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#@local S,b,comps,display,e,f,g,h,imglist,imgset,ind,ker,m,max,notation,p,per
#@local q,tmp,val,x,y
#
gap> START_TEST("trans.tst");
gap> display := UserPreference("TransformationDisplayLimit");;
gap> notation := UserPreference("NotationForTransformations");;
gap> SetUserPreference("TransformationDisplayLimit", 100);;
gap> SetUserPreference("NotationForTransformations", "input");;
# Test the kernel code
#
# Test TransformationNC
gap> TransformationNC([2, 1, 1]);
Transformation( [ 2, 1, 1 ] )
gap> TransformationNC([1 .. 3]);
IdentityTransformation
gap> TransformationNC(List([1 .. 65537], i -> 1));
<transformation on 65537 pts with rank 1>
gap> IsTrans4Rep(last);
true
gap> TransformationNC(List([1 .. 65536], i -> 1));
<transformation on 65536 pts with rank 1>
gap> IsTrans2Rep(last);
true
# Test TransformationListListNC
gap> TransformationListListNC("a", [1, 2, 3]);
Error, TransformationListListNC: <src> must have the same length as <ran> (len\
gths are 1 and 3)
gap> TransformationListListNC([1], [1, 2, 3]);
Error, TransformationListListNC: <src> must have the same length as <ran> (len\
gths are 1 and 3)
gap> TransformationListListNC("abc", [1, 2, 3]);
Error, TransformationListListNC: <src>[3] must be a positive small integer (no\
t a character)
gap> TransformationListListNC([1, 2, 3], "abc");
Error, TransformationListListNC: <ran>[3] must be a positive small integer (no\
t a character)
gap> TransformationListListNC([-1, 2, 3], [4, 5, 6]);
Error, TransformationListListNC: <src>[1] must be a positive small integer (no\
t the integer -1)
gap> TransformationListListNC([1, 2, 3], [4, -5, 6]);
Error, TransformationListListNC: <ran>[2] must be a positive small integer (no\
t the integer -5)
gap> TransformationListListNC([1, 2, 3], [4, 5, 6]);
Transformation( [ 4, 5, 6, 4, 5, 6 ] )
gap> TransformationListListNC([1, 2, 3], [65536, 65536, 65536]);
<transformation on 65536 pts with rank 65533>
gap> TransformationListListNC([1, 2, 3], [65537, 65537, 65537]);
<transformation on 65537 pts with rank 65534>
gap> TransformationListListNC([2, 1, 3], [4, 4, 4]);
Transformation( [ 4, 4, 4, 4 ] )
gap> TransformationListListNC((), ());
Error, TransformationListListNC: <src> must be a small list (not a permutation\
(small))
gap> TransformationListListNC([], ());
Error, TransformationListListNC: <ran> must be a small list (not a permutation\
(small))
gap> TransformationListListNC([], []);
IdentityTransformation
gap> TransformationListListNC([1..100000], [1..100000]);
IdentityTransformation
gap> TransformationListList([1..1000000], Concatenation([100000], [2..1000000]));
<transformation on 100000 pts with rank 99999>
gap> TransformationListList([1..1000000], Concatenation([2], [2..1000000]));
Transformation( [ 2, 2 ] )
# Test DegreeOfTransformation
gap> f := TransformationListListNC([1, 2], [1, 1]) ^ (3, 4);;
gap> DegreeOfTransformation(f);
2
gap> f := TransformationListListNC([1, 2], [1, 1]) ^ (3, 65537);;
gap> DegreeOfTransformation(f);
2
gap> DegreeOfTransformation(());
Error, DegreeOfTransformation: <f> must be a transformation (not a permutation\
(small))
# Test RANK_TRANS
gap> RANK_TRANS(Transformation([1, 2, 3]));
0
gap> RANK_TRANS(Transformation([1, 2, 1]));
2
gap> RANK_TRANS(Transformation([1, 2, 1]) ^ (4, 65537));
2
gap> RANK_TRANS("a");
Error, RANK_TRANS: <f> must be a transformation (not a list (string))
gap> RANK_TRANS(IdentityTransformation);
0
gap> RANK_TRANS(Transformation([1 .. 10]));
0
# Test RANK_TRANS_INT
gap> RANK_TRANS_INT(Transformation([1, 2, 1]), 0);
0
gap> RANK_TRANS_INT(Transformation([1, 2, 1]), 2);
2
gap> RANK_TRANS_INT(Transformation([1, 2, 1]), -2);
Error, RANK_TRANS_INT: <n> must be a non-negative small integer (not the integ\
er -2)
gap> RANK_TRANS_INT(Transformation([1, 2, 1]), "a");
Error, RANK_TRANS_INT: <n> must be a non-negative small integer (not a list (s\
tring))
gap> RANK_TRANS_INT("a", 2);
Error, RANK_TRANS_INT: <f> must be a transformation (not a list (string))
gap> RANK_TRANS_INT(Transformation([65537], [1]), 10);
10
# Test RANK_TRANS_LIST
gap> RANK_TRANS_LIST(Transformation([1, 2, 1]), 2);
Error, RANK_TRANS_LIST: <list> must be a small list (not the integer 2)
gap> RANK_TRANS_LIST(Transformation([1, 2, 1]), "a");
Error, RANK_TRANS_LIST: <list>[1] must be a positive small integer (not a char\
acter)
gap> RANK_TRANS_LIST(Transformation([1, 2, 1]) ^ (1, 65537), "a");
Error, RANK_TRANS_LIST: <list>[1] must be a positive small integer (not a char\
acter)
gap> RANK_TRANS_LIST(Transformation([1, 2, 1]), [1, 3]);
1
gap> RANK_TRANS_LIST(Transformation([1, 2, 1, 5, 5]), [1 .. 10]);
8
gap> RANK_TRANS_LIST(Transformation([1, 2, 1, 5, 5]), []);
0
gap> RANK_TRANS_LIST("a", [1, 3]);
Error, RANK_TRANS_LIST: <f> must be a transformation (not a list (string))
gap> RANK_TRANS_LIST(Transformation([65537], [1]),
> Concatenation([1], [65536 .. 70000]));
4465
gap> RANK_TRANS_LIST(Transformation([65537], [1]), []);
0
# Test IS_ID_TRANS
gap> IS_ID_TRANS(IdentityTransformation);
true
gap> IS_ID_TRANS(Transformation([2, 1]) ^ 2);
true
gap> IS_ID_TRANS(Transformation([65537, 1], [1, 65537]) ^ 2);
true
gap> IS_ID_TRANS(());
Error, IS_ID_TRANS: <f> must be a transformation (not a permutation (small))
# Test LARGEST_MOVED_PT_TRANS
gap> LARGEST_MOVED_PT_TRANS(IdentityTransformation);
0
gap> LARGEST_MOVED_PT_TRANS(Transformation([1, 2, 1, 4, 5]));
3
gap> LARGEST_MOVED_PT_TRANS(Transformation([65537], [1]));
65537
gap> LARGEST_MOVED_PT_TRANS("a");
Error, LARGEST_MOVED_PT_TRANS: <f> must be a transformation (not a list (strin\
g))
# Test LARGEST_IMAGE_PT
gap> LARGEST_IMAGE_PT(IdentityTransformation);
0
gap> LARGEST_IMAGE_PT(Transformation([1, 2, 1, 4, 5]));
2
gap> LARGEST_IMAGE_PT(Transformation([65537], [1]));
65536
gap> LARGEST_IMAGE_PT("a");
Error, LARGEST_IMAGE_PT: <f> must be a transformation (not a list (string))
# Test SMALLEST_MOVED_PT_TRANS
gap> SMALLEST_MOVED_PT_TRANS(IdentityTransformation);
fail
gap> SMALLEST_MOVED_PT_TRANS(Transformation([1, 2, 1, 4, 5]));
3
gap> SMALLEST_MOVED_PT_TRANS(Transformation([65537], [1]));
65537
gap> SMALLEST_MOVED_PT_TRANS("a");
Error, SMALLEST_MOVED_PT_TRANS: <f> must be a transformation (not a list (stri\
ng))
# Test SMALLEST_IMAGE_PT
gap> SMALLEST_IMAGE_PT(IdentityTransformation);
fail
gap> SMALLEST_IMAGE_PT(Transformation([1, 2, 1, 4, 5]));
1
gap> SMALLEST_IMAGE_PT(Transformation([65537], [1]));
