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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346#############################################################################
##
#A testall.tst IntPic package Manuel Delgado
##
## (based on the cooresponding file of the 'example' package,
## by Alexander Konovalov)
##
## To create a test file, place GAP prompts, input and output exactly as
## they must appear in the GAP session. Do not remove lines containing
## START_TEST and STOP_TEST statements.
##
## The first line starts the test. START_TEST reinitializes the caches and
## the global random number generator, in order to be independent of the
## reading order of several test files. Furthermore, the assertion level
## is set to 2 by START_TEST and set back to the previous value in the
## subsequent STOP_TEST call.
##
## The argument of STOP_TEST may be an arbitrary identifier string.
##
gap> START_TEST("IntPic package: testall.tst");
# Note that you may use comments in the test file
# and also separate parts of the test by empty lines
# First load the package without banner (the banner must be suppressed to
# avoid reporting discrepancies in the case when the package is already
# loaded)
gap> LoadPackage("intpic",false);
true
# Check that the data are consistent
gap> rg := [801..999];;
gap> flen := 15;;
gap> primes := Filtered(rg,IsPrime);
[ 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929,
937, 941, 947, 953, 967, 971, 977, 983, 991, 997 ]
gap> twins := Filtered(primes, p -> IsPrime(p+2)); #A list consisting of the first
[ 809, 821, 827, 857, 881 ]
gap> #elements of pairs of twin primes
gap> rgnp := Difference(rg,primes);
[ 801, 802, 803, 804, 805, 806, 807, 808, 810, 812, 813, 814, 815, 816, 817, 818, 819, 820, 822,
824, 825, 826, 828, 830, 831, 832, 833, 834, 835, 836, 837, 838, 840, 841, 842, 843, 844, 845,
846, 847, 848, 849, 850, 851, 852, 854, 855, 856, 858, 860, 861, 862, 864, 865, 866, 867, 868,
869, 870, 871, 872, 873, 874, 875, 876, 878, 879, 880, 882, 884, 885, 886, 888, 889, 890, 891,
892, 893, 894, 895, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, 906, 908, 909, 910, 912,
913, 914, 915, 916, 917, 918, 920, 921, 922, 923, 924, 925, 926, 927, 928, 930, 931, 932, 933,
934, 935, 936, 938, 939, 940, 942, 943, 944, 945, 946, 948, 949, 950, 951, 952, 954, 955, 956,
957, 958, 959, 960, 961, 962, 963, 964, 965, 966, 968, 969, 970, 972, 973, 974, 975, 976, 978,
979, 980, 981, 982, 984, 985, 986, 987, 988, 989, 990, 992, 993, 994, 995, 996, 998, 999 ]
gap> arr := [primes,
> [1],
> Union(twins,twins+2),
> # now the non primes...
> Filtered(rgnp,u->(u mod 2)=0),
> Filtered(rgnp,u->(u mod 3)=0),
> Filtered(rgnp,u->(u mod 5)=0),
> [],[], # to avoid some colors
> Filtered(rgnp,u->(u mod 7)=0),
> Filtered(rgnp,u->(u mod 11)=0),
> Filtered(rgnp,u->(u mod 13)=0),
> Filtered(rgnp,u->(u mod 17)=0),
> Filtered(rgnp,u->(u mod 19)=0),
> Filtered(rgnp,u->(u mod 23)=0),
> Filtered(rgnp,u->(u mod 29)=0),
> Filtered(rgnp,u->(u mod 31)=0),
> Filtered(rgnp,u->(u mod 37)=0),
> Filtered(rgnp,u->(u mod 41)=0),
> Filtered(rgnp,u->(u mod 43)=0),
> Filtered(rgnp,u->(u mod 47)=0),
> Filtered(rgnp,u->(u mod 53)=0)];
[ [ 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929,
937, 941, 947, 953, 967, 971, 977, 983, 991, 997 ], [ 1 ],
[ 809, 811, 821, 823, 827, 829, 857, 859, 881, 883 ],
