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)
Module-level Functions
x) |
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Class: Singular
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*x1*x2
AUTHORS: David Joyner and William Stein
self, [maxread=None], [script_subdirectory=None], [logfile=user], [server=1000]) |
Functions: clear,
console,
current_ring,
current_ring_name,
eval,
get,
ideal,
LIB,
lib,
list,
load,
matrix,
ring,
set,
set_ring,
setring,
string,
trait_names,
version
self, var) |
Clear the variable named var.
(Not actually done right now since it causes too many problems.)
self) |
Returns the current ring of the runnging Singular session.
sage: r = MPolynomialRing(GF(127),3,'xyz', order="revlex") sage: r._singular_() // characteristic : 127 // number of vars : 3 // block 1 : ordering rp // : names x y z // block 2 : ordering C sage: singular.current_ring() // characteristic : 127 // number of vars : 3 // block 1 : ordering rp // : names x y z // block 2 : ordering C
self) |
Returns the Singular name of the currently active ring in Singular.
OUTPUT: currently active ring's name
sage: r = MPolynomialRing(GF(127),3,'xyz') sage: r._singular_().name() == singular.current_ring_name() True
self, x, [allow_semicolon=False]) |
Send the code x to the Singular interpreter and return the output as a string.
sage: singular.eval('2 > 1') '1' sage: singular.eval('2 + 2') '4'
self, var) |
Get string representation of variable named var.
self) |
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
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*x1*x2
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).
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).
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).
self, nrows, ncols, [entries=None]) |
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
Author: Martin Albrecht (malb@informatik.uni-bremen.de), 2006-01-14
self, [char=lp], [vars=(x)], [order=0]) |
Create a Singular ring and makes it the current ring.
INPUT: char -- characteristic of the base ring (see examples below) vars -- a tuple or string that defines the variable names order -- string -- the monomial order (default: 'lp') 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).
We first declare
with degree reverse lexicographic ordering.
sage: R = singular.ring(0, '(x,y,z)', 'dp') sage: R // 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
:
sage: R3 = singular.ring(7, '(x(1..10))', 'ds')
This is a polynomial ring over the transcendtal extension
of
:
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
self, type, name, value) |
Set the variable with given name to the given value.
self) |
Return a list of all Singular commands.
Special Functions: __call__,
__reduce__,
_create,
_equality_symbol,
_false_symbol,
_quit_string,
_read_in_file_command,
_start,
_true_symbol
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. Morever if foo is a function then X.foo(y,z,...) calls foo(X, y, z, ...) and returns the corresponding object.
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
Class: SingularElement
self, parent, type, value, [is_name=False]) |
Functions: is_zero,
sage_flattened_str_list,
sage_poly,
sage_polystring,
sage_structured_str_list,
set_ring,
trait_names,
type
self, R, [kcache=None]) |
Returns a SAGE polynomial in the ring r matching the provided poly which is a singular polynomial.
INPUT: R -- MPolynomialRing: you *must* take care it matches the current singular ring as, e.g., returned by singular.current_ring() kcache -- (default: None); an optional dictionary for faster finite field lookups, this is mainly useful for finite extension fields OUTPUT: MPolynomial
sage: R = MPolynomialRing(GF(2**8),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),1,'x') sage: f=R('a^20*x^3+x^2+a^10') sage: f._singular_().sage_poly(R)==f True
sage: R.<XxZaa5,y> = PolynomialRing(Q,2) sage: f = XxZaa5 * y^3 -(1/9)* XxZaa5 + 1 sage: singular(f) XxZaa5*y^3-1/9*XxZaa5+1 sage: R(singular(f)) 1 - 1/9*XxZaa5 + XxZaa5*y^3
Author: Martin Albrecht (2006-05-18)
self) |
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()
.
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'
self) |
If self is a Singular list of lists of Singular elements, returns corresponding SAGE list of lists of strings.
self) |
Returns the internal type of this element.
sage: R = MPolynomialRing(GF(2**8),2,'x') sage: R._singular_().type() 'ring' sage: fs = singular('x0^2','poly') sage: fs.type() 'poly'
Special Functions: __len__,
__reduce__,
__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.
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
Class: SingularFunction
Special Functions: _sage_doc_
Class: SingularFunctionElement
Special Functions: _sage_doc_
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