1
gap> SMALLEST_IMAGE_PT("a");
Error, SMALLEST_IMAGE_PT: <f> must be a transformation (not a list (string))
# Test NR_MOVED_PTS_TRANS
gap> NR_MOVED_PTS_TRANS(IdentityTransformation);
0
gap> NR_MOVED_PTS_TRANS(Transformation([1, 2, 1, 4, 5]));
1
gap> NR_MOVED_PTS_TRANS(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]));
7
gap> NR_MOVED_PTS_TRANS(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1));
4464
gap> NR_MOVED_PTS_TRANS("a");
Error, NR_MOVED_PTS_TRANS: <f> must be a transformation (not a list (string))
# Test MOVED_PTS_TRANS
gap> MOVED_PTS_TRANS(IdentityTransformation);
[ ]
gap> MOVED_PTS_TRANS(Transformation([1, 2, 1, 4, 5]));
[ 3 ]
gap> MOVED_PTS_TRANS(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]));
[ 3, 6, 7, 8, 9, 10, 11 ]
gap> MOVED_PTS_TRANS(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1))
> = [65537 .. 70000];
true
gap> MOVED_PTS_TRANS(Transformation([2, 3, 1]) ^ 3);
[ ]
gap> MOVED_PTS_TRANS("a");
Error, MOVED_PTS_TRANS: <f> must be a transformation (not a list (string))
# Test FLAT_KERNEL_TRANS
gap> FLAT_KERNEL_TRANS(IdentityTransformation);
[ ]
gap> FLAT_KERNEL_TRANS(Transformation([1, 2, 1, 4, 5]));
[ 1, 2, 1, 3, 4 ]
gap> FLAT_KERNEL_TRANS(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]));
[ 1, 2, 1, 3, 4, 1, 1, 1, 1, 1, 1 ]
gap> FLAT_KERNEL_TRANS(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1))
> = Concatenation([1 .. 65536], [65537 .. 70000] * 0 + 1);
true
gap> FLAT_KERNEL_TRANS("a");
Error, FLAT_KERNEL_TRANS: <f> must be a transformation (not a list (string))
# Test FLAT_KERNEL_TRANS_INT
gap> FLAT_KERNEL_TRANS_INT(IdentityTransformation, -1);
Error, FLAT_KERNEL_TRANS_INT: <n> must be a non-negative small integer (not th\
e integer -1)
gap> FLAT_KERNEL_TRANS_INT(IdentityTransformation, "a");
Error, FLAT_KERNEL_TRANS_INT: <n> must be a non-negative small integer (not a \
list (string))
gap> FLAT_KERNEL_TRANS_INT(IdentityTransformation, 10);
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]
gap> FLAT_KERNEL_TRANS_INT(IdentityTransformation, 0);
[ ]
gap> FLAT_KERNEL_TRANS_INT(Transformation([1, 2, 1, 4, 5]), 0);
[ ]
gap> FLAT_KERNEL_TRANS_INT(Transformation([1, 2, 1, 4, 5]), 3);
[ 1, 2, 1 ]
gap> FLAT_KERNEL_TRANS_INT(Transformation([1, 2, 1, 4, 5]), 10);
[ 1, 2, 1, 3, 4, 5, 6, 7, 8, 9 ]
gap> FLAT_KERNEL_TRANS_INT(Transformation([1, 2, 1, 4, 5]), 5);
[ 1, 2, 1, 3, 4 ]
gap> FLAT_KERNEL_TRANS_INT(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 0);
[ ]
gap> FLAT_KERNEL_TRANS_INT(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 7);
[ 1, 2, 1, 3, 4, 1, 1 ]
gap> FLAT_KERNEL_TRANS_INT(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 14);
[ 1, 2, 1, 3, 4, 1, 1, 1, 1, 1, 1, 5, 6, 7 ]
gap> FLAT_KERNEL_TRANS_INT(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 11);
[ 1, 2, 1, 3, 4, 1, 1, 1, 1, 1, 1 ]
gap> FLAT_KERNEL_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 70000)
> = Concatenation([1 .. 65536], [65537 .. 70000] * 0 + 1);
true
gap> FLAT_KERNEL_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 65555)
> = Concatenation([1 .. 65536], [65537 .. 65555] * 0 + 1);
true
gap> FLAT_KERNEL_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 70010)
> = Concatenation([1 .. 65536], [65537 .. 70000] * 0 + 1, List([1 .. 10], x -> x + 65536));
true
gap> FLAT_KERNEL_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 10);
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]
gap> FLAT_KERNEL_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 0);
[ ]
gap> FLAT_KERNEL_TRANS_INT("a", 2);
Error, FLAT_KERNEL_TRANS_INT: <f> must be a transformation (not a list (string\
))
# Test IMAGE_SET_TRANS
gap> IMAGE_SET_TRANS(IdentityTransformation);
[ ]
gap> IMAGE_SET_TRANS(Transformation([1, 2, 1, 4, 5]));
[ 1, 2, 4, 5 ]
gap> IsSet(last);
true
gap> IMAGE_SET_TRANS(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]));
[ 1, 2, 4, 5 ]
gap> IsSet(last);
true
gap> IMAGE_SET_TRANS(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1))
> = [1 .. 65536];
true
gap> IMAGE_SET_TRANS("a");
Error, IMAGE_SET_TRANS: <f> must be a transformation (not a list (string))
gap> IMAGE_SET_TRANS(Transformation([2, 1, 2, 4, 5]));
[ 1, 2, 4, 5 ]
gap> IsSet(last);
true
gap> IMAGE_SET_TRANS(Transformation([4, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]));
[ 1, 2, 4, 5 ]
gap> IsSet(last);
true
gap> IMAGE_SET_TRANS(Transformation([1], [65537]))
> = [2 .. 65537];
true
gap> f := ID_TRANS4;;
gap> IsTrans4Rep(f);
true
gap> IMAGE_SET_TRANS(f);
[ ]
gap> FLAT_KERNEL_TRANS(f);
[ ]
# Test IMAGE_SET_TRANS_INT
gap> IMAGE_SET_TRANS_INT(IdentityTransformation, -1);
Error, IMAGE_SET_TRANS_INT: <n> must be a non-negative small integer (not the \
integer -1)
gap> IMAGE_SET_TRANS_INT(IdentityTransformation, "a");
Error, IMAGE_SET_TRANS_INT: <n> must be a non-negative small integer (not a li\
st (string))
gap> IMAGE_SET_TRANS_INT(IdentityTransformation, 10);
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]
gap> IMAGE_SET_TRANS_INT(IdentityTransformation, 0);
[ ]
gap> IMAGE_SET_TRANS_INT(Transformation([1, 2, 1, 4, 5]), 0);
[ ]
gap> IMAGE_SET_TRANS_INT(Transformation([2, 1, 1, 4, 5]), 3);
[ 1, 2 ]
gap> IMAGE_SET_TRANS_INT(Transformation([2, 1, 1, 4, 5]), 10);
[ 1, 2, 4, 5, 6, 7, 8, 9, 10 ]
gap> IMAGE_SET_TRANS_INT(Transformation([1, 2, 1, 4, 5]), 5);
[ 1, 2, 4, 5 ]
gap> IMAGE_SET_TRANS_INT(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 0);
[ ]
gap> IMAGE_SET_TRANS_INT(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 7);
[ 1, 2, 4, 5 ]
gap> IMAGE_SET_TRANS_INT(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 14);
[ 1, 2, 4, 5, 12, 13, 14 ]
gap> IMAGE_SET_TRANS_INT(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 11);
[ 1, 2, 4, 5 ]
gap> IMAGE_SET_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 70000)
> = [1 .. 65536];
true
gap> IMAGE_SET_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 65555)
> = [1 .. 65536];
true
gap> IMAGE_SET_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 70010)
> = Concatenation([1 .. 65536], List([1 .. 10], x -> x + 70000));
true
gap> IMAGE_SET_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 10);
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]
gap> IMAGE_SET_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 0);
[ ]
gap> IMAGE_SET_TRANS_INT("a", 2);
Error, IMAGE_SET_TRANS_INT: <f> must be a transformation (not a list (string))