[ 802, 804, 806, 808, 810, 812, 814, 816, 818, 820, 822, 824, 826, 828, 830, 832, 834, 836, 838,
840, 842, 844, 846, 848, 850, 852, 854, 856, 858, 860, 862, 864, 866, 868, 870, 872, 874,
876, 878, 880, 882, 884, 886, 888, 890, 892, 894, 896, 898, 900, 902, 904, 906, 908, 910,
912, 914, 916, 918, 920, 922, 924, 926, 928, 930, 932, 934, 936, 938, 940, 942, 944, 946,
948, 950, 952, 954, 956, 958, 960, 962, 964, 966, 968, 970, 972, 974, 976, 978, 980, 982,
984, 986, 988, 990, 992, 994, 996, 998 ],
[ 801, 804, 807, 810, 813, 816, 819, 822, 825, 828, 831, 834, 837, 840, 843, 846, 849, 852, 855,
858, 861, 864, 867, 870, 873, 876, 879, 882, 885, 888, 891, 894, 897, 900, 903, 906, 909,
912, 915, 918, 921, 924, 927, 930, 933, 936, 939, 942, 945, 948, 951, 954, 957, 960, 963,
966, 969, 972, 975, 978, 981, 984, 987, 990, 993, 996, 999 ],
[ 805, 810, 815, 820, 825, 830, 835, 840, 845, 850, 855, 860, 865, 870, 875, 880, 885, 890, 895,
900, 905, 910, 915, 920, 925, 930, 935, 940, 945, 950, 955, 960, 965, 970, 975, 980, 985,
990, 995 ], [ ], [ ], [ 805, 812, 819, 826, 833, 840, 847, 854, 861, 868, 875, 882, 889,
896, 903, 910, 917, 924, 931, 938, 945, 952, 959, 966, 973, 980, 987, 994 ],
[ 803, 814, 825, 836, 847, 858, 869, 880, 891, 902, 913, 924, 935, 946, 957, 968, 979, 990 ],
[ 806, 819, 832, 845, 858, 871, 884, 897, 910, 923, 936, 949, 962, 975, 988 ],
[ 816, 833, 850, 867, 884, 901, 918, 935, 952, 969, 986 ],
[ 817, 836, 855, 874, 893, 912, 931, 950, 969, 988 ],
[ 805, 828, 851, 874, 897, 920, 943, 966, 989 ], [ 812, 841, 870, 899, 928, 957, 986 ],
[ 806, 837, 868, 899, 930, 961, 992 ], [ 814, 851, 888, 925, 962, 999 ],
[ 820, 861, 902, 943, 984 ], [ 817, 860, 903, 946, 989 ], [ 846, 893, 940, 987 ],
[ 848, 901, 954 ] ]
gap>
gap> tkz := IP_TikzArrayOfIntegers(rg,flen,rec(cell_width := "27",highlights:=arr));;
#gap> IP_Splash(tkz);;
gap> rg := [81..89];;
gap> len := 5;;
gap> arr := [Filtered(rg,IsPrime),Filtered(rg,u->(u mod 2)=0),
> Filtered(rg,u->(u mod 3)=0)];;
gap> tkz := IP_TikzArrayOfIntegers(rg,len,rec(highlights:=arr));;
#gap> IP_Splash(tkz);;
#############################################################################
# Some more elaborated tests
gap> a := 8;; b := 19;;
gap> ns := NumericalSemigroup(a,b);;
gap> c := ConductorOfNumericalSemigroup(ns);;
gap> origin := 2*c-1;
251
gap> ground := [origin..origin+b-1];;
gap>
gap> height:=2;;
gap> depth:=8;;
gap> xaxis := [origin];;
gap> for n in [1..b-1] do
> Add(xaxis, origin+n*a);
> od;
gap> yaxis := [];;
gap> for n in [-depth..height] do
> Add(yaxis, origin+n*b);
> od;
gap>
gap> table := IP_TableWithModularOrder(origin,a,b,depth,height,false,false);
[ [ 99, 107, 115, 123, 131, 139, 147, 155, 163, 171, 179, 187, 195, 203, 211,
219, 227, 235, 243 ],
[ 118, 126, 134, 142, 150, 158, 166, 174, 182, 190, 198, 206, 214, 222,
230, 238, 246, 254, 262 ],
[ 137, 145, 153, 161, 169, 177, 185, 193, 201, 209, 217, 225, 233, 241,
249, 257, 265, 273, 281 ],
[ 156, 164, 172, 180, 188, 196, 204, 212, 220, 228, 236, 244, 252, 260,
268, 276, 284, 292, 300 ],
[ 175, 183, 191, 199, 207, 215, 223, 231, 239, 247, 255, 263, 271, 279,
287, 295, 303, 311, 319 ],
[ 194, 202, 210, 218, 226, 234, 242, 250, 258, 266, 274, 282, 290, 298,
306, 314, 322, 330, 338 ],
[ 213, 221, 229, 237, 245, 253, 261, 269, 277, 285, 293, 301, 309, 317,
