singular: a GAP interface to Singular

https://gap-packages.github.io/singular/

This is the README file for the package singular; a GAP interface to the computer algebra system Singular https://www.singular.uni-kl.de/.

The package has no maintainer at the moment. To make a version of the Singular package working under GAP 4.5, in 2011 a bug in the interface was fixed by Paul Smith and a new package archive for the GAP 4.5 release was prepared in 2012 by Alexander Konovalov. Currently we do not plan any further development of this package. The rest of this file belongs to the README of the package from its previous release on 2006/07/23.

Installing singular:

unpack singular.tar.gz in the pkg subdirectory of the GAP root directory.
If the Singular executable is in your search path, then it is ok: GAP will find it. If not, edit the file pkg/singular/gap/singular.g: at the beginning of this file, the full path to the Singular executable on your system must be added. For instance:
```
 sing_exec:="/usr/local/bin/Singular";
```
Alteratively, one can give this path inside a GAP session, with the same command.
It should work. From within GAP things are started with
```
 gap> LoadPackage("singular");
 true
```
The documentation is in the doc subdirectory: it is more up-to-date than this README file.

Preliminary announcement of August 2003 (and preliminary documentation):

Dear Gap developers, this is the announcement that the experimental version of the package “singular” has been released.

This package, written by Willem de Graaf and myself, provides an interface to the system Singular (“SINGULAR is a Computer Algebra system for polynomial computations with emphasis on the special needs of commutative algebra, algebraic geometry, and singularity theory. SINGULAR’s main computational objects are ideals and modules over a large variety of baserings. The baserings are polynomial rings or localizations thereof over a field (e.g., finite fields, the rationals, floats, algebraic extensions, transcendental extensions) or quotient rings with respect to an ideal. SINGULAR features one of the fastest and most general implementations of various algorithms for computing Groebner resp. standard bases. The implementation includes Buchberger’s algorithm (if the ordering is a well ordering) and Mora’s algorithm (if the ordering is a tangent cone ordering) as special cases. Furthermore, it provides polynomial factorizations, resultant, characteristic set and gcd computations, syzygy and free-resolution computations, and many more related functionalities.” See https://www.singular.uni-kl.de/ . Singular is not included in the package, but can be downloaded for free from that site.)

This package can hang the Gap session (you will have to type -C twice, and you will lose the content of the session, if it was not saved with SaveWorkspace). This should not happen during normal use (please report if it happens to you), but only with code designed to hang Gap, such as SingularLibrary("all"); SingularInterface("execute", ["pause()"], "def" );

Hints, bug reports, patches, requests of other functionalities, and so on are welcome, please submit them at https://github.com/gap-packages/singular/issues Please add the output of SingularReportInformation(); to your report.

# load

LoadPackage("singular");


# specify the Singular executable (not needed if Singular is in the path)

sing_exec:= "/home/wdg/Singular/2-0-3/ix86-Linux/Singular";


# let's define some Gap objects

R:=PolynomialRing( Rationals, ["x", "y", "z"] : old );;
gen:=GeneratorsOfLeftOperatorRingWithOne(R);;
x:=gen[1];;y:=gen[2];;z:=gen[3];;
pol1:=-3*x*z^3+x^3+x*y*z;;
pol2:=-3*x^2*z^3+x^4+x^2*y*z-3*x*z^3+x^3+x*y*z;;
pol3:=x*y+x*z+x+y+z;;
I:=Ideal( R, [ pol1, pol2, pol3] );;


# set the basering in singular (this is done automatically by the other
# functions when the arguments are rings or ideals).

SingularSetBaseRing( R );


# Let be "Singfunc" the name of a function of Singular, and GapList a list
# of Gap objects. Then the function
#
# SingularInterface( "Singfunc", GapList, type_output );
#
# will convert the objects in the list GapList info Singular objects, will
# apply Singfunc to them from within Singular, and will convert to output
# back into a Gap objects.
# The argument type_output must be one of "def",
# "ideal", "int", "intmat", "intvec", "link", "list", "map", "matrix",
# "module", "number", "poly", "proc", "qring", "resolution", "ring",
# "string", "vector", and tells to the interface the type in Singular of
# the output of Singfunc. In doubt you can use "def".
# See in the documentation of Singular the chapter "4. Data types".

SingularInterface( "jacob", [ pol1 ], "ideal" );
SingularInterface( "dim", [ I ], "int" );
SingularInterface( "std", [ I ], "ideal" );

# when the output is an ideal, use GeneratorsOfTwoSidedIdeal to get the
# generators.


# this calculates the Groebner Basis

GroebnerBasis( I );


# sometimes we need only to know whether the Groebner Basis is trivial
# (i.e. equal to the unit) or not.

HasTrivialGroebnerBasis( I );


# This loads (in Singular) the library general.lib

SingularLibrary( "general.lib");


# the gcd of polynomials (also multivariate ones)

GcdUsingSingular( pol1, pol2, pol3 );


# factorizations of polynomials (also multivariate ones)

FactorsUsingSingularNC( pol1 );


# this checks also the output of Singular

FactorsUsingSingular( pol2 );


# As i/o streams do consume system resources, and only a limited number
# can be open at any time, it is wise to close Singular when it will be
# not needed anymore.

CloseSingular();

# Singular will start again when one of the functions above is called, or
# by StartSingular();

# Not that the time used by Singular is not reported by the function 
# Runtimes(); until the Singular session is terminated. The cpu time resp. 
# the wall clock time used by a singular session can by get with:

Int( SingularCommand( "", "timer" ) );
Int( SingularCommand( "", "rtimer" ) );

Greetings, Marco Costantini

Addendum

** Reserved chars or strings:

Don’t use the following chars or strings with the interface:

@ marks the end of the Singular output

’ delimits the useful Singular output

$ the interface discards all the ‘$’ sent to Singular

GAP_… all the names of the Singular variables defined by the interface begin with “GAP_”: don’t use these names for your variables

** Type conversions:

type    Gap -> Singular                 Singular -> Gap
        * := sets basering              U := only on Unix or with Gap >=4.4.2

def     (no sense)                      U (ask Singular for the type)
ideal   *ParseGapIdealToSingIdeal       done
int     ParseToSingInt                  Int
intmat  ParseGapIntmatToSingIntmat      U done
intvec  ParseGapIntvecToSingIntvec      done
link                                    U (done)
list    ParseGapListToSingList          U done
map	(planned)
matrix  done                            U done
module	*ParseGapModuleToSingModule	(U) done
number  ParseGapNumberToSingNumber      ParseSingNumberToGapNumber
poly    ParseGapPolyToSingPoly          ParseSingPolyToGapPoly
proc                                    U ParseSingProcToGapFunction
qring
resolution
ring    *ParseGapRingToSingRing         (planned)
string  done                            x->x;
vector  ParseGapVectorToSingVector      (U) done