# Test IMAGE_LIST_TRANS_INT
gap> IMAGE_LIST_TRANS_INT(IdentityTransformation, -1);
Error, IMAGE_LIST_TRANS_INT: <n> must be a non-negative small integer (not the\
integer -1)
gap> IMAGE_LIST_TRANS_INT(IdentityTransformation, "a");
Error, IMAGE_LIST_TRANS_INT: <n> must be a non-negative small integer (not a l\
ist (string))
gap> IMAGE_LIST_TRANS_INT(IdentityTransformation, 10);
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]
gap> IMAGE_LIST_TRANS_INT(IdentityTransformation, 0);
[ ]
gap> IMAGE_LIST_TRANS_INT(Transformation([1, 2, 1, 4, 5]), 0);
[ ]
gap> IMAGE_LIST_TRANS_INT(Transformation([2, 1, 1, 4, 5]), 3);
[ 2, 1, 1 ]
gap> IMAGE_LIST_TRANS_INT(Transformation([2, 1, 1, 4, 5]), 10);
[ 2, 1, 1, 4, 5, 6, 7, 8, 9, 10 ]
gap> IMAGE_LIST_TRANS_INT(Transformation([1, 2, 1, 4, 5]), 5);
[ 1, 2, 1, 4, 5 ]
gap> IMAGE_LIST_TRANS_INT(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 0);
[ ]
gap> IMAGE_LIST_TRANS_INT(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 7);
[ 1, 2, 1, 4, 5, 1, 1 ]
gap> IMAGE_LIST_TRANS_INT(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 14);
[ 1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1, 12, 13, 14 ]
gap> IMAGE_LIST_TRANS_INT(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 11);
[ 1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1 ]
gap> IMAGE_LIST_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 70000)
> = Concatenation([1 .. 65536], [65537 .. 70000] * 0 + 1);
true
gap> IMAGE_LIST_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 65555)
> = Concatenation([1 .. 65536], [65537 .. 65555] * 0 + 1);
true
gap> IMAGE_LIST_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 70010)
> = Concatenation([1 .. 65536], [65537 .. 70000] * 0 + 1, List([1 .. 10], x -> x + 70000));
true
gap> IMAGE_LIST_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 10);
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]
gap> IMAGE_LIST_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 0);
[ ]
gap> IMAGE_LIST_TRANS_INT("a", 2);
Error, IMAGE_LIST_TRANS_INT: <f> must be a transformation (not a list (string)\
)
# Test KERNEL_TRANS 1
gap> KERNEL_TRANS(IdentityTransformation, -1);
Error, KERNEL_TRANS: <n> must be a non-negative small integer (not the integer\
-1)
gap> KERNEL_TRANS(IdentityTransformation, "a");
Error, KERNEL_TRANS: <n> must be a non-negative small integer (not a list (str\
ing))
gap> KERNEL_TRANS(IdentityTransformation, 10);
[ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ], [ 9 ], [ 10 ] ]
gap> KERNEL_TRANS(IdentityTransformation, 0);
[ ]
gap> KERNEL_TRANS(Transformation([1, 2, 1, 4, 5]), 0);
[ ]
gap> KERNEL_TRANS(Transformation([1, 2, 1, 4, 5]), 3);
[ [ 1, 3 ], [ 2 ] ]
gap> KERNEL_TRANS(Transformation([1, 2, 1, 4, 5]), 10);
[ [ 1, 3 ], [ 2 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ], [ 9 ], [ 10 ] ]
gap> KERNEL_TRANS(Transformation([1, 2, 1, 4, 5]), 5);
[ [ 1, 3 ], [ 2 ], [ 4 ], [ 5 ] ]
gap> KERNEL_TRANS(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 0);
[ ]
gap> KERNEL_TRANS(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 7);
[ [ 1, 3, 6, 7 ], [ 2 ], [ 4 ], [ 5 ] ]
gap> KERNEL_TRANS(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 14);
[ [ 1, 3, 6, 7, 8, 9, 10, 11 ], [ 2 ], [ 4 ], [ 5 ], [ 12 ], [ 13 ], [ 14 ] ]
gap> KERNEL_TRANS(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 11);
[ [ 1, 3, 6, 7, 8, 9, 10, 11 ], [ 2 ], [ 4 ], [ 5 ] ]
gap> KERNEL_TRANS("a", 2);
Error, KERNEL_TRANS: <f> must be a transformation (not a list (string))
gap> KERNEL_TRANS(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 10);
[ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ], [ 9 ], [ 10 ] ]
gap> KERNEL_TRANS(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 0);
[ ]
# Test KERNEL_TRANS 2
gap> f := Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1);;
gap> ker := KERNEL_TRANS(f, 70000);;
gap> Length(ker) = RankOfTransformation(f, 70000);
true
gap> Union(ker) = [1 .. 70000];
true
gap> max := Maximum(List(ker, Length));
4465
gap> tmp := First(ker, x -> Length(x) = max);;
gap> ForAll(tmp, x -> x ^ f = tmp[1] ^ f);
true
gap> Filtered([1 .. DegreeOfTransformation(f)], x -> x ^ f = tmp[1] ^ f) = tmp;
true
# Test KERNEL_TRANS 3
gap> f := Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1);;
gap> ker := KERNEL_TRANS(f, 65555);;
gap> Length(ker) = RankOfTransformation(f, 65555);
true
gap> Union(ker) = [1 .. 65555];
true
gap> max := Maximum(List(ker, Length));
20
gap> tmp := First(ker, x -> Length(x) = max);;
gap> ForAll(tmp, x -> x ^ f = tmp[1] ^ f);
true
gap> Filtered([1 .. 65555], x -> x ^ f = tmp[1] ^ f) = tmp;
true
# Test KERNEL_TRANS 4
gap> f := Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1);;
gap> ker := KERNEL_TRANS(f, 70010);;
gap> Length(ker) = RankOfTransformation(f, 70010);
true
gap> Union(ker) = [1 .. 70010];
true
gap> max := Maximum(List(ker, Length));
4465
gap> tmp := First(ker, x -> Length(x) = max);;
gap> ForAll(tmp, x -> x ^ f = tmp[1] ^ f);
true
gap> Filtered([1 .. 70010], x -> x ^ f = tmp[1] ^ f) = tmp;
true
# Test PREIMAGES_TRANS_INT
gap> PREIMAGES_TRANS_INT(IdentityTransformation, 0);
Error, PREIMAGES_TRANS_INT: <pt> must be a positive small integer (not the int\
eger 0)
gap> PREIMAGES_TRANS_INT(IdentityTransformation, -1);
Error, PREIMAGES_TRANS_INT: <pt> must be a positive small integer (not the int\
eger -1)
gap> PREIMAGES_TRANS_INT(IdentityTransformation, "a");
Error, PREIMAGES_TRANS_INT: <pt> must be a positive small integer (not a list \
(string))
gap> PREIMAGES_TRANS_INT("a", 2);
Error, PREIMAGES_TRANS_INT: <f> must be a transformation (not a list (string))
gap> PREIMAGES_TRANS_INT(IdentityTransformation, 10);
[ 10 ]
gap> PREIMAGES_TRANS_INT(Transformation([2, 1, 1, 4, 5]), 3);
[ ]
gap> PREIMAGES_TRANS_INT(Transformation([2, 1, 1, 4, 5]), 1);
[ 2, 3 ]
gap> PREIMAGES_TRANS_INT(Transformation([2, 1, 1, 4, 5]), 10);
[ 10 ]
gap> PREIMAGES_TRANS_INT(Transformation([1, 2, 1, 4, 5]), 2);
[ 2 ]
gap> PREIMAGES_TRANS_INT(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 1);
[ 1, 3, 6, 7, 8, 9, 10, 11 ]
gap> PREIMAGES_TRANS_INT(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 14);
[ 14 ]
gap> PREIMAGES_TRANS_INT(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 11);
[ ]
gap> PREIMAGES_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 1)
> = Concatenation([1], [65537 .. 70000]);
true
gap> PREIMAGES_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 2);
[ 2 ]