325, 333, 341, 349, 357 ],
[ 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336,
344, 352, 360, 368, 376 ],
[ 251, 259, 267, 275, 283, 291, 299, 307, 315, 323, 331, 339, 347, 355,
363, 371, 379, 387, 395 ],
[ 270, 278, 286, 294, 302, 310, 318, 326, 334, 342, 350, 358, 366, 374,
382, 390, 398, 406, 414 ],
[ 289, 297, 305, 313, 321, 329, 337, 345, 353, 361, 369, 377, 385, 393,
401, 409, 417, 425, 433 ] ]
gap> arr := [xaxis,yaxis,ground];
[ [ 251, 259, 267, 275, 283, 291, 299, 307, 315, 323, 331, 339, 347, 355,
363, 371, 379, 387, 395 ],
[ 99, 118, 137, 156, 175, 194, 213, 232, 251, 270, 289 ], [ 251 .. 269 ] ]
gap> tkz:=IP_TikzArrayOfIntegers(table,rec(highlights:=arr));;
#gap> IP_Splash(tkz);;
gap> tkz:=IP_TikzArrayOfIntegers(table,rec(highlights:=arr,shape_only:=" ",
> cell_width := "6",colsep:="1",rowsep:="1",inner_sep:="2",
> line_color:="black!20"));;
#gap> IP_Splash(tkz);;
gap> Print(tkz);
%tikz
\begin{tikzpicture}[every node/.style={draw,scale=1pt,
minimum width=6pt,inner sep=2pt,
line width=0pt,draw=black!20}]
\matrix[row sep=1pt,column sep=1pt]
{\node[fill=green]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };\\
\node[fill=green]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };\\
\node[left color=red,right color=green,middle color=blue]{ };&
\node[left color=red,right color=blue]{ };&
\node[left color=red,right color=blue]{ };&
\node[fill=red]{ };&
\node[fill=red]{ };&
\node[fill=red]{ };&
\node[fill=red]{ };&
\node[fill=red]{ };&
\node[fill=red]{ };&
\node[fill=red]{ };&
\node[fill=red]{ };&
\node[fill=red]{ };&
\node[fill=red]{ };&
\node[fill=red]{ };&
\node[fill=red]{ };&
\node[fill=red]{ };&
\node[fill=red]{ };&
\node[fill=red]{ };&
\node[fill=red]{ };\\
\node[fill=green]{ };&
\node[]{ };&
\node[]{ };&
\node[fill=blue]{ };&
\node[fill=blue]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };\\
\node[fill=green]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[fill=blue]{ };&
\node[fill=blue]{ };&
\node[fill=blue]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };\\
\node[fill=green]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[fill=blue]{ };&
\node[fill=blue]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };\\
\node[fill=green]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[fill=blue]{ };&
\node[fill=blue]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };\\
\node[fill=green]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[fill=blue]{ };&
\node[fill=blue]{ };&
\node[fill=blue]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };\\
\node[fill=green]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[fill=blue]{ };&
\node[fill=blue]{ };&
\node[]{ };&
\node[]{ };\\
\node[fill=green]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[fill=blue]{ };&
\node[fill=blue]{ };\\
\node[fill=green]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };&
\node[]{ };\\
};
\end{tikzpicture}
#############################################################################
#############################################################################
# Examples from the manual
# (These examples use at least a funtion from each file)
## functions.xml ##
gap> rg := [81..89];
[ 81 .. 89 ]
gap> len := 10;
10
gap> arr := [Filtered(rg,IsPrime),Filtered(rg,u->(u mod 2)=0),
> Filtered(rg,u->(u mod 3)=0)];
[ [ 83, 89 ], [ 82, 84, 86, 88 ], [ 81, 84, 87 ] ]
