| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/singular/tst/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 26.7.2025 mit Größe 22 kB |
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# Start
gap> START_TEST( "Test of the singular package" ); gap> SetInfoLevel( InfoSingular, 1 ); gap> StartSingular(); # # Examples from README file # gap> R:=PolynomialRing( Rationals, ["x", "y", "z"] : new ); Rationals[x,y,z] gap> gen:=GeneratorsOfLeftOperatorRingWithOne(R); [ x, y, z ] gap> x:=gen[1]; x gap> y:=gen[2]; y gap> z:=gen[3]; z gap> pol1:=-3*x*z^3+x^3+x*y*z; -3*x*z^3+x^3+x*y*z gap> pol2:=-3*x^2*z^3+x^4+x^2*y*z-3*x*z^3+x^3+x*y*z; -3*x^2*z^3+x^4+x^2*y*z-3*x*z^3+x^3+x*y*z gap> pol3:=x*y+x*z+x+y+z; x*y+x*z+x+y+z gap> I:=Ideal( R, [ pol1, pol2, pol3] ); <two-sided ideal in Rationals[x,y,z], (3 generators)> gap> SingularSetBaseRing( R ); gap> J:=SingularInterface( "jacob", [ pol1 ], "ideal" ); <two-sided ideal in Rationals[x,y,z], (3 generators)> gap> GeneratorsOfTwoSidedIdeal( J ); [ -3*z^3+3*x^2+y*z, x*z, -9*x*z^2+x*y ] gap> SingularInterface( "dim", [ I ], "int" ); 2 gap> std:=SingularInterface( "std", [ I ], "ideal" ); <two-sided ideal in Rationals[x,y,z], (3 generators)> gap> GeneratorsOfTwoSidedIdeal( std ); [ x*y+x*z+x+y+z, 3*y*z^3+3*z^4-y^2*z-y*z^2+x^2-x-y-z, 3*x*z^3-x^3+x*z^2+x*z+y*z+z^2 ] gap> GroebnerBasis( I ); [ x*y+x*z+x+y+z, 3*y*z^3+3*z^4-y^2*z-y*z^2+x^2-x-y-z, 3*x*z^3-x^3+x*z^2+x*z+y*z+z^2 ] gap> HasTrivialGroebnerBasis( I ); false gap> SingularLibrary( "general.lib"); gap> GcdUsingSingular( pol1, pol2, pol3 ); 1 gap> FactorsUsingSingularNC( pol1 ); [ -1, x, 3*z^3-x^2-y*z ] gap> FactorsUsingSingular( pol2 ); [ -1, x, x+1, 3*z^3-x^2-y*z ] # # Examples from manual # gap> SetInfoLevel( InfoSingular, 2 ); gap> G:= SymmetricGroup( 3 ); Sym( [ 1 .. 3 ] ) gap> R:= PolynomialRing( GF(2), 3 ); GF(2)[x_1,x_2,x_3] gap> gens:=GeneratorsOfInvariantRing( R, G ); #I running SingularInterface( "invariant_ring", [ "matrix", "matrix" ], "list" )... #I done SingularInterface. [ x_1+x_2+x_3, x_1*x_2+x_1*x_3+x_2*x_3, x_1*x_2*x_3 ] gap> I:= Ideal( R, gens ); <two-sided ideal in GF(2)[x_1,x_2,x_3], (3 generators)> gap> GB:=GroebnerBasis( I ); #I running GroebnerBasis... #I done GroebnerBasis. [ x_1+x_2+x_3, x_2^2+x_2*x_3+x_3^2, x_3^3 ] gap> R:= PolynomialRing( Rationals, ["x","y","z"] : old ); Rationals[x,y,z] gap> i:= IndeterminatesOfPolynomialRing(R); [ x, y, z ] gap> x:= i[1]; x gap> y:= i[2]; y gap> z:= i[3]; z gap> r:= [ x*y*z -x^2*z, x^2*y*z-x*y^2*z-x*y*z^2, x*y-x*z-y*z]; [ -x^2*z+x*y*z, x^2*y*z-x*y^2*z-x*y*z^2, x*y-x*z-y*z ] gap> I:= Ideal( R, r ); <two-sided ideal in Rationals[x,y,z], (3 generators)> gap> GroebnerBasis( I ); #I running GroebnerBasis... #I done GroebnerBasis. [ x*y-x*z-y*z, x^2*z-x*z^2-y*z^2, x*z^3+y*z^3, -x*z^3+y^2*z^2-y*z^3 ] gap> R:= PolynomialRing( Rationals, 3 ); Rationals[x,y,z] gap> i:= IndeterminatesOfPolynomialRing( R ); [ x, y, z ] gap> pols:= [i[1]+i[2]+i[3], i[1]*i[2]+i[1]*i[3]+i[2]*i[3], i[1]*i[2]*i[3]]; [ x+y+z, x*y+x*z+y*z, x*y*z ] gap> o:= MonomialLexOrdering(); MonomialLexOrdering() gap> GBASIS:= GAPGBASIS; rec( GroebnerBasis := function( elms, order ) ... end, name := "naive GAP version of Buchberger's algorithm" ) gap> gg:=GroebnerBasis( pols, o ); # This is the internal GAP method. [ x+y+z, x*y+x*z+y*z, x*y*z, -y^2-y*z-z^2, z^3 ] gap> GBASIS:= SINGULARGBASIS; rec( GroebnerBasis := function( pols, O ) ... end, name := "singular interface for GroebnerBasis" ) gap> gs:=GroebnerBasis( pols, o ); #I running GroebnerBasis... #I done GroebnerBasis. [ z^3, y^2+y*z+z^2, x+y+z ] gap> (gg[1]=gs[1] and -gg[4]=gs[2] and gg[5]=gs[3]) or (gg[5]=gs[1] and -gg[4]=gs[2] and gg[ true gap> I:=Ideal(R, gs); <two-sided ideal in Rationals[x,y,z], (3 generators)> gap> SingularInterface("reduce", [ gg[2], I ], "poly" ); #I running SingularInterface( "reduce", [ "poly", "ideal" ], "poly" )... #I done SingularInterface. 0 gap> SingularInterface("reduce", [ gg[3], I ], "poly" ); #I running SingularInterface( "reduce", [ "poly", "ideal" ], "poly" )... #I done SingularInterface. 0 gap> gs[2] in I; #I running GroebnerBasis... #I done GroebnerBasis. true gap> R:= PolynomialRing( GaussianRationals, ["x","y","z"] : old ); GaussianRationals[x,y,z] gap> i:= IndeterminatesOfPolynomialRing(R); [ x, y, z ] gap> x:= i[1]; x gap> y:= i[2]; y gap> z:= i[3]; z gap> f:= (x*y-z)*(x*y*z+y^2*z+x^2*z); x^3*y*z+x^2*y^2*z+x*y^3*z-x^2*z^2-x*y*z^2-y^2*z^2 gap> g:= (x*y-z)*(x*y*z^2+x*y^2*z+x^2*y*z); x^3*y^2*z+x^2*y^3*z+x^2*y^2*z^2-x^2*y*z^2-x*y^2*z^2-x*y*z^3 gap> I:= Ideal( R, [f,g] ); <two-sided ideal in GaussianRationals[x,y,z], (2 generators)> gap> HasTrivialGroebnerBasis( I ); #I running HasTrivialGroebnerBasis... #I done HasTrivialGroebnerBasis. false gap> R:= PolynomialRing( Rationals, ["x","y","z"] : old ); Rationals[x,y,z] gap> i:= IndeterminatesOfPolynomialRing(R); [ x, y, z ] gap> x:= i[1]; x gap> y:= i[2]; y gap> z:= i[3]; z gap> f:= (x*y-z)*(x*y*z+y^2*z+x^2*z); x^3*y*z+x^2*y^2*z+x*y^3*z-x^2*z^2-x*y*z^2-y^2*z^2 gap> g:= (x*y-z)*(x*y*z^2+x*y^2*z+x^2*y*z); x^3*y^2*z+x^2*y^3*z+x^2*y^2*z^2-x^2*y*z^2-x*y^2*z^2-x*y*z^3 gap> SingularSetBaseRing( R ); gap> gcd := GcdUsingSingular( f, g );; gap> gcd in [-x*y*z+z^2, x*y*z-z^2]; true gap> f:= (x*y-z)*(x*y*z+y^2*z+x^2*z); x^3*y*z+x^2*y^2*z+x*y^3*z-x^2*z^2-x*y*z^2-y^2*z^2 gap> SingularSetBaseRing( R ); gap> facs := FactorsUsingSingularNC( f );; #I running SingularInterface( "factorize", [ "poly" ], "list" )... #I done SingularInterface. gap> SortedList(facs); [ -1, z, -x*y+z, x^2+x*y+y^2 ] gap> m:=[[1,1,1],[0,1,1],[0,0,1]]*One(GF(3)); [ [ Z(3)^0, Z(3)^0, Z(3)^0 ], [ 0*Z(3), Z(3)^0, Z(3)^0 ], [ 0*Z(3), 0*Z(3), Z(3)^0 ] ] gap> G:= Group( [m] ); Group( [ [ [ Z(3)^0, Z(3)^0, Z(3)^0 ], [ 0*Z(3), Z(3)^0, Z(3)^0 ], [ 0*Z(3), 0*Z(3), Z(3)^0 ] ] ]) gap> R:= PolynomialRing( GF(3), 3 ); GF(3)[x_1,x_2,x_3] gap> GeneratorsOfInvariantRing( R, G ); #I running SingularInterface( "invariant_ring", [ "matrix" ], "list" )... #I done SingularInterface. [ x_3, x_1*x_3+x_2^2+x_2*x_3, x_1^3+x_1^2*x_3-x_1*x_2^2-x_1*x_2*x_3 ] gap> R:= PolynomialRing( Rationals, ["x","y","z"] : old ); Rationals[x,y,z] gap> i:= IndeterminatesOfPolynomialRing(R); [ x, y, z ] gap> x:= i[1]; x gap> y:= i[2]; y gap> z:= i[3]; z gap> f:= (x*y-z)*(x*y*z+y^2*z+x^2*z); x^3*y*z+x^2*y^2*z+x*y^3*z-x^2*z^2-x*y*z^2-y^2*z^2 gap> g:= (x*y-z)*(x*y*z^2+x*y^2*z+x^2*y*z); x^3*y^2*z+x^2*y^3*z+x^2*y^2*z^2-x^2*y*z^2-x*y^2*z^2-x*y*z^3 gap> I:= Ideal( R, [f,g] ); <two-sided ideal in Rationals[x,y,z], (2 generators)> gap> SingularLibrary("primdec.lib"); gap> pd:=SingularInterface("primdecGTZ", [ I ], "def" );; #I running SingularInterface( "primdecGTZ", [ "ideal" ], "def" )... #I done SingularInterface. #I Singular output of type "list" gap> Length(pd); 4 gap> gens := List(pd,x->List(x,GeneratorsOfTwoSidedIdeal));; gap> SortedList( gens ); [ [ [ z ], [ z ] ], [ [ y^2+y*z+z^2, x+y+z ], [ y^2+y*z+z^2, x+y+z ] ], [ [ x*y-z ], [ x*y-z ] ], [ [ y^3, x*y, x^2+y^2 ], [ y, x ] ] ] # # ParseSingProcToGapFunction # gap> SingCommandInStreamOutStream( "", "proc a1 () { return ( 35 ) };" ); "" gap> SingCommandInStreamOutStream( "", "proc a2 (e2) { return ( a1 ) };" ); "" gap> SingCommandInStreamOutStream( "", "proc a3 (e3) { return ( a2 ) };" ); "" gap> f := SingularInterface( "a3", [ 1 ], "proc" ); #I running SingularInterface( "a3", [ "int" ], "proc" )... #I done SingularInterface. function( e2 ) ... end gap> g := f( 10 ); #I running SingularInterface( "GAP_proc", [ "int" ], "def" )... #I done SingularInterface. #I Singular output of type "proc" function( ) ... end gap> g( ); #I running SingularInterface( "GAP_proc", "...", "def" )... #I done SingularInterface. #I Singular output of type "int" 35 gap> SingCommandInStreamOutStream( "", > "proc asd ( t ) { return (t+1 ) ;return();};" ); "" gap> SingCommandInStreamOutStream( "", > "proc asd2 (){return (asd ) ;return(); };" ); "" gap> f := SingularInterface( "asd2", [ ], "proc" ); #I running SingularInterface( "asd2", "...", "proc" )... #I done SingularInterface. function( t ) ... end gap> f( 19 ); #I running SingularInterface( "GAP_proc", [ "int" ], "def" )... #I done SingularInterface. #I Singular output of type "int" 20 # # Check the conversion of numbers and polynomials for the various # CoefficientsRing # gap> SingularCommand("proc id_func (a){return (a);}", ""); # id_func = identity "" gap> R:=PolynomialRing( GF(32003), ["x"] : old );; gap> SingularSetBaseRing( R ); gap> SingularInterface("id_func", [Z(32003)], "def"); #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" Z(32003) gap> One(SingularBaseRing); Z(32003)^0 gap> SingularInterface("id_func", [last], "def"); #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" Z(32003)^0 # gap> x:=Indeterminate(Rationals);; gap> F1:=AlgebraicExtension(Rationals, x^5+4*x+1); <algebraic extension over the Rationals of degree 5> gap> e1:=RootOfDefiningPolynomial(F1); a gap> x:=Indeterminate(GF(5));; gap> F2:=AlgebraicExtension(GF(5), x^5+4*x+1);; gap> e2:=RootOfDefiningPolynomial(F2); a # gap> field_element := [ > [ Rationals, 23 ], > [ GF(2), Z(2) ], > [ GF(7), Z(7)^2 ], > [ GF(32), Z(32)^3 ], > [ GF(25), Z(25)^4 ], > [ CF(3), -E(3) ], > [ CF(25), Random(CF(25)) ], > [ CF(25), E(5) ], > [ F1, e1^2 + e1 ], > [ F2, e2^3+One(F2) ] > ];; # gap> for i in field_element do > > R := PolynomialRing( i[1], 2 ); > SingularSetBaseRing( R ); > > # test of numbers > u1:=i[2]; > u2:=SingularInterface( "id_func", [u1], "def" ); > if u1<>u2 then Error( "wrong conversion of number!\n"); fi; > u1:=Zero(i[1]); > u2:=SingularInterface( "id_func", [u1], "def" ); > if u1<>u2 then Error( "wrong conversion of number!\n"); fi; > u1:=One(i[1]); > u2:=SingularInterface( "id_func", [u1], "def" ); > if u1<>u2 then Error( "wrong conversion of number!\n"); fi; > > # test of polynomials > gen := GeneratorsOfLeftOperatorRingWithOne(R); > p1 := (i[2]*gen[1]+i[2]*gen[2])^4; > p2 := SingularInterface( "id_func", [p1], "def" ); > if p1<>p2 then Error( "wrong conversion of polynomial!\n"); fi; > p1:=Zero(R); > p2:=SingularInterface( "id_func", [p1], "def" ); > if p1<>p2 then Error( "wrong conversion of zero polynomial!\n"); fi; > p1:=One(R); > p2:=SingularInterface( "id_func", [p1], "def" ); > if p1<>p2 then Error( "wrong conversion of zero polynomial!\n"); fi; > > od; #I running SingularInterface( "id_func", [ "int" ], "def" )... #I done SingularInterface. #I Singular output of type "int" #I running SingularInterface( "id_func", [ "int" ], "def" )... #I done SingularInterface. #I Singular output of type "int" #I running SingularInterface( "id_func", [ "int" ], "def" )... #I done SingularInterface. #I Singular output of type "int" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "int" ], "def" )... #I done SingularInterface. #I Singular output of type "int" #I running SingularInterface( "id_func", [ "int" ], "def" )... #I done SingularInterface. #I Singular output of type "int" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "int" ], "def" )... #I done SingularInterface. #I Singular output of type "int" #I running SingularInterface( "id_func", [ "int" ], "def" )... #I done SingularInterface. #I Singular output of type "int" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "int" ], "def" )... #I done SingularInterface. #I Singular output of type "int" #I running SingularInterface( "id_func", [ "int" ], "def" )... #I done SingularInterface. #I Singular output of type "int" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "number" ], "def" )... #I done SingularInterface. #I Singular output of type "number" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" #I running SingularInterface( "id_func", [ "poly" ], "def" )... #I done SingularInterface. #I Singular output of type "poly" # # test the string conversion gap> s1:=[32..126];; gap> s2:=List("$'@", INT_CHAR);; gap> s1:=Difference(s1,s2);; gap> s3:=List(s1,CHAR_INT);; gap> ConvertToStringRep(s3); gap> s4:=SingularInterface("id_func", [s3], "def"); #I running SingularInterface( "id_func", [ "string" ], "def" )... #I done SingularInterface. #I Singular output of type "string" " !\"#%&()*+,-./0123456789:;<=>?ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklm\ nopqrstuvwxyz{|}~" gap> s3=s4; true # # Check the conversion of various types of object # gap> x:=X(GF(5),"x" : new );; gap> y:=X(GF(5),"y",[x] : new );; gap> ring:=PolynomialRing(GF(5),[x,y]);; gap> SingularSetBaseRing(ring); # gap> ideal:=Ideal(ring,[x*y, x+y]); <two-sided ideal in GF(5)[x,y], (2 generators)> gap> int:=123456; 123456 gap> intmat:=[[12,34],[56,78]]; [ [ 12, 34 ], [ 56, 78 ] ] gap> intvec:=[98765,4321]; [ 98765, 4321 ] gap> bigint:=18446744073709551616; 18446744073709551616 gap> bigintmat:=[[18446744073709551616,34],[56,432109876543210]]; [ [ 18446744073709551616, 34 ], [ 56, 432109876543210 ] ] gap> map:=AlgebraGeneralMappingByImages(ring,ring,[x,y],[x+y,x-y]); [ x, y ] -> [ x+y, x-y ] gap> matrix:=[[x+y, x*y],[x+y+x*y,x^2+y^2]]; [ [ x+y, x*y ], [ x*y+x+y, x^2+y^2 ] ] gap> module:=LeftModuleByGenerators( ring, [[x+y+x*y,x-y], [x+x^2+x^3,y+x^2+y^3]]); <free left module over PolynomialRing( GF(5), ["x", "y"] ), with 2 generators> gap> number:=Z(5)^3; Z(5)^3 gap> poly:=x^3+y^3+Z(5)^3*x^2+Z(5)^3*x*y+y^2+Z(5)^3*y; x^3+y^3+Z(5)^3*x^2+Z(5)^3*x*y+y^2+Z(5)^3*y gap> proc:=function() end; function( ) ... end gap> string:="ciao"; "ciao" gap> vector:=[x^3+y^3,+(5)^3*x^2+Z(5)^3,x*y+y^2+Z(5)^3*y]; [ x^3+y^3, Z(5)^3, x*y+y^2+Z(5)^3*y ] # gap> list1 := [ ideal, int, intmat, intvec, map, matrix, module, number, > poly, proc, ring, string, vector, bigint, bigintmat ]; [ <two-sided ideal in GF(5)[x,y], (2 generators)>, 123456, [ [ 12, 34 ], [ 56, 78 ] ], [ 98765, 4321 ], [ x, y ] -> [ x+y, x-y ], [ [ x+y, x*y ], [ x*y+x+y, x^2+y^2 ] ], <free left module over PolynomialRing( GF(5), ["x", "y"] ), with 2 generators>, Z(5)^3, x^3+y^3+Z(5)^3*x^2+Z(5)^3*x*y+y^2+Z(5)^3*y, function( ) ... end, GF(5)[x,y], "ciao", [ x^3+y^3, Z(5)^3, x*y+y^2+Z(5)^3*y ], 18446744073709551616, [ [ 18446744073709551616, 34 ], [ 56, 432109876543210 ] ] ] gap> List( list1, SingularType); [ "ideal", "int", "intmat", "intvec", "map", "matrix", "module", "number", "poly", "proc", "ring", "string", "vector", "bigint", "bigintmat" ] # gap> list2 := [ ideal, int, intmat, intvec, matrix, module, number, > poly, string, vector, bigint, bigintmat ]; [ <two-sided ideal in GF(5)[x,y], (2 generators)>, 123456, [ [ 12, 34 ], [ 56, 78 ] ], [ 98765, 4321 ], [ [ x+y, x*y ], [ x*y+x+y, x^2+y^2 ] ], <free left module over PolynomialRing( GF(5), ["x", "y"] ), with 2 generators>, Z(5)^3, x^3+y^3+Z(5)^3*x^2+Z(5)^3*x*y+y^2+Z(5)^3*y, "ciao", [ x^3+y^3, Z(5)^3, x*y+y^2+Z(5)^3*y ], 18446744073709551616, [ [ 18446744073709551616, 34 ], [ 56, 432109876543210 ] ] ] gap> list3 := SingularInterface( "id_func", [list2], "def" ); #I running SingularInterface( "id_func", [ "list" ], "def" )... #I done SingularInterface. #I Singular output of type "list" #I running SingularInterface( "matrix", "...", "matrix" )... #I done SingularInterface. #I running SingularInterface( "matrix", "...", "matrix" )... #I done SingularInterface. [ <two-sided ideal in GF(5)[x,y], (2 generators)>, 123456, [ [ 12, 34 ], [ 56, 78 ] ], [ 98765, 4321 ], [ [ x+y, x*y ], [ x*y+x+y, x^2+y^2 ] ], <free left module over PolynomialRing( GF(5), ["x", "y"] ), with 2 generators>, Z(5)^3, x^3+y^3+Z(5)^3*x^2+Z(5)^3*x*y+y^2+Z(5)^3*y, "ciao", [ x^3+y^3, Z(5)^3, x*y+y^2+Z(5)^3*y ], 18446744073709551616, [ [ 18446744073709551616, 34 ], [ 56, 432109876543210 ] ] ] # gap> for i in [2,3,4,5,7,8,9,10] do > if list2[i] <> list3[i] then > Error( "wrong conversion!\n"); > fi; > od; # # test of GapInterface # gap> cc:=ConvertGapObjToSingObj(matrix);; gap> SingularCommand(Concatenation( "matrix mm = ", cc),"print(mm)"); "x_1+x_2, x_1*x_2, \nx_1*x_2+x_1+x_2,x_1^2+x_2^2" gap> SingularCommand(Concatenation( "matrix mm = ", cc), "print(mm, \"%l\")"); "matrix(ideal(x_1+x_2,x_1*x_2,x_1*x_2+x_1+x_2,x_1^2+x_2^2),2,2)" # gap> GapInterface(TransposedMat, ["mm"], "mm2"); #I Singular output of type "matrix" gap> SingularCommand("","transpose(mm2)==mm"); "1" # # this should be at the end of the test file: # gap> [ SingularNr.Process, SingularNr.Input, SingularNr.Output ]; [ 0, 1156, 1156 ] gap> SingularBaseRing; GF(5)[x,y] gap> CoefficientsRing( SingularBaseRing ); GF(5) gap> SingWriteAndReadUntilDone("1;GAP_Apostrophe();2;GAP_Apostrophe();"); "1\n'\n2\n'\n> @\n> " gap> SingularInterface( "string", "GAP_Done", "string" ); #I running SingularInterface( "string", "...", "string" )... #I done SingularInterface. "\n return ( \"@\" ) \n\n;return();\n\n" gap> CloseSingular(); gap> SetInfoLevel( InfoSingular, 1 ); # gap> STOP_TEST( "test", 10000 ); [ zur Elbe Produktseite wechseln0.44Quellennavigators Analyse erneut starten ] |
2026-03-28