gap> PREIMAGES_TRANS_INT(Transformation([65537 .. 70000], [65537 .. 70000] * 0 + 1), 65555);
[ ]
# Test AS_TRANS_PERM_INT
gap> AS_TRANS_PERM_INT((1, 2, 3), "a");
Error, AS_TRANS_PERM_INT: <deg> must be a non-negative small integer (not a li\
st (string))
gap> AS_TRANS_PERM_INT((1, 2, 3), -1);
Error, AS_TRANS_PERM_INT: <deg> must be a non-negative small integer (not the \
integer -1)
gap> AS_TRANS_PERM_INT("a", 3);
Error, AS_TRANS_PERM_INT: <p> must be a permutation (not a list (string))
gap> AS_TRANS_PERM_INT((1, 2, 3), 0);
IdentityTransformation
gap> AS_TRANS_PERM_INT((1, 2, 3), 1);
Transformation( [ 2, 2 ] )
gap> AS_TRANS_PERM_INT((1, 2, 3), 2);
Transformation( [ 2, 3, 3 ] )
gap> AS_TRANS_PERM_INT((1, 2, 3), 3);
Transformation( [ 2, 3, 1 ] )
gap> AsPermutation(last) = (1, 2, 3);
true
gap> AS_TRANS_PERM_INT((1, 65537), 0);
IdentityTransformation
gap> AS_TRANS_PERM_INT((1, 65537), 1);
<transformation on 65537 pts with rank 65536>
gap> f := AS_TRANS_PERM_INT((1, 65537), 2);
<transformation on 65537 pts with rank 65536>
gap> PREIMAGES_TRANS_INT(f, 65537);
[ 1, 65537 ]
gap> last in KernelOfTransformation(f);
true
gap> AS_TRANS_PERM_INT((1, 65537), 3);
<transformation on 65537 pts with rank 65536>
gap> AS_TRANS_PERM_INT((1, 65537), 65537);
<transformation on 65537 pts with rank 65537>
gap> AsPermutation(last) = (1, 65537);
true
gap> AS_TRANS_PERM_INT((1, 2)(3, 65537), 2);
Transformation( [ 2, 1 ] )
# Test AS_TRANS_PERM
gap> AS_TRANS_PERM((1, 2, 3));
Transformation( [ 2, 3, 1 ] )
gap> AS_TRANS_PERM("a");
Error, AS_TRANS_PERM: <p> must be a permutation (not a list (string))
gap> AS_TRANS_PERM((1, 65537));
<transformation on 65537 pts with rank 65537>
gap> AS_TRANS_PERM((1, 65537) * (1, 65537));
IdentityTransformation
gap> AS_TRANS_PERM((1, 37) * (1, 37));
IdentityTransformation
# Test AS_PERM_TRANS
gap> AS_PERM_TRANS(Transformation([2, 3, 1]));
(1,2,3)
gap> AS_PERM_TRANS(Transformation([2, 3, 2]));
fail
gap> AS_PERM_TRANS(Transformation([1, 65537], [65537, 1]));
(1,65537)
gap> AS_PERM_TRANS(Transformation([1, 65537], [65537, 65537]));
fail
gap> AS_PERM_TRANS(());
Error, AS_PERM_TRANS: <f> must be a transformation (not a permutation (small))
# Test PermutationOfImage
gap> PermutationOfImage(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]));
fail
gap> PermutationOfImage(Transformation([3, 8, 1, 9, 9, 4, 10, 5, 10, 6]));
fail
gap> PermutationOfImage(Transformation([65537], [1]));
()
gap> PermutationOfImage(Transformation([1, 2, 3, 4, 5, 6, 7, 8, 9, 1]));
()
gap> PermutationOfImage(Transformation([2, 3, 1, 4, 5, 6, 7, 8, 9, 2]));
(1,2,3)
gap> PermutationOfImage(Transformation([1 .. 65537], x -> x + 1));
fail
gap> PermutationOfImage(1);
Error, PermutationOfImage: <f> must be a transformation (not the integer 1)
# Test RestrictedTransformation
gap> RestrictedTransformation(IdentityTransformation, [1, -1]);
Error, RestrictedTransformation: <list>[2] must be a positive small integer (n\
ot the integer -1)
gap> RestrictedTransformation(IdentityTransformation, "a");
Error, RestrictedTransformation: <list>[1] must be a positive small integer (n\
ot a character)
gap> RestrictedTransformation(IdentityTransformation, [1,, 3]);
Error, List Element: <list>[2] must have an assigned value
gap> RestrictedTransformation(IdentityTransformation, [1 .. 10]);
IdentityTransformation
gap> RestrictedTransformation(IdentityTransformation, [0]);
Error, RestrictedTransformation: <list>[1] must be a positive small integer (n\
ot the integer 0)
gap> RestrictedTransformation(Transformation([1, 2, 1, 4, 5]), [1, 3, 5]);
Transformation( [ 1, 2, 1 ] )
gap> RestrictedTransformation(Transformation([2, 1, 1, 4, 5]), [1 .. 3]);
Transformation( [ 2, 1, 1 ] )
gap> RestrictedTransformation(Transformation([2, 1, 1, 4, 5]), [1 .. 10]);
Transformation( [ 2, 1, 1 ] )
gap> RestrictedTransformation(Transformation([1, 2, 1, 4, 5]), [1 .. 5]);
Transformation( [ 1, 2, 1 ] )
gap> RestrictedTransformation(Transformation([1, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 0);
Error, RestrictedTransformation: <list> must be a small list (not the integer \
0)
gap> RestrictedTransformation(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1), [1 .. 65536]);
IdentityTransformation
gap> RestrictedTransformation(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1), [65537 .. 65555]);
<transformation on 65555 pts with rank 65536>
gap> RestrictedTransformation(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1), [1, -1]);
Error, RestrictedTransformation: <list>[2] must be a positive small integer (n\
ot the integer -1)
gap> RestrictedTransformation("a", [1 .. 10]);
Error, RestrictedTransformation: <f> must be a transformation (not a list (str\
ing))
gap> RestrictedTransformation(Transformation([3, 2, 3]), [1]);
Transformation( [ 3, 2, 3 ] )
gap> RestrictedTransformation(Transformation([1], [65537]), [1]);
<transformation on 65537 pts with rank 65536>
# Test AS_TRANS_TRANS
gap> AS_TRANS_TRANS(IdentityTransformation, -1);
Error, AS_TRANS_TRANS: <m> must be a non-negative small integer (not the integ\
er -1)
gap> AS_TRANS_TRANS(IdentityTransformation, "a");
Error, AS_TRANS_TRANS: <m> must be a non-negative small integer (not a list (s\
tring))
gap> AS_TRANS_TRANS(IdentityTransformation, 3);
IdentityTransformation
gap> AS_TRANS_TRANS(IdentityTransformation, 10);
IdentityTransformation
gap> AS_TRANS_TRANS(IdentityTransformation, 0);
IdentityTransformation
gap> AS_TRANS_TRANS(Transformation([1, 2, 1, 4, 5]), 3);
Transformation( [ 1, 2, 1 ] )
gap> AS_TRANS_TRANS(Transformation([1, 2, 1, 4, 5]), 7);
Transformation( [ 1, 2, 1 ] )
gap> AS_TRANS_TRANS(Transformation([2, 2, 1, 4, 5, 1, 1, 1, 1, 1, 1]), 1);
fail
gap> AS_TRANS_TRANS(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1), 65536);
IdentityTransformation
gap> AS_TRANS_TRANS(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1), 65555);
<transformation on 65555 pts with rank 65536>
gap> AS_TRANS_TRANS(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1), 70010);
<transformation on 70000 pts with rank 65536>
gap> AS_TRANS_TRANS(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1), 0);
IdentityTransformation
gap> AS_TRANS_TRANS(Transformation([65537], [70000]), 65537);
fail
gap> AS_TRANS_TRANS(Transformation([1], [65537]), 1);
fail
gap> AS_TRANS_TRANS(Transformation([1], [65537]), 0);
IdentityTransformation
gap> AS_TRANS_TRANS("a", 10);