gap> tkz := IP_TikzArrayOfIntegers(rg,len,rec(highlights:=arr));
"%tikz\n\\begin{tikzpicture}[every node/.style={draw,scale=1pt,\nminimum width\
=20pt,inner sep=3pt,\nline width=0pt,draw=black}]\n\\matrix[row sep=2pt,column\
sep=2pt]\n{\\node[fill=blue]{81};&\n\\node[fill=green]{82};&\n\\node[fill=red\
]{83};&\n\\node[left color=green,right color=blue]{84};&\n\\node[]{85};&\n\\no\
de[fill=green]{86};&\n\\node[fill=blue]{87};&\n\\node[fill=green]{88};&\n\\nod\
e[fill=red]{89};\\\\\n};\n\\end{tikzpicture}\n"
gap> Print(tkz);
%tikz
\begin{tikzpicture}[every node/.style={draw,scale=1pt,
minimum width=20pt,inner sep=3pt,
line width=0pt,draw=black}]
\matrix[row sep=2pt,column sep=2pt]
{\node[fill=blue]{81};&
\node[fill=green]{82};&
\node[fill=red]{83};&
\node[left color=green,right color=blue]{84};&
\node[]{85};&
\node[fill=green]{86};&
\node[fill=blue]{87};&
\node[fill=green]{88};&
\node[fill=red]{89};\\
};
\end{tikzpicture}
gap> d := DivisorsInt(30);
[ 1, 2, 3, 5, 6, 10, 15, 30 ]
gap> IP_SimpleTikzArrayOfIntegers(d);;
gap> d30 := DivisorsInt(30);
[ 1, 2, 3, 5, 6, 10, 15, 30 ]
gap> d40 := DivisorsInt(40);
[ 1, 2, 4, 5, 8, 10, 20, 40 ]
gap> tkz := IP_SimpleTikzArrayOfIntegers([d30,d40]);;
gap> a := 8;; b := 19;;
gap> ns := NumericalSemigroup(a,b);;
gap> c := ConductorOfNumericalSemigroup(ns);;
gap> origin := 2*c-1;
251
gap> ground := [origin..origin+b-1];;
gap>
gap> height:=2;;
gap> depth:=8;;
gap> xaxis := [origin];;
gap> for n in [1..b-1] do
> Add(xaxis, origin+n*a);
> od;
gap> yaxis := [];;
gap> for n in [-depth..height] do
> Add(yaxis, origin+n*b);
> od;
gap>
gap> table := IP_TableWithModularOrder(origin,a,b,depth,height,false,false);;
gap> arr := [xaxis,yaxis,ground];
[ [ 251, 259, 267, 275, 283, 291, 299, 307, 315, 323, 331, 339, 347, 355,
363, 371, 379, 387, 395 ],
[ 99, 118, 137, 156, 175, 194, 213, 232, 251, 270, 289 ], [ 251 .. 269 ] ]
gap> tkz:=IP_TikzArrayOfIntegers(table,rec(highlights:=arr));;
gap> tkz:=IP_TikzArrayOfIntegers(table,rec(highlights:=arr,shape_only:=" ",
> cell_width := "6",colsep:="1",rowsep:="1",inner_sep:="2",
> line_color:="black!20"));;
gap> table := IP_TableWithModularOrder(origin,a,b,depth,50,true,true);;
gap> tkz:=IP_TikzArrayOfIntegers(table,rec(highlights:=arr));;
## colors.xml ##
gap> IP_ColorsRedTones; #red
[ "red", "red!50", "red!20", "red!80!green!50", "red!80!blue!60" ]
gap> IP_ColorsGreenTones; #green
[ "green", "green!50", "green!20", "green!80!red!50", "green!80!blue!60" ]
gap> IP_ColorsBlueTones; #blue
[ "blue", "blue!50", "blue!20", "blue!80!red!50", "blue!80!green!60" ]
gap> IP_ColorsCompRedTones; # cyan (complement of red)
[ "-red", "-red!50", "-red!20", "-red!80!green!50", "-red!80!blue!60" ]
gap> IP_ColorsCompGreenTones; # magenta (complement of green)
[ "-green", "-green!50", "-green!20", "-green!80!red!50", "-green!80!blue!60" ]
gap> IP_ColorsCompBlueTones; # yellow (complement of blue)
[ "-blue", "-blue!50", "-blue!20", "-blue!80!red!50", "-blue!80!green!60" ]
gap> IP_ColorsDGrayTones; # dark gray
[ "black!80", "black!70", "black!60", "black!50", "black!40" ]
gap> IP_ColorsLGrayTones; # light gray
[ "black!30", "black!25", "black!20", "black!15", "black!10" ]
gap> ListsOfIP_Colors;
[ [ "red", "red!50", "red!20", "red!80!green!50", "red!80!blue!60" ],
[ "green", "green!50", "green!20", "green!80!red!50", "green!80!blue!60" ],
