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gap> START_TEST("polynomials.tst");
gap> f := GF(5);;
gap> z := Zero(f);;
gap> o := One(f);;
gap> two := o+o;;
gap> three := o+o+o;;
gap> x := X(f);;
#
gap> mat_cvec := CVEC_MakeExample(f,[x-o],[[10]]);
<cmat 10x10 over GF(5,1)>
gap> mat_gap := Unpack(mat_cvec);;
gap> ConvertToMatrixRep(mat_gap);
5
gap> cpol_gap := CharacteristicPolynomial(mat_gap);;
gap> cpol_cvec := CharacteristicPolynomialOfMatrix(mat_cvec);;
gap> cpol_gap = cpol_cvec.poly;
true
gap> mpol_gap := MinimalPolynomial(BaseDomain(mat_cvec),mat_gap);;
gap> mpol_cvec := CVEC_MinimalPolynomial(mat_cvec);;
gap> mpol_gap = mpol_cvec;
true
gap> cpol_mpol_cvec := CharAndMinimalPolynomialOfMatrix(mat_cvec);;
gap> cpol_gap = cpol_mpol_cvec.charpoly;
true
gap> mpol_gap = cpol_mpol_cvec.minpoly;
true
#
gap> mat_cvec := CVEC_MakeExample(f,[x-o],[[1,5,10]]);
<cmat 16x16 over GF(5,1)>
gap> mat_gap := Unpack(mat_cvec);;
gap> ConvertToMatrixRep(mat_gap);
5
gap> cpol_gap := CharacteristicPolynomial(mat_gap);;
gap> cpol_cvec := CharacteristicPolynomialOfMatrix(mat_cvec);;
gap> cpol_gap = cpol_cvec.poly;
true
gap> mpol_gap := MinimalPolynomial(BaseDomain(mat_cvec),mat_gap);;
gap> mpol_cvec := CVEC_MinimalPolynomial(mat_cvec);;
gap> mpol_gap = mpol_cvec;
true
gap> cpol_mpol_cvec := CharAndMinimalPolynomialOfMatrix(mat_cvec);;
gap> cpol_gap = cpol_mpol_cvec.charpoly;
true
gap> mpol_gap = cpol_mpol_cvec.minpoly;
true
#
gap> mat_cvec := CVEC_MakeExample(f,[x-o,x-two],[[1,2,3,4,5],[5,4,3,2,1]]);
<cmat 30x30 over GF(5,1)>
gap> mat_gap := Unpack(mat_cvec);;
gap> ConvertToMatrixRep(mat_gap);
5
gap> cpol_gap := CharacteristicPolynomial(mat_gap);;
gap> cpol_cvec := CharacteristicPolynomialOfMatrix(mat_cvec);;
gap> cpol_gap = cpol_cvec.poly;
true
gap> mpol_gap := MinimalPolynomial(BaseDomain(mat_cvec),mat_gap);;
gap> mpol_cvec := CVEC_MinimalPolynomial(mat_cvec);;
gap> mpol_gap = mpol_cvec;
true
gap> cpol_mpol_cvec := CharAndMinimalPolynomialOfMatrix(mat_cvec);;
gap> cpol_gap = cpol_mpol_cvec.charpoly;
true
gap> mpol_gap = cpol_mpol_cvec.minpoly;
true
#
gap> mat_cvec := CVEC_MakeExample(f,[x^2+two*x+three],[[1,10,20]]);
<cmat 62x62 over GF(5,1)>
gap> mat_gap := Unpack(mat_cvec);;
gap> ConvertToMatrixRep(mat_gap);
5
gap> cpol_gap := CharacteristicPolynomial(mat_gap);;
gap> cpol_cvec := CharacteristicPolynomialOfMatrix(mat_cvec);;
gap> cpol_gap = cpol_cvec.poly;
true
gap> mpol_gap := MinimalPolynomial(BaseDomain(mat_cvec),mat_gap);;
gap> mpol_cvec := CVEC_MinimalPolynomial(mat_cvec);;
gap> mpol_gap = mpol_cvec;
true
gap> cpol_mpol_cvec := CharAndMinimalPolynomialOfMatrix(mat_cvec);;
gap> cpol_gap = cpol_mpol_cvec.charpoly;
true
gap> mpol_gap = cpol_mpol_cvec.minpoly;
true
#
gap> mat_cvec := CVEC_MakeExample(f,[CyclotomicPolynomial(f,97),x-o],[[1,3],[1,100]]);
<cmat 485x485 over GF(5,1)>
gap> mat_gap := Unpack(mat_cvec);;
gap> ConvertToMatrixRep(mat_gap);
5
gap> cpol_gap := CharacteristicPolynomial(mat_gap);;
gap> cpol_cvec := CharacteristicPolynomialOfMatrix(mat_cvec);;
gap> cpol_gap = cpol_cvec.poly;
true
gap> mpol_gap := MinimalPolynomial(BaseDomain(mat_cvec),mat_gap);;
gap> mpol_cvec := CVEC_MinimalPolynomial(mat_cvec);;
gap> mpol_gap = mpol_cvec;
true
gap> cpol_mpol_cvec := CharAndMinimalPolynomialOfMatrix(mat_cvec);;
gap> cpol_gap = cpol_mpol_cvec.charpoly;
true
gap> mpol_gap = cpol_mpol_cvec.minpoly;
true
# this lower triangular matrix causes infinite loop in earlier versions of cvec
gap> mat_gap := ImmutableMatrix(GF(19),Z(19)^0 *
> [[16,0,0,0,0,0,0,0,0,0],
> [5,2,0,0,0,0,0,0,0,0],
> [9,6,7,0,0,0,0,0,0,0],
> [15,9,1,2,0,0,0,0,0,0],
> [7,14,8,2,9,0,0,0,0,0],
> [12,3,17,5,1,12,0,0,0,0],
> [7,11,0,4,6,9,10,0,0,0],
> [8,3,15,16,17,18,18,12,0,0],
> [6,3,7,12,1,12,11,14,10,0],
> [18,14,7,17,16,15,13,13,3,8]]);;
gap> mat_cvec := CMat(mat_gap);
<cmat 10x10 over GF(19,1)>
gap> cpol_gap := CharacteristicPolynomial(mat_gap);;
gap> cpol_cvec := CharacteristicPolynomialOfMatrix(mat_cvec);;
gap> cpol_gap = cpol_cvec.poly;
true
gap> mpol_gap := MinimalPolynomial(BaseDomain(mat_cvec),mat_gap);;
gap> mpol_cvec := CVEC_MinimalPolynomial(mat_cvec);;
gap> mpol_gap = mpol_cvec;
true
gap> cpol_mpol_cvec := CharAndMinimalPolynomialOfMatrix(mat_cvec);;
gap> cpol_gap = cpol_mpol_cvec.charpoly;
true
gap> mpol_gap = cpol_mpol_cvec.minpoly;
true
#
gap> STOP_TEST("polynomials.tst", 0);
[ Dauer der Verarbeitung: 0.17 Sekunden
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