1##############################################################################
2##
3#W  number.tst                 Utils Package                       Stefan Kohl
4##
5#Y  Copyright (C) 2015-2018, The GAP Group
6##
7
8gap> ReadPackage( "utils", "tst/loadall.g" );;
9gap> UtilsLoadingComplete;
10true
11
12## SubSection 4.1.1
13gap> AllSmoothIntegers( 3, 1000 );
14[ 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96,
15  108, 128, 144, 162, 192, 216, 243, 256, 288, 324, 384, 432, 486, 512, 576,
16  648, 729, 768, 864, 972 ]
17gap> AllSmoothIntegers( [5,11,17], 1000 );
18[ 1, 5, 11, 17, 25, 55, 85, 121, 125, 187, 275, 289, 425, 605, 625, 935 ]
19gap> Length( last );
2016
21gap> List( [3..20], n -> Length( AllSmoothIntegers( [5,11,17], 10^n ) ) );
22[ 16, 29, 50, 78, 114, 155, 212, 282, 359, 452, 565, 691, 831, 992, 1173,
23  1374, 1595, 1843 ]
24
25## SubSection 4.1.2
26gap> AllProducts([1..4],3);
27[ 1, 2, 3, 4, 2, 4, 6, 8, 3, 6, 9, 12, 4, 8, 12, 16, 2, 4, 6, 8, 4, 8, 12,
28  16, 6, 12, 18, 24, 8, 16, 24, 32, 3, 6, 9, 12, 6, 12, 18, 24, 9, 18, 27,
29  36, 12, 24, 36, 48, 4, 8, 12, 16, 8, 16, 24, 32, 12, 24, 36, 48, 16, 32,
30  48, 64 ]
31gap> Set(last);
32[ 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 64 ]
33gap> AllProducts( [(1,2,3),(2,3,4)], 2 );
34[ (2,4,3), (1,2)(3,4), (1,3)(2,4), (1,3,2) ]
35
36## SubSection 4.1.3
37gap> RestrictedPartitions( 20, [4..10] );
38[ [ 4, 4, 4, 4, 4 ], [ 5, 5, 5, 5 ], [ 6, 5, 5, 4 ], [ 6, 6, 4, 4 ],
39  [ 7, 5, 4, 4 ], [ 7, 7, 6 ], [ 8, 4, 4, 4 ], [ 8, 6, 6 ], [ 8, 7, 5 ],
40  [ 8, 8, 4 ], [ 9, 6, 5 ], [ 9, 7, 4 ], [ 10, 5, 5 ], [ 10, 6, 4 ],
41  [ 10, 10 ] ]
42gap> RestrictedPartitionsWithoutRepetitions( 20, [4..10] );
43[ [ 10, 6, 4 ], [ 9, 7, 4 ], [ 9, 6, 5 ], [ 8, 7, 5 ] ]
44gap> RestrictedPartitionsWithoutRepetitions( 10^2, List([1..10], n->n^2 ) );
45[ [ 100 ], [ 64, 36 ], [ 49, 25, 16, 9, 1 ] ]
46
47## SubSection 4.1.4
48gap> n := 2^251;;
49gap> NextProbablyPrimeInt( n );
503618502788666131106986593281521497120414687020801267626233049500247285301313
51
52## SubSection 4.1.6
53gap> iter := PrimeNumbersIterator();;
54gap> for i in [1..100] do  p := NextIterator(iter);  od;
55gap> p;
56541
57gap> sum := 0;;
58gap> ## "prime number race" 1 vs. 3 mod 4
59gap> for p in PrimeNumbersIterator() do
60>       if p <> 2 then sum := sum + E(4)^(p-1); fi;
61>       if sum > 0 then break; fi;
62>    od;
63gap> p;
6426861
65
66## this final example takes quite a while: use examples/number.g
67## gap> sum := 0;;
68## gap> ## "prime number race" 1 vs. 5 mod 8
69## gap> for p in PrimeNumbersIterator() do
70## >       if p mod 8 in [1,5] then sum := sum + E(4)^((p-1)/2); fi;
71## >       if sum > 0 then break; fi;
72## >    od;
73## gap> p;
74## 588067889
75
76#############################################################################
77##
78#E  number.tst  . . . . . . . . . . . . . . . . . . . . . . . . . . ends here
79