[ "blue", "blue!50", "blue!20", "blue!80!red!50", "blue!80!green!60" ],
[ "-red", "-red!50", "-red!20", "-red!80!green!50", "-red!80!blue!60" ],
[ "-green", "-green!50", "-green!20", "-green!80!red!50",
"-green!80!blue!60" ],
[ "-blue", "-blue!50", "-blue!20", "-blue!80!red!50", "-blue!80!green!60" ],
[ "black!80", "black!70", "black!60", "black!50", "black!40" ],
[ "black!30", "black!25", "black!20", "black!15", "black!10" ] ]
gap> IP_Colors;
[ "red", "red!50", "red!20", "red!80!green!50", "red!80!blue!60", "green",
"green!50", "green!20", "green!80!red!50", "green!80!blue!60", "blue",
"blue!50", "blue!20", "blue!80!red!50", "blue!80!green!60", "-red",
"-red!50", "-red!20", "-red!80!green!50", "-red!80!blue!60", "-green",
"-green!50", "-green!20", "-green!80!red!50", "-green!80!blue!60", "-blue",
"-blue!50", "-blue!20", "-blue!80!red!50", "-blue!80!green!60", "black!80",
"black!70", "black!60", "black!50", "black!40", "black!30", "black!25",
"black!20", "black!15", "black!10" ]
gap> ShuffledIP_colors;
[ "red", "green", "blue", "-red", "-green", "-blue", "black!80", "black!30",
"red!50", "green!50", "blue!50", "-red!50", "-green!50", "-blue!50",
"black!70", "black!25", "red!20", "green!20", "blue!20", "-red!20",
"-green!20", "-blue!20", "black!60", "black!20", "red!80!green!50",
"green!80!red!50", "blue!80!red!50", "-red!80!green!50", "-green!80!red!50",
"-blue!80!red!50", "black!50", "black!15", "red!80!blue!60",
"green!80!blue!60", "blue!80!green!60", "-red!80!blue!60",
"-green!80!blue!60", "-blue!80!green!60", "black!40", "black!10" ]
gap> m3 := Filtered([1..40],i->i mod 3=0);
[ 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39 ]
gap> m5 := Filtered([1..40],i->i mod 5=0);
[ 5, 10, 15, 20, 25, 30, 35, 40 ]
gap> m7 := Filtered([1..40],i->i mod 7=0);
[ 7, 14, 21, 28, 35 ]
gap>
gap> arr := [[],[],m3,[],m5,[],m7];;
gap> tkz:=IP_TikzArrayOfIntegers([1..40],10,rec(highlights:=arr));;
## visualisation.xml ##
gap> Print(IP_Preamble);
\documentclass{minimal}
\usepackage{amsmath}
\usepackage[active,tightpage]{preview}
\setlength\PreviewBorder{1pt}
\usepackage{pgf}
\usepackage{tikz}
\usepgfmodule{plot}
\usepgflibrary{plothandlers}
\usetikzlibrary{shapes.geometric}
\usetikzlibrary{shadings}
\begin{document}
\begin{preview}
gap> tikzfile := "tikz_pic_for_complete_document.tex";;
gap> file := "pic_for_complete_document.tex";;
gap>
gap> arr := [[1,2,3,4,5,6],[1,2,3,4,5],[1,2,3,4],[1,2,3],[1,2],[1]];;
gap> tkz := IP_TikzArrayOfIntegers([1..10],5,rec(highlights:=arr));;
gap>
gap> FileString(tikzfile,tkz);
642
gap> FileString(file,Concatenation(IP_Preamble,tkz,IP_Closing));
961
gap> rg := Filtered([801..889],u->(u mod 2)<>0);;
gap> flen := 15;;
gap> twins := Filtered(Primes, p -> p + 2 in Primes);;
gap> arr := [Primes,Union(twins,twins+2),Filtered(rg,u->(u mod 3)=0)];;
gap> tkz := IP_TikzArrayOfIntegers(rg,flen,rec(highlights:=arr));;
gap> cls := IP_ColorsCompRedTones;;
gap> rg := Filtered([801..889],u->(u mod 2)<>0);;
gap> flen := 15;;
gap> twins := Filtered(Primes, p -> p + 2 in Primes);;
gap> arr := [Primes,Union(twins,twins+2),Filtered(rg,u->(u mod 3)=0)];;
gap> tkz := IP_TikzArrayOfIntegers(rg,flen,rec(colors := cls,highlights:=arr));;
gap> cls := IP_ColorsDGrayTones;;
gap> rg := Filtered([801..889],u->(u mod 2)<>0);;
gap> flen := 15;;
gap> twins := Filtered(Primes, p -> p + 2 in Primes);;
