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 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.

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:

1. singular_console() - A function that dumps you into an interactive command-line Singular session.
2. 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 computed using Singular.
3. singular.eval(expr) - Evaluation of arbitrary Singular expressions, with the result returned as a string.

Tutorial

EXAMPLES: First we illustrate multivariate polynomial factorization:

sage: R1 = singular.ring(0, '(x,y)', 'dp')
sage: R1
//   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 and each exponent back to Sage objects as well.

sage: R.<x, y> = PolynomialRing(QQ,2)
sage: g = eval(f.sage_polystring()); 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: eval(F[1][2].sage_polystring())
x^6 - 2*x^3*y^2 - x^2*y^3 + y^4

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

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 :

sage: _=singular.LIB('sing.lib')     # assign to _ to suppress printing
sage: f.milnor()
4

The Jacobian applied twice yields the Hessian matrix of , 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.det()
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 . 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')
        //   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)')             
...
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'>

class sage.interfaces.singular.Singular(maxread=1000, script_subdirectory=None, logfile=None, server=None, server_tmpdir=None)

Bases: sage.interfaces.expect.Expect

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

LIB(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)

clear(var)

Clear the variable named var.

EXAMPLES:

sage: singular.set('int', 'x', '2')
sage: singular.get('x')
'2'
sage: singular.clear('x')
sage: singular.get('x')
'`x`'

console()

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            

cputime(t=None)

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

current_ring()

Returns the current ring of the running Singular session.

EXAMPLES:

sage: r = PolynomialRing(GF(127),3,'xyz', order='invlex')
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

current_ring_name()

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

eval(x, allow_semicolon=True, strip=True, **kwds)

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 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()

get(var)

Get string representation of variable named var.

EXAMPLES:

sage: singular.set('int', 'x', '2')
sage: singular.get('x')
'2'

ideal(*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

lib(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)

list(x)

Creates a list in Singular from a Sage list x.

EXAMPLES:

sage: singular.list([1,2])
[1]:
   1
[2]:
   2

load(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)

matrix(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)

option(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

ring(char=0, vars='(x)', order='lp', check=True)

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 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 transcendental 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

set(type, name, value)

Set the variable with given name to the given value.

EXAMPLES:

sage: singular.set('int', 'x', '2')
sage: singular.get('x')
'2'

set_ring(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()
//   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()
//   characteristic : 7
//   number of vars : 2
//        block   1 : ordering ds
//                  : names    a b 
//        block   2 : ordering C

setring(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()
//   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()
//   characteristic : 7
//   number of vars : 2
//        block   1 : ordering ds
//                  : names    a b 
//        block   2 : ordering C

string(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

trait_names()

Return a list of all Singular commands.

EXAMPLES:

sage: singular.trait_names()
['exteriorPower',
 ...
 'stdfglm']

version()

EXAMPLES:

class sage.interfaces.singular.SingularElement(parent, type, value, is_name=False)

Bases: sage.interfaces.expect.ExpectElement

attrib(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'

sage_flattened_str_list()

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']

sage_matrix(R, sparse=True)

Returns Sage matrix for self

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]

sage_poly(R, kcache=None)

Returns a Sage polynomial in the ring r matching the provided poly which is a singular polynomial.

INPUT:

• R - PolynomialRing: 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

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

AUTHOR:

• Martin Albrecht (2006-05-18)

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

sage_polystring()

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'

sage_structured_str_list()

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']

set_ring()

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()
//   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()
//   characteristic : 7
//   number of vars : 2
//        block   1 : ordering ds
//                  : names    a b 
//        block   2 : ordering C

trait_names()

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.trait_names()
['exteriorPower',
 ...
 'stdfglm']

type()

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'

class sage.interfaces.singular.SingularFunction(parent, name)

Bases: sage.interfaces.expect.ExpectFunction

class sage.interfaces.singular.SingularFunctionElement(obj, name)

Bases: sage.interfaces.expect.FunctionElement

sage.interfaces.singular.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()

sage.interfaces.singular.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

sage.interfaces.singular.is_SingularElement(x)

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

sage.interfaces.singular.reduce_load()

Note that this returns an invalid Singular object!

EXAMPLES:

sage: from sage.interfaces.singular import reduce_load
sage: reduce_load()
(invalid object -- defined in terms of closed session)

sage.interfaces.singular.reduce_load_Singular()

EXAMPLES:

sage: from sage.interfaces.singular import reduce_load_Singular
sage: reduce_load_Singular()
Singular

sage.interfaces.singular.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        

sage.interfaces.singular.singular_version()

Returns the version of Singular being used.

EXAMPLES: