.singular import SingularGBDefaultContext
sage: P.<a,b,c> = PolynomialRing(QQ,3, order='lex')
sage: I = sage.rings.ideal.Katsura(P,3)
sage: singular.option('noredTail')
sage: singular.option('noredThrough')
sage: Is = I._singular_()
sage: gb = Is.groebner()
sage: gb
84*c^4-40*c^3+c^2+c,
7*b+210*c^3-79*c^2+3*c,
a+2*b+2*c-1
::
sage: with SingularGBDefaultContext(): rgb = Is.groebner()
sage: rgb
84*c^4-40*c^3+c^2+c,
7*b+210*c^3-79*c^2+3*c,
7*a-420*c^3+158*c^2+8*c-7
Note that both bases are Groebner bases because they have
pairwise prime leading monomials but that the monic version of
the last element in ``rgb`` is smaller than the last element
of ``gb`` with respect to the lexicographical term ordering. ::
sage: (7*a-420*c^3+158*c^2+8*c-7)/7 < (a+2*b+2*c-1)
True
.. note::
This context is used automatically internally whenever a
Groebner basis is computed so the user does not need to use
it manually.
"""
if singular is None:
from sage.interfaces.all import singular as singular_default
singular = singular_default
self.singular = singular
def __enter__(self):
"""
EXAMPLE::
sage: from sage.interfaces.singular import SingularGBDefaultContext
sage: P.<a,b,c> = PolynomialRing(QQ,3, order='lex')
sage: I = sage.rings.ideal.Katsura(P,3)
sage: singular.option('noredTail')
sage: singular.option('noredThrough')
sage: Is = I._singular_()
sage: with SingularGBDefaultContext(): rgb = Is.groebner()
sage: rgb
84*c^4-40*c^3+c^2+c,
7*b+210*c^3-79*c^2+3*c,
7*a-420*c^3+158*c^2+8*c-7
"""
from sage.interfaces.singular import SingularError
try:
self.bck_degBound = int(self.singular.eval('degBound'))
except SingularError:
self.bck_degBound = int(0)
try:
self.bck_multBound = int(self.singular.eval('multBound'))
except SingularError:
self.bck_multBound = int(0)
self.o = self.singular.option("get")
self.singular.option('set',self.singular._saved_options)
self.singular.option("redSB")
self.singular.option("redTail")
try:
self.singular.eval('degBound=0')
except SingularError:
pass
try:
self.singular.eval('multBound=0')
except SingularError:
pass
def __exit__(self, typ, value, tb):
"""
EXAMPLE::
sage: from sage.interfaces.singular import SingularGBDefaultContext
sage: P.<a,b,c> = PolynomialRing(QQ,3, order='lex')
sage: I = sage.rings.ideal.Katsura(P,3)
sage: singular.option('noredTail')
sage: singular.option('noredThrough')
sage: Is = I._singular_()
sage: with SingularGBDefaultContext(): rgb = Is.groebner()
sage: rgb
84*c^4-40*c^3+c^2+c,
7*b+210*c^3-79*c^2+3*c,
7*a-420*c^3+158*c^2+8*c-7
"""
from sage.interfaces.singular import SingularError
self.singular.option("set",self.o)
try:
self.singular.eval('degBound=%d'%self.bck_degBound)
except SingularError:
pass
try:
self.singular.eval('multBound=%d'%self.bck_multBound)
except SingularError:
pass
def singular_gb_standard_options(func):
r"""
Decorator to force a reduced Singular groebner basis.
TESTS::
sage: P.<a,b,c,d,e> = PolynomialRing(GF(127))
sage: J = sage.rings.ideal.Cyclic(P).homogenize()
sage: from sage.misc.sageinspect import sage_getsource
sage: "basis" in sage_getsource(J.interreduced_basis) #indirect doctest
True
The following tests against a bug that was fixed in :trac:`11298`::
sage: from sage.misc.sageinspect import sage_getsourcelines, sage_getargspec
sage: P.<x,y> = QQ[]
sage: I = P*[x,y]
sage: sage_getargspec(I.interreduced_basis)
ArgSpec(args=['self'], varargs=None, keywords=None, defaults=None)
sage: sage_getsourcelines(I.interreduced_basis)
([' @singular_gb_standard_options\n',
' @libsingular_gb_standard_options\n',
' def interreduced_basis(self):\n', '
...
' return self.basis.reduced()\n'], ...)
.. note::
This decorator is used automatically internally so the user
does not need to use it manually.
"""
from sage.misc.decorators import sage_wraps
@sage_wraps(func)
def wrapper(*args, **kwds):
with SingularGBDefaultContext():
return func(*args, **kwds)
return wrapper
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