Error, AS_TRANS_TRANS: <f> must be a transformation (not a list (string))
# Test TRIM_TRANS
gap> TRIM_TRANS(IdentityTransformation, -1);
Error, TRIM_TRANS: <m> must be a non-negative small integer (not the integer -\
1)
gap> TRIM_TRANS(IdentityTransformation, "a");
Error, TRIM_TRANS: <m> must be a non-negative small integer (not a list (strin\
g))
gap> TRIM_TRANS(IdentityTransformation, 3);
gap> TRIM_TRANS(IdentityTransformation, 10);
gap> TRIM_TRANS(IdentityTransformation, 0);
gap> TRIM_TRANS(Transformation([1, 2, 1, 1, 1]), 3);
gap> TRIM_TRANS(Transformation([1, 2, 1, 1, 1]), 7);
gap> TRIM_TRANS(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1), 65536);
gap> TRIM_TRANS(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1), 10);
gap> TRIM_TRANS(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1), 65555);
gap> TRIM_TRANS(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1), 70010);
gap> TRIM_TRANS(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1), 0);
gap> TRIM_TRANS("a", 10);
Error, TRIM_TRANS: <f> must be a transformation (not a list (string))
# Test for the issue with caching the degree of a transformation in PR #384
gap> x := Transformation([1, 1]) ^ (1,2)(3,70000);
Transformation( [ 2, 2 ] )
gap> IsTrans4Rep(x);
true
gap> HASH_FUNC_FOR_TRANS(x, 101);;
gap> x;
Transformation( [ 2, 2 ] )
gap> x := Transformation([1, 1]) ^ (1,70000);
<transformation on 70000 pts with rank 69999>
gap> IsTrans4Rep(x);
true
gap> HASH_FUNC_FOR_TRANS(x, 101);;
# Test IsInjectiveListTrans
gap> f := Transformation([9, 3, 2, 3, 1, 8, 2, 7, 8, 3, 12, 10]);;
gap> IsInjectiveListTrans([1, 2, 3, 6, 5], f);
true
gap> IsInjectiveListTrans([1 .. 5], f);
false
gap> f := Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1);;
gap> IsInjectiveListTrans(ImageSetOfTransformation(f), f);
true
gap> IsInjectiveListTrans([1 .. RankOfTransformation(f) + 1], f);
false
gap> IsInjectiveListTrans([1 .. RankOfTransformation(f) + 1],
> ImageListOfTransformation(f));
false
gap> f := Transformation([12, 3, 4, 12, 1, 2, 12, 1, 5, 1, 10, 7]);;
gap> IsInjectiveListTrans([1 .. 3], f);
true
gap> IsInjectiveListTrans([1 .. 4], f);
false
gap> IsInjectiveListTrans([1 .. 4], ImageListOfTransformation(f));
false
gap> IsInjectiveListTrans([1 .. 3], ImageListOfTransformation(f));
true
gap> f := Transformation([11, 9, 3, 8, 10, 11, 6, 1, 8, 8, 4, 11]);;
gap> RankOfTransformation(f);
8
gap> IsInjectiveListTrans([1 .. 5], f);
true
gap> IsInjectiveListTrans([1 .. 6], f);
false
gap> f := Transformation([5, 5, 3, 10, 10, 10, 2, 12, 11, 9, 1, 6]);;
gap> IsInjectiveListTrans([2, 3], f);
true
gap> IsInjectiveListTrans([2, 3, 4, 7], f);
true
gap> IsInjectiveListTrans([2, 3, 4, 5, 7], f);
false
gap> IsInjectiveListTrans([65536], f);
true
gap> IsInjectiveListTrans([1 .. 65536], f);
false
gap> IsInjectiveListTrans([1 .. 65536], ImageListOfTransformation(f));
false
gap> IsInjectiveListTrans([65536], ImageListOfTransformation(f));
true
gap> IsInjectiveListTrans(1, f);
Error, IsInjectiveListTrans: <list> must be a small list (not the integer 1)
gap> IsInjectiveListTrans([1], 1);
Error, IsInjectiveListTrans: <obj> must be a transformation or a list (not the\
integer 1)
gap> IsInjectiveListTrans([1, 2], "def");
Error, IsInjectiveListTrans: <obj>[1] must be a positive small integer (not a \
character)
gap> IsInjectiveListTrans(ID_TRANS4, "def");
Error, IsInjectiveListTrans: <list> must be a small list (not a transformation\
(large))
gap> IsInjectiveListTrans([1, 2], [2,3]);
Error, <obj> must be a list of positive small integers in the range [1 .. 2]
gap> IsInjectiveListTrans([1, []], f);
Error, IsInjectiveListTrans: <list>[2] must be a positive small integer (not a\
n empty plain list)
gap> IsInjectiveListTrans([1, []], [1, 2, 3]);
Error, IsInjectiveListTrans: <list>[2] must be a positive small integer (not a\
n empty plain list)
gap> IsInjectiveListTrans([1, []], ID_TRANS4);
Error, IsInjectiveListTrans: <list>[2] must be a positive small integer (not a\
n empty plain list)
# Test PermLeftQuoTransformationNC
gap> f := Transformation([3, 8, 1, 9, 9, 4, 10, 5, 10, 6]);;
gap> PermLeftQuoTransformationNC(f, f);
()
gap> p := (1, 9, 10, 8)(4, 5, 6);;
gap> PermLeftQuoTransformationNC(f * p, f);
(1,8,10,9)(4,6,5)
gap> PermLeftQuoTransformationNC(f * p, f ^ (20, 21));
(1,8,10,9)(4,6,5)
gap> PermLeftQuoTransformationNC(f, f * p);
(1,9,10,8)(4,5,6)
gap> p := (1, 8, 4, 6, 3, 10, 5);;
gap> PermLeftQuoTransformationNC(f, f * p);
(1,8,4,6,3,10,5)
gap> PermLeftQuoTransformationNC(f * p, f);
(1,5,10,3,6,4,8)
gap> f := Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1)
> * (1,65, 1414, 13485)(139, 1943, 858, 65536);;
gap> p := (1, 10, 20)(414, 1441, 59265);;
gap> PermLeftQuoTransformationNC(f * p, f) = p ^ -1;
true
gap> PermLeftQuoTransformationNC(f, f * p) = p;
true
gap> f := Transformation([2, 6, 7, 2, 6, 9, 9, 1, 11, 1, 12, 5]);;
gap> PermLeftQuoTransformationNC(f, f * (1, 2, 3));
(1,2,3)
gap> g := f * (1, 2, 5);;
gap> PermLeftQuoTransformationNC(f, g);
(1,2,5)
gap> PermLeftQuoTransformationNC(g, f);
(1,5,2)
gap> f := Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1);;
gap> g := f * (12849, 19491, 3501, 1593)(1341, 19414, 194)(1413, 19);;
gap> p := PermLeftQuoTransformationNC(f, g);
(19,1413)(194,1341,19414)(1593,12849,19491,3501)
gap> p := PermLeftQuoTransformationNC(f, g ^ (70001, 70002));
(19,1413)(194,1341,19414)(1593,12849,19491,3501)
gap> q := PermLeftQuoTransformationNC(g, f);
(19,1413)(194,19414,1341)(1593,3501,19491,12849)
gap> p = q ^ -1;
true
gap> q = p ^ -1;
true
gap> PermLeftQuoTransformationNC((), IdentityTransformation);
Error, PermLeftQuoTransformationNC: <f> must be a transformation (not a permut\
ation (small))
gap> PermLeftQuoTransformationNC(IdentityTransformation, ());
Error, PermLeftQuoTransformationNC: <g> must be a transformation (not a permut\
ation (small))
gap> PermLeftQuoTransformationNC((), ());
Error, PermLeftQuoTransformationNC: <f> must be a transformation (not a permut\
ation (small))
gap> g := Transformation([3, 8, 1, 9, 9, 4, 10, 5, 10, 6]);;
gap> f := (g ^ (2, 20)) * (1, 3, 8)(6, 9);;
gap> PermLeftQuoTransformationNC(f, g);
(1,20)(2,8,3)(6,9)
gap> f := Transformation([3, 8, 1, 9, 1, 3, 10, 5, 10, 6]);;
gap> g := (f ^ (2, 65537)) * (1, 3, 8)(6, 9);;
gap> PermLeftQuoTransformationNC(f, g);
(1,3,8,2)(6,9)
gap> PermLeftQuoTransformationNC(g, f);
(1,65537)(2,8,3)(6,9)
gap> g := Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1);;