gap> arr := [Primes,Union(twins,twins+2),Filtered(rg,u->(u mod 3)=0)];;
gap> tkz := IP_TikzArrayOfIntegers(rg,flen,rec(colors := cls,highlights:=arr));;
gap> cls := ["blue","-blue","black"];;
gap> rg := Filtered([801..889],u->(u mod 2)<>0);;
gap> flen := 15;;
gap> twins := Filtered(Primes, p -> p + 2 in Primes);;
gap> arr := [Primes,Union(twins,twins+2),Filtered(rg,u->(u mod 3)=0)];;
gap> tkz := IP_TikzArrayOfIntegers(rg,flen,rec( colors := cls,highlights:=arr));;
gap> ns := NumericalSemigroup(11,19,30,42,59);;
gap> cls := ShuffleIP_Colors([IP_ColorsGreenTones,IP_ColorsCompBlueTones]);;
gap> flen := 20;;
gap> #some notable elements
gap> arr := [SmallElementsOfNumericalSemigroup(ns),
> GapsOfNumericalSemigroup(ns),
> MinimalGeneratingSystemOfNumericalSemigroup(ns),
> FundamentalGapsOfNumericalSemigroup(ns),
> [ConductorOfNumericalSemigroup(ns)],
> PseudoFrobeniusOfNumericalSemigroup(ns)];;
gap>
gap> tkz := IP_TikzArrayOfIntegers(flen,rec(colors := cls,highlights:=arr));;
gap> row_length := 200;; # the legth of each row
gap> columns := 50;; # the number of colums
gap> n := row_length*columns;
10000
gap>
gap> ##compute the primes less than n
gap> # Primes is a GAP variable representing the list of primes less than 1000
gap> mp := Maximum(Primes);
997
gap> newprimes := [];;
gap> while mp < n do
> mp := NextPrimeInt(mp);
> Add(newprimes, mp);
> od;
gap> small_primes := Union(Primes, newprimes);;
gap> ##compute the first element of each pair of twin primes less than n
gap> twins := Filtered(small_primes, p -> IsPrime(p+2));;
gap>
gap> rg := [1..n];;
gap>
gap> arr := [Intersection(small_primes,rg),[],[],
> Intersection(Union(twins,twins+2),rg),[],[],[],[],[],[],[],
> [],[],[],[],[],[],Difference(rg,small_primes)];;
gap>
gap> tkz:=IP_TikzArrayOfIntegers([1..n],row_length,rec(highlights:=arr,
> cell_width := "6",colsep:="0",rowsep:="0",inner_sep:="2",
> shape_only:=" ",line_width:="0",line_color:="black!20" ));;
## options.xml ##
gap> RecNames(IP_TikzDefaultOptionsForArraysOfIntegers);
[ "other", "colors", "highlights", "shape_only", "colsep", "rowsep",
"cell_width", "allow_adjust_cell_width", "scale", "inner_sep",
"line_width", "line_color" ]
gap> IP_TikzDefaultOptionsForArraysOfIntegers;
rec( allow_adjust_cell_width := "10", cell_width := "30",
colors := [ "red", "green", "blue", "-red", "-green", "-blue", "black!80",
"black!30", "red!50", "green!50", "blue!50", "-red!50", "-green!50",
"-blue!50", "black!70", "black!25", "red!20", "green!20", "blue!20",
"-red!20", "-green!20", "-blue!20", "black!60", "black!20",
"red!80!green!50", "green!80!red!50", "blue!80!red!50",
"-red!80!green!50", "-green!80!red!50", "-blue!80!red!50", "black!50",
"black!15", "red!80!blue!60", "green!80!blue!60", "blue!80!green!60",
"-red!80!blue!60", "-green!80!blue!60", "-blue!80!green!60", "black!40",
"black!10" ], colsep := "2", highlights := [ [ ] ], inner_sep := "3",
line_color := "black", line_width := "0", other := [ ], rowsep := "2",
scale := "1", shape_only := "false" )
## routines_for_NS.xml ##
gap> ns1 := NumericalSemigroup(3,5);;
gap> TikzCodeForNumericalSemigroup(ns1,[[3,4],"pseudo_frobenius"],20);
"%tikz\n\\begin{tikzpicture}[every node/.style={draw,scale=1pt,\nminimum width\
=20pt,inner sep=3pt,\nline width=0pt,draw=black}]\n\\matrix[row sep=2pt,column\