gap> f := g ^ (70001, 70002);;
gap> PermLeftQuoTransformationNC(f, g);
()
# Test TRANS_IMG_KER_NC
gap> f := Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1);;
gap> g := TRANS_IMG_KER_NC(ImageSetOfTransformation(f),
> FlatKernelOfTransformation(f));;
gap> g = TRANS_IMG_KER_NC(ImageSetOfTransformation(g),
> FlatKernelOfTransformation(g));
true
gap> f := Transformation([4, 6, 9, 3, 9, 5, 11, 6, 3, 8, 7, 1]);;
gap> g := TRANS_IMG_KER_NC(ImageSetOfTransformation(f),
> FlatKernelOfTransformation(f));
Transformation( [ 1, 3, 4, 5, 4, 6, 7, 3, 5, 8, 9, 11 ] )
gap> FlatKernelOfTransformation(g) = FlatKernelOfTransformation(f);
true
gap> ImageSetOfTransformation(g) = ImageSetOfTransformation(f);
true
gap> f := Transformation([7, 1, 4, 5, 4, 2, 5, 7, 6, 4, 1, 4]);;
gap> g := TRANS_IMG_KER_NC(ImageSetOfTransformation(f),
> FlatKernelOfTransformation(f));
Transformation( [ 1, 2, 4, 5, 4, 6, 5, 1, 7, 4, 2, 4 ] )
gap> KernelOfTransformation(g) = KernelOfTransformation(f);
true
gap> ImageSetOfTransformation(f) = ImageSetOfTransformation(g);
true
gap> g ^ 2 = g;
false
gap> TRANS_IMG_KER_NC([5, 4 .. 1], [1 .. 5]);
Transformation( [ 5, 4, 3, 2, 1 ] )
# Test IDEM_IMG_KER_NC
gap> f := AsTransformation((4,21,13,62,7,56,9,77,91,43,99)
> (14,27,87,72,57,85));;
gap> g := IDEM_IMG_KER_NC(ImageSetOfTransformation(f),
> FlatKernelOfTransformation(f));;
gap> g = f ^ 0;
true
gap> f := Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1);;
gap> g := IDEM_IMG_KER_NC(ImageSetOfTransformation(f),
> FlatKernelOfTransformation(f));;
gap> g ^ 2 = g;
true
gap> f := Transformation([4, 6, 9, 3, 9, 5, 11, 6, 3, 8, 7, 1]) ^ 4;;
gap> g := IDEM_IMG_KER_NC(ImageSetOfTransformation(f),
> FlatKernelOfTransformation(f));
Transformation( [ 3, 3, 3, 9, 3, 9, 7, 3, 9, 9, 11, 9 ] )
gap> g ^ 2 = g;
true
gap> f = g;
true
gap> FlatKernelOfTransformation(g) = FlatKernelOfTransformation(f);
true
gap> ImageSetOfTransformation(g) = ImageSetOfTransformation(f);
true
gap> f := Transformation([9, 1, 4, 5, 4, 2, 5, 9, 6, 4, 1, 4]);;
gap> g := IDEM_IMG_KER_NC(ImageSetOfTransformation(f),
> FlatKernelOfTransformation(f));
Transformation( [ 1, 2, 5, 4, 5, 6, 4, 1, 9, 5, 2, 5 ] )
gap> g ^ 2 = g;
true
gap> KernelOfTransformation(g) = KernelOfTransformation(f);
true
gap> ImageSetOfTransformation(f) = ImageSetOfTransformation(g);
true
gap> g ^ 2 = g;
true
gap> IDEM_IMG_KER_NC([5, 4 .. 1], [1 .. 5]);
IdentityTransformation
# Test InverseOfTransformation
gap> InverseOfTransformation(IdentityTransformation);
IdentityTransformation
gap> f := Transformation( [ 5, 9, 1, 7, 9, 5, 2, 8, 4, 1 ] );;
gap> g := InverseOfTransformation(f);
Transformation( [ 3, 7, 1, 9, 1, 1, 4, 8, 2, 1 ] )
gap> f * g * f = f and g * f * g = g;
true
gap> f := Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1);;
gap> g := InverseOfTransformation(f);;
gap> f * g * f = f and g * f * g = g;
true
gap> g := InverseOfTransformation(1);
Error, InverseOfTransformation: <f> must be a transformation (not the integer \
1)
# Test INV_LIST_TRANS
gap> f := Transformation([9, 3, 2, 3, 1, 8, 2, 7, 8, 3, 12, 10]);;
gap> g := INV_LIST_TRANS([1, 2, 3, 6, 5], f);
Transformation( [ 5, 3, 2, 4, 5, 6, 7, 6, 1 ] )
gap> ForAll([1, 2, 3, 6, 5], i -> (i ^ f) ^ g = i);
true
gap> f := Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1);;
gap> g := INV_LIST_TRANS(ImageSetOfTransformation(f), f);
IdentityTransformation
gap> ForAll(ImageSetOfTransformation(f), i -> (i ^ f) ^ g = i);
true
gap> f := Transformation([12, 3, 4, 12, 1, 2, 12, 1, 5, 1, 10, 7]);;
gap> g := INV_LIST_TRANS([1 .. 3], f);
Transformation( [ 1, 2, 2, 3, 5, 6, 7, 8, 9, 10, 11, 1 ] )
gap> ForAll([1 .. 3], i -> (i ^ f) ^ g = i);
true
gap> f := Transformation([11, 9, 3, 8, 10, 11, 6, 1, 8, 8, 4, 11]);;
gap> g := INV_LIST_TRANS([1 .. 5], f);
Transformation( [ 1, 2, 3, 4, 5, 6, 7, 4, 2, 5, 1 ] )
gap> ForAll([1 .. 5], i -> (i ^ f) ^ g = i);
true
gap> f := Transformation([5, 5, 3, 10, 10, 10, 2, 12, 11, 9, 1, 6]);;
gap> g := INV_LIST_TRANS([2, 3], f);
Transformation( [ 1, 2, 3, 4, 2 ] )
gap> ForAll([2, 3], i -> (i ^ f) ^ g = i);
true
gap> g := INV_LIST_TRANS([2, 3, 4, 7], f);
Transformation( [ 1, 7, 3, 4, 2, 6, 7, 8, 9, 4 ] )
gap> ForAll([2, 3, 4, 7], i -> (i ^ f) ^ g = i);
true
gap> g := INV_LIST_TRANS([65536], f);
IdentityTransformation
gap> INV_LIST_TRANS([1, -1], f);
Error, INV_LIST_TRANS: <list>[2] must be a positive small integer (not the int\
eger -1)
gap> INV_LIST_TRANS("a", f);
Error, INV_LIST_TRANS: <list>[1] must be a positive small integer (not a chara\
cter)
gap> INV_LIST_TRANS(0, f);
Error, INV_LIST_TRANS: <list> must be a dense list (not the integer 0)
gap> INV_LIST_TRANS([1, 2], "a");
Error, INV_LIST_TRANS: <f> must be a transformation (not a list (string))
gap> INV_LIST_TRANS([1, -1], Transformation([1], [65537]));
Error, INV_LIST_TRANS: <list>[2] must be a positive small integer (not the int\
eger -1)
# IndexPeriodOfTransformation
gap> f := Transformation([4, 3, 8, 9, 3, 5, 8, 10, 5, 6, 2, 8]);;
gap> val := IndexPeriodOfTransformation(f);
[ 3, 5 ]
gap> ind := val[1];; per := val[2];;
gap> RankOfTransformation(f ^ (ind - 1), DegreeOfTransformation(f)) >
> RankOfTransformation(f ^ ind, DegreeOfTransformation(f));
true
gap> f ^ (ind + per) = f ^ ind;
true
gap> ForAny([1 .. per - 1], m -> f ^ (ind + m) = f ^ ind);
false
gap> f := Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1)
> * (14918, 184, 141)(14140, 124);;
gap> val := IndexPeriodOfTransformation(f);
[ 1, 6 ]
gap> ind := val[1];; per := val[2];;
gap> RankOfTransformation(f ^ (ind - 1), DegreeOfTransformation(f)) >
> RankOfTransformation(f ^ ind, DegreeOfTransformation(f));
true
gap> f ^ (ind + per) = f ^ ind;
true
gap> ForAny([1 .. per - 1], m -> f ^ (ind + m) = f ^ ind);
false
gap> f := Transformation([1, 65537, 2, 4, 6],
> [65537, 2, 3, 5, 7]);;
gap> IndexPeriodOfTransformation(f);
[ 3, 1 ]
gap> f := Transformation(
> [5, 23, 27, 8, 21, 49, 36, 33, 4, 44, 3, 49, 48, 18, 10, 30, 47, 3, 41, 35,
> 33, 15, 39, 19, 37, 24, 26, 2, 16, 47, 9, 7, 28, 47, 25, 21, 50, 23, 18, 42, 26,
> 40, 40, 4, 43, 27, 45, 35, 40, 14]);;
gap> val := IndexPeriodOfTransformation(f);
[ 14, 4 ]
gap> ind := val[1];; per := val[2];;
gap> RankOfTransformation(f ^ (ind - 1), DegreeOfTransformation(f)) >
> RankOfTransformation(f ^ ind, DegreeOfTransformation(f));
true
gap> f ^ (ind + per) = f ^ ind;
true
gap> ForAny([1 .. per - 1], m -> f ^ (ind + m) = f ^ ind);
false
gap> f ^ 18 = f ^ 14;
true
gap> f :=
> Transformation( [ 74, 33, 77, 60, 65, 37, 24, 22, 16, 49, 58, 16, 62, 7, 69,
> 38, 97, 44, 56, 5, 3, 74, 89, 28, 95, 94, 56, 6, 38, 58, 45, 63, 32, 32,
> 38, 27, 36, 28, 81, 41, 85, 95, 55, 19, 58, 16, 65, 55, 61, 87, 40, 37, 89,
> 47, 48, 42, 82, 37, 34, 25, 26, 19, 44, 13, 15, 27, 41, 99, 15, 69, 8, 19,
> 85, 8, 96, 8, 69, 97, 31, 22, 71, 39, 91, 13, 76, 53, 37, 78, 27, 91, 46,
> 32, 64, 70, 84, 92, 37, 68, 10, 68 ] );;
gap> val := IndexPeriodOfTransformation(f);
[ 10, 42 ]
gap> ind := val[1];; per := val[2];;
gap> RankOfTransformation(f ^ (ind - 1), DegreeOfTransformation(f)) >
> RankOfTransformation(f ^ ind, DegreeOfTransformation(f));
true
gap> f ^ (ind + per) = f ^ ind;
true
gap> ForAny([1 .. per - 1], m -> f ^ (ind + m) = f ^ ind);
false
gap> f :=
> Transformation( [ 45, 51, 70, 26, 87, 94, 23, 19, 86, 46, 45, 51, 57, 13, 67,
> 5, 38, 20, 51, 25, 67, 91, 38, 29, 43, 44, 84, 71, 11, 39, 52, 40, 12, 58,
> 1, 83, 9, 27, 1, 25, 86, 83, 15, 38, 86, 61, 43, 16, 55, 16, 96, 46, 46,
> 70, 29, 11, 13, 8, 14, 67, 84, 17, 79, 44, 59, 19, 35, 19, 61, 49, 32, 24,
> 45, 71, 2, 90, 12, 4, 43, 61, 63, 64, 34, 92, 77, 19, 8, 23, 85, 26, 87, 8,
> 76, 18, 48, 33, 8, 7, 38, 39 ] );;
gap> val := IndexPeriodOfTransformation(f);
[ 13, 4 ]
gap> ind := val[1];; per := val[2];;
gap> RankOfTransformation(f ^ (ind - 1), DegreeOfTransformation(f)) >
> RankOfTransformation(f ^ ind, DegreeOfTransformation(f));
true
gap> f ^ (ind + per) = f ^ ind;
true
gap> ForAny([1 .. per - 1], m -> f ^ (ind + m) = f ^ ind);
false
gap> f :=
> Transformation( [ 14, 24, 70, 1, 50, 72, 13, 64, 65, 68, 54, 20, 69, 32, 88,
> 60, 93, 100, 37, 27, 15, 7, 84, 95, 84, 36, 8, 20, 90, 55, 78, 48, 93, 10,
> 51, 76, 26, 83, 29, 39, 93, 48, 51, 93, 50, 92, 95, 51, 31, 17, 76, 43, 5,
> 19, 94, 11, 70, 84, 22, 95, 5, 44, 44, 6, 7, 56, 4, 57, 94, 100, 86, 30,
> 38, 80, 77, 60, 45, 99, 38, 11, 60, 62, 76, 50, 13, 48, 27, 82, 68, 99, 17,
> 81, 16, 3, 14, 90, 22, 71, 41, 98 ] );;
gap> val := IndexPeriodOfTransformation(f);
[ 16, 7 ]
gap> ind := val[1];; per := val[2];;
gap> RankOfTransformation(f ^ (ind - 1), DegreeOfTransformation(f)) >
> RankOfTransformation(f ^ ind, DegreeOfTransformation(f));
true
gap> f ^ (ind + per) = f ^ ind;
true
gap> ForAny([1 .. per - 1], m -> f ^ (ind + m) = f ^ ind);
false
gap> IndexPeriodOfTransformation(IdentityTransformation);
[ 1, 1 ]
gap> IndexPeriodOfTransformation("a");
Error, IndexPeriodOfTransformation: <f> must be a transformation (not a list (\
string))
gap> IndexPeriodOfTransformation(Transformation([2, 1]));
[ 1, 2 ]
# Test SMALLEST_IDEM_POW_TRANS
gap> f := Transformation([4, 3, 8, 9, 3, 5, 8, 10, 5, 6, 2, 8]);;
gap> m := SMALLEST_IDEM_POW_TRANS(f);
5
gap> IsIdempotent(f ^ m);
true
gap> f ^ (2 * m) = f ^ m;
true
gap> f := Transformation([5, 23, 27, 8, 21, 49, 36, 33, 4, 44, 3, 49, 48, 18,
> 10, 30, 47, 3, 41, 35, 33, 15, 39, 19, 37, 24, 26, 2, 16, 47, 9, 7, 28, 47,
> 25, 21, 50, 23, 18, 42, 26, 40, 40, 4, 43, 27, 45, 35, 40, 14]);;
gap> SMALLEST_IDEM_POW_TRANS(f);
16
gap> f ^ 32 = f ^ 16;
true
gap> ForAny([1 .. 15], x -> f ^ (2 * x) = f ^ x);
false
# POW_KER_PERM
gap> POW_KER_PERM([], (1,2,3));
[ ]
gap> POW_KER_PERM([1 .. 5], (1,2,3));
[ 1, 2, 3, 4, 5 ]
gap> POW_KER_PERM([1 .. 5] * 1, (1,2,3));
[ 1, 2, 3, 4, 5 ]
gap> POW_KER_PERM([1 .. 5] * 0 + 1, (1,2,3));
[ 1, 1, 1, 1, 1 ]
gap> POW_KER_PERM([1 .. 3], (1,2,3)(4,5));
[ 1, 2, 3 ]
gap> POW_KER_PERM([1 .. 3] * 1, (1,2,3)(4,5));
[ 1, 2, 3 ]
gap> POW_KER_PERM([1 .. 3] * 0 + 1, (1,2,3)(4,5));
[ 1, 1, 1 ]
gap> POW_KER_PERM([1 .. 3], (1,2,3)(4,5));
[ 1, 2, 3 ]
gap> POW_KER_PERM([1 .. 65537], (1, 65537)) = [1 .. 65537];
true
gap> POW_KER_PERM([1 .. 65537] * 1, (1, 65537)) = [1 .. 65537];
true
gap> POW_KER_PERM([1 .. 65538] * 0 + 1, (1, 65537)) = [1 .. 65538] * 0 + 1;
true
gap> POW_KER_PERM([1 .. 100], (1,2,3)(65537, 65538)) = [1 .. 100];
true
gap> POW_KER_PERM([1 .. 100] * 1, (1,2,3)(65537, 65538)) = [1 .. 100];
true
gap> POW_KER_PERM([1 .. 100] * 0 + 1, (1,2,3)(65537, 65538)) = [1 .. 100] * 0 + 1;
true
gap> POW_KER_PERM([1, 2], 1);
Error, POW_KER_PERM: <p> must be a permutation (not the integer 1)
gap> POW_KER_PERM(1, 2);
Error, POW_KER_PERM: <p> must be a permutation (not the integer 2)
gap> Set(SymmetricGroup(3), p -> POW_KER_PERM([1, 1, 2], p));
[ [ 1, 1, 2 ], [ 1, 2, 1 ], [ 1, 2, 2 ] ]
gap> Set(SymmetricGroup(3), p -> POW_KER_PERM([1, 2, 3], p));
[ [ 1, 2, 3 ] ]
gap> Set(SymmetricGroup(3), p -> POW_KER_PERM([1, 1, 1], p));
[ [ 1, 1, 1 ] ]
# ON_KERNEL_ANTI_ACTION
gap> f := Transformation([84, 99, 9, 73, 33, 70, 77, 69, 41, 18, 63, 29, 42,
> 33, 75, 56, 79, 63, 89, 90, 64, 98, 49, 35, 89, 71, 3, 70, 20, 2, 26, 11,
> 39, 9, 7, 89, 90, 48, 89, 85, 8, 56, 42, 10, 61, 25, 98, 55, 39, 92, 62, 21,
> 34, 57, 44, 14, 14, 92, 53, 64, 59, 84, 12, 87, 78, 10, 83, 30, 32, 53, 44, 68,
> 73, 2, 86, 23, 48, 47, 14, 79, 93, 15, 23, 76, 34, 97, 77, 55, 11, 33, 47, 91,
> 87, 87, 67, 93, 18, 59, 86]);;
gap> g := Transformation([16, 99, 73, 60, 74, 17, 95, 85, 49, 79, 4, 33, 66,
> 15, 44, 77, 73, 41, 55, 93, 84, 67, 68, 69, 94, 31, 2, 29, 5, 42, 10, 63, 58,
> 34, 72, 4, 53, 93, 89, 67, 34, 15, 57, 29, 4, 62, 76, 20, 34, 52, 22, 35,
> 75, 29, 98, 22, 29, 78, 40, 46, 28, 6, 15, 55, 6, 90, 16, 12, 12, 65, 55, 26,
> 66, 89, 36, 36, 25, 61, 57, 83, 38, 41, 93, 2, 39, 87, 85, 26, 17, 83, 92, 97,
> 43, 30, 15, 5, 13, 94, 44]);;
gap> ON_KERNEL_ANTI_ACTION(FlatKernelOfTransformation(g), f, 0);
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 5, 13, 14, 15, 11, 16, 17, 18,
19, 9, 20, 16, 18, 21, 6, 22, 23, 24, 25, 26, 3, 27, 16, 17, 28, 16, 29,
30, 14, 11, 31, 32, 19, 19, 33, 26, 34, 35, 36, 9, 37, 37, 11, 11, 34, 38,
18, 39, 1, 40, 30, 41, 31, 22, 42, 43, 38, 37, 8, 4, 23, 44, 45, 28, 46,
11, 15, 47, 2, 45, 13, 9, 48, 7, 33, 25, 5, 46, 49, 30, 30, 50, 47, 10, 39,
44 ]
gap> last = FlatKernelOfTransformation(f * g);
true
gap> f := Transformation([2, 12, 11, 8, 18, 14, 6, 2, 9, 17, 3, 15, 2, 18,
> 17, 1, 20, 4, 19, 12]) ^ (1, 65537);;
gap> g := Transformation([11, 12, 9, 13, 20, 20, 2, 14, 18, 20, 7, 3, 19, 9,
> 18, 20, 18, 11, 5, 16]);;
gap> ON_KERNEL_ANTI_ACTION(FlatKernelOfTransformation(g, 65537), f, 0)
> = FlatKernelOfTransformation(f * g, 65537);
true
gap> ON_KERNEL_ANTI_ACTION([1 .. 65538], f, 0)
> = FlatKernelOfTransformation(f, 65538);
true
gap> h := f * g ^ 3 * f * g * f ^ 10;
<transformation on 65537 pts with rank 65522>