sep=2pt]\n{\\node[]{0};&\n\\node[]{1};&\n\\node[]{2};&\n\\node[fill=red]{3};&\
\n\\node[fill=red]{4};&\n\\node[]{5};&\n\\node[]{6};&\n\\node[fill=green]{7};&\
\n\\node[]{8};&\n\\node[]{9};&\n\\node[]{10};&\n\\node[]{11};&\n\\node[]{12};&\
\n\\node[]{13};&\n\\node[]{14};&\n\\node[]{15};&\n\\node[]{16};&\n\\node[]{17}\
;&\n\\node[]{18};&\n\\node[]{19};&\n\\node[]{20};\\\\\n};\n\\end{tikzpicture}\
\n"
gap> SetOfNumericalSemigroups(rec(set:=rec(genus:=6),filter:=rec(type:= 2),
> order:="multiplicity"));
[ <Numerical semigroup with 3 generators>,
<Numerical semigroup with 3 generators>,
<Numerical semigroup with 4 generators>,
<Numerical semigroup with 5 generators>,
<Numerical semigroup with 5 generators>,
<Numerical semigroup with 6 generators> ]
gap> SetOfNumericalSemigroups(rec(set:=rec(genus:=6),filter:=rec(type:= 2), order:="frobenius"));
[ <Numerical semigroup with 3 generators>,
<Numerical semigroup with 5 generators>,
<Numerical semigroup with 5 generators>,
<Numerical semigroup with 3 generators>,
<Numerical semigroup with 4 generators>,
<Numerical semigroup with 6 generators> ]
gap> List(last,MinimalGeneratingSystem);
[ [ 3, 10, 11 ], [ 5, 6, 7 ], [ 5, 6, 8 ], [ 3, 8, 13 ], [ 4, 7, 9 ],
[ 6, 7, 8, 9, 11 ] ]
#gap> ns1 := NumericalSemigroup(3,5);;
#gap> ns2 := NumericalSemigroup(5,7,11);;
#gap> DrawSetOfNumericalSemigroups(ns1,rec(splash:=
#> rec(viewer := "evince"),highlights :=
#> ["pseudo_frobenius","small_elements","min_generators"]));
#gap> DrawSetOfNumericalSemigroups(ns1,ns2,rec(splash:=
#> rec(viewer := "evince"),highlights :=
#> ["pseudo_frobenius","small_elements","min_generators"]));
#gap> DrawSetOfNumericalSemigroups([ns1,ns2],rec(splash:=
#> rec(viewer := "evince"),highlights :=
#> ["small_elements","min_generators"]));
gap> frob := 15;;
gap> tipo := 2;;
gap> set := SetOfNumericalSemigroups(rec(set := rec(frobenius := frob),
> filter := rec(type:= tipo),order := "embedding_dimension"));
[ <Numerical semigroup with 3 generators>,
<Numerical semigroup with 3 generators>,
<Numerical semigroup with 4 generators>,
<Numerical semigroup with 5 generators>,
<Numerical semigroup with 5 generators>,
<Numerical semigroup with 5 generators>,
<Numerical semigroup with 6 generators>,
<Numerical semigroup with 6 generators>,
<Numerical semigroup with 6 generators> ]
gap> ns := NumericalSemigroup(4,9,19);;
gap> SmallElements(ns);
[ 0, 4, 8, 9, 12, 13, 16 ]
gap> MinimalGeneratingSystem(ns);
[ 4, 9, 19 ]
gap> ForcedIntegersForPseudoFrobenius(PseudoFrobeniusOfNumericalSemigroup(ns));
[ [ 1, 2, 3, 5, 6, 7, 14, 15 ], [ 0, 8, 9, 12, 13, 16 ] ]
gap> rg := [800..900];;
gap> flen := 15;;
gap> primes := Filtered(rg,IsPrime);
[ 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887 ]
gap> twins := Filtered(primes, p -> IsPrime(p+2));
[ 809, 821, 827, 857, 881 ]
gap> rgnp := Difference(rg,primes);
[ 800, 801, 802, 803, 804, 805, 806, 807, 808, 810, 812, 813, 814, 815, 816,
817, 818, 819, 820, 822, 824, 825, 826, 828, 830, 831, 832, 833, 834, 835,
836, 837, 838, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851,
852, 854, 855, 856, 858, 860, 861, 862, 864, 865, 866, 867, 868, 869, 870,
871, 872, 873, 874, 875, 876, 878, 879, 880, 882, 884, 885, 886, 888, 889,
890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900 ]
gap> arr := [primes,
> [1],
> Union(twins,twins+2),
> # now the non primes...
> Filtered(rgnp,u->(u mod 2)=0),
> Filtered(rgnp,u->(u mod 3)=0),
> Filtered(rgnp,u->(u mod 5)=0),
> [],[], # to avoid some colors
> Filtered(rgnp,u->(u mod 7)=0),
> Filtered(rgnp,u->(u mod 11)=0),
> Filtered(rgnp,u->(u mod 13)=0),
> Filtered(rgnp,u->(u mod 17)=0),
> Filtered(rgnp,u->(u mod 19)=0),
> Filtered(rgnp,u->(u mod 23)=0),
> Filtered(rgnp,u->(u mod 29)=0),
> Filtered(rgnp,u->(u mod 31)=0),
> Filtered(rgnp,u->(u mod 37)=0),
> Filtered(rgnp,u->(u mod 41)=0),
> Filtered(rgnp,u->(u mod 43)=0),
> Filtered(rgnp,u->(u mod 47)=0),
> Filtered(rgnp,u->(u mod 53)=0)];
[ [ 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887
], [ 1 ], [ 809, 811, 821, 823, 827, 829, 857, 859, 881, 883 ],
[ 800, 802, 804, 806, 808, 810, 812, 814, 816, 818, 820, 822, 824, 826,
828, 830, 832, 834, 836, 838, 840, 842, 844, 846, 848, 850, 852, 854,
856, 858, 860, 862, 864, 866, 868, 870, 872, 874, 876, 878, 880, 882,
884, 886, 888, 890, 892, 894, 896, 898, 900 ],
[ 801, 804, 807, 810, 813, 816, 819, 822, 825, 828, 831, 834, 837, 840,
843, 846, 849, 852, 855, 858, 861, 864, 867, 870, 873, 876, 879, 882,
885, 888, 891, 894, 897, 900 ],
[ 800, 805, 810, 815, 820, 825, 830, 835, 840, 845, 850, 855, 860, 865,
870, 875, 880, 885, 890, 895, 900 ], [ ], [ ],
[ 805, 812, 819, 826, 833, 840, 847, 854, 861, 868, 875, 882, 889, 896 ],
[ 803, 814, 825, 836, 847, 858, 869, 880, 891 ],
[ 806, 819, 832, 845, 858, 871, 884, 897 ], [ 816, 833, 850, 867, 884 ],
[ 817, 836, 855, 874, 893 ], [ 805, 828, 851, 874, 897 ],
[ 812, 841, 870, 899 ], [ 806, 837, 868, 899 ], [ 814, 851, 888 ],
[ 820, 861 ], [ 817, 860 ], [ 846, 893 ], [ 848 ] ]
gap> a := 8;; b := 19;;
gap> ns := NumericalSemigroup(a,b);;
gap> c := ConductorOfNumericalSemigroup(ns);;
gap> origin := 2*c-1;
251
gap> ground := [origin..origin+b-1];;
gap>
gap> height:=2;;
gap> depth:=8;;
gap> xaxis := [origin];;
gap> for n in [1..b-1] do
> Add(xaxis, origin+n*a);
> od;
gap> yaxis := [];;
gap> for n in [-depth..height] do
> Add(yaxis, origin+n*b);
> od;
gap>
gap> table := IP_TableWithModularOrder(origin,a,b,depth,height,false,false);;
gap> arr := [xaxis,yaxis,ground];
[ [ 251, 259, 267, 275, 283, 291, 299, 307, 315, 323, 331, 339, 347, 355, 363, 371, 379,
387, 395 ], [ 99, 118, 137, 156, 175, 194, 213, 232, 251, 270, 289 ], [ 251 .. 269 ]
]
gap> tkz:=IP_TikzArrayOfIntegers(table,rec(highlights:=arr,shape_only:=" ",
> cell_width := "6",colsep:="1",rowsep:="1",inner_sep:="2",
> line_color:="black!20", other :=
> ["\\draw[postaction={draw,line width=1pt,red}] (-80pt,-8pt) rectangle (16pt,40pt);",
> "\\draw[postaction={draw,line width=1pt,blue}] (-16pt,8pt) rectangle (80pt,-40pt);"]));;
gap> STOP_TEST( "testall.tst", 10000 );
## The first argument of STOP_TEST should be the name of the test file.
## The number is a proportionality factor that is used to output a
## "GAPstone" speed ranking after the file has been completely processed.
## For the files provided with the distribution this scaling is roughly
## equalized to yield the same numbers as produced by the test file
## tst/combinat.tst. For package tests, you may leave it unchnaged.
#############################################################################
##
#E