gap> ON_KERNEL_ANTI_ACTION(FlatKernelOfTransformation(g), h, 0)
> = FlatKernelOfTransformation(h * g);
Error, ON_KERNEL_ANTI_ACTION: the length of <ker> must be at least 65537
gap> ON_KERNEL_ANTI_ACTION([1 .. 10],
> Transformation([7, 1, 4, 3, 2, 7, 7, 6, 6, 5]), 0);
[ 1, 2, 3, 4, 5, 1, 1, 6, 6, 7 ]
gap> ON_KERNEL_ANTI_ACTION([0],
> Transformation([7, 1, 4, 3, 2, 7, 7, 6, 6, 5]), 15);
[ 1, 2, 3, 4, 5, 1, 1, 6, 6, 7, 8, 9, 10, 11, 12 ]
gap> ON_KERNEL_ANTI_ACTION([0],
> Transformation([7, 1, 4, 3, 2, 7, 7, 6, 6, 5]), 5);
[ 1, 2, 3, 4, 5 ]
gap> ON_KERNEL_ANTI_ACTION([0],
> Transformation([7, 1, 4, 3, 2, 7, 7, 6, 6, 5]), 10);
[ 1, 2, 3, 4, 5, 1, 1, 6, 6, 7 ]
gap> ON_KERNEL_ANTI_ACTION([1 .. 15],
> Transformation([7, 1, 4, 3, 2, 7, 7, 6, 6, 5]), 0);
[ 1, 2, 3, 4, 5, 1, 1, 6, 6, 7, 8, 9, 10, 11, 12 ]
gap> ON_KERNEL_ANTI_ACTION([1 .. 5],
> Transformation([5, 1, 5, 3, 2, 7, 7, 6, 6, 5]), 0);
Error, ON_KERNEL_ANTI_ACTION: the length of <ker> must be at least 10
gap> ON_KERNEL_ANTI_ACTION([1 .. 5], IdentityTransformation, 0);
[ 1, 2, 3, 4, 5 ]
gap> ON_KERNEL_ANTI_ACTION([1 .. 5], (), 0);
Error, ON_KERNEL_ANTI_ACTION: <f> must be a transformation (not a permutation \
(small))
gap> ON_KERNEL_ANTI_ACTION([], IdentityTransformation, 10);
[ ]
gap> ON_KERNEL_ANTI_ACTION([], IdentityTransformation, 10);
[ ]
gap> f := ID_TRANS4;;
gap> IsTrans4Rep(f);
true
gap> ON_KERNEL_ANTI_ACTION([], f, 10);
[ ]
gap> ON_KERNEL_ANTI_ACTION([], f, 10);
[ ]
# INV_KER_TRANS
gap> f := Transformation([9, 5, 3, 5, 10, 3, 1, 9, 6, 7]);;
gap> g := RightOne(f) * (2,4)(3,6,5);
Transformation( [ 1, 1, 6, 6, 3, 5, 7, 7 ] )
gap> ker := FlatKernelOfTransformation(g, DegreeOfTransformation(f));
[ 1, 1, 2, 2, 3, 4, 5, 5, 6, 7 ]
gap> h := INV_KER_TRANS(ker, f);
Transformation( [ 7, 7, 6, 6, 4, 9, 10, 10, 8, 5 ] )
gap> OnKernelAntiAction(OnKernelAntiAction(ker, f), h) = ker;
true
gap> h * f * g = g;
true
gap> ker := FlatKernelOfTransformation(g, DegreeOfTransformation(f) + 2);
[ 1, 1, 2, 2, 3, 4, 5, 5, 6, 7, 8, 9 ]
gap> h := INV_KER_TRANS(ker, f);
Transformation( [ 7, 7, 6, 6, 4, 9, 10, 10, 8, 5 ] )
gap> OnKernelAntiAction(OnKernelAntiAction(ker, f), h) = ker;
true
gap> h * f * g = g;
true
gap> f := AsTransformation((1,2,3));;
gap> h := INV_KER_TRANS([1 .. 65537], f);
Transformation( [ 3, 1, 2 ] )
gap> OnKernelAntiAction(OnKernelAntiAction([1 .. 65537], f), h) = [1 .. 65537];
true
gap> h * f * IdentityTransformation = IdentityTransformation;
true
gap> f := Transformation([9, 5, 3, 5, 10, 3, 1, 9, 6, 7]) ^ (1, 65537);;
gap> g := RightOne(f) * (2,4)(3,6,5);;
gap> ker := FlatKernelOfTransformation(g, DegreeOfTransformation(f));;
gap> h := INV_KER_TRANS(ker, f);
<transformation on 65537 pts with rank 65534>
gap> OnKernelAntiAction(OnKernelAntiAction(ker, f), h) = ker;
true
gap> h * f * g = g;
true
gap> ker := FlatKernelOfTransformation(g, DegreeOfTransformation(f) + 2);;
gap> h := INV_KER_TRANS(ker, f);
<transformation on 65537 pts with rank 65534>
gap> OnKernelAntiAction(OnKernelAntiAction(ker, f), h) = ker;
true
gap> h * f * g = g;
true
gap> f := AsTransformation((1,2,65537));;
gap> h := INV_KER_TRANS([1 .. 65537], f);
<transformation on 65537 pts with rank 65537>
gap> OnKernelAntiAction(OnKernelAntiAction([1 .. 65537], f), h) = [1 .. 65537];
true
gap> h * f * IdentityTransformation = IdentityTransformation;
true
gap> f := AsTransformation((1,2)(3,65537));;
gap> h := INV_KER_TRANS([1, 2], f);
Transformation( [ 2, 1 ] )
gap> h := INV_KER_TRANS([1, 2], [1]);
Error, INV_KER_TRANS: <f> must be a transformation (not a strictly-sorted plai\
n list of cyclotomics)
# IS_IDEM_TRANS
gap> IS_IDEM_TRANS(IdentityTransformation);
true
gap> IS_IDEM_TRANS(Transformation([1, 2, 1]));
true
gap> IS_IDEM_TRANS(Transformation([1, 1, 2]));
false
gap> IS_IDEM_TRANS(Transformation([65537], [1]));
true
gap> IS_IDEM_TRANS(Transformation([1, 65537], [2, 1]));
false
gap> IS_IDEM_TRANS(());
Error, IS_IDEM_TRANS: <f> must be a transformation (not a permutation (small))
# COMPONENT_REPS_TRANS
gap> COMPONENT_REPS_TRANS(Transformation([1, 2, 1]));
[ [ 3 ], [ 2 ] ]
gap> COMPONENT_REPS_TRANS(Transformation([1, 1, 1]));
[ [ 2, 3 ] ]
gap> COMPONENT_REPS_TRANS(Transformation([1, 1, 2]));
[ [ 3 ] ]
gap> f := Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]);;
gap> COMPONENT_REPS_TRANS(f);
[ [ 3, 4, 8, 10 ] ]
gap> f := Transformation([3, 8, 1, 9, 9, 4, 10, 5, 10, 6, 12, 11, 14, 13, 15,
> 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28,
> 31, 30, 29]);;
gap> COMPONENT_REPS_TRANS(f);
[ [ 2, 7 ], [ 1 ], [ 11 ], [ 13 ], [ 15 ], [ 16 ], [ 17 ], [ 18 ], [ 19 ],
[ 20 ], [ 21 ], [ 22 ], [ 23 ], [ 24 ], [ 25 ], [ 26 ], [ 27 ], [ 28 ],
[ 29 ], [ 30 ] ]
gap> COMPONENT_REPS_TRANS(IdentityTransformation);
[ ]
gap> f :=
> Transformation([9, 45, 53, 15, 42, 97, 71, 66, 7, 88, 6, 98, 95, 36, 20, 59,
> 94, 6, 81, 70, 65, 29, 78, 37, 74, 48, 52, 4, 32, 93, 18, 13, 55, 94, 49, 42,
> 99, 46, 35, 84, 52, 79, 80, 7, 85, 53, 89, 70, 79, 27, 84, 99, 9, 73, 33, 70,
> 77, 69, 41, 18, 63, 29, 42, 33, 75, 56, 79, 63, 89, 90, 64, 98, 49, 35, 100,
> 89, 71, 3, 70, 20, 2, 26, 11, 39, 9, 7, 89, 90, 48, 89, 85, 8, 56, 42, 10,
> 61, 25, 98, 55, 39]);;
gap> COMPONENT_REPS_TRANS(f);
[ [ 1, 16, 19, 23, 24, 38, 44, 50, 57, 86, 91 ],
[ 5, 14, 17, 21, 22, 28, 30, 31, 34, 40, 43, 47, 51, 54, 58, 60, 62, 67,
68, 76, 82, 83, 87, 92, 96 ], [ 12, 72 ] ]
gap> Set(ComponentRepsOfTransformation(f), x ->
> Union(List(x, i -> ComponentTransformationInt(f, i))))
> = Set(ComponentsOfTransformation(f), AsSSortedList);
true
gap> f := Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1)
> * (14918, 184, 141)(14140, 124);;
gap> COMPONENT_REPS_TRANS(f);;
gap> COMPONENT_REPS_TRANS("a");
Error, COMPONENT_REPS_TRANS: <f> must be a transformation (not a list (string)\
)
# NR_COMPONENTS_TRANS
gap> NR_COMPONENTS_TRANS(Transformation([1, 2, 1]));
2
gap> NR_COMPONENTS_TRANS(Transformation([1, 1, 1]));
1
gap> NR_COMPONENTS_TRANS(Transformation([1, 1, 2]));
1
gap> f := Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]);;
gap> NR_COMPONENTS_TRANS(f);
1
gap> f := Transformation([3, 8, 1, 9, 9, 4, 10, 5, 10, 6, 12, 11, 14, 13, 15,
> 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28,
> 31, 30, 29]);;
gap> NR_COMPONENTS_TRANS(f);
20
gap> NR_COMPONENTS_TRANS(IdentityTransformation);
0
gap> f :=
> Transformation([9, 45, 53, 15, 42, 97, 71, 66, 7, 88, 6, 98, 95, 36, 20, 59,
> 94, 6, 81, 70, 65, 29, 78, 37, 74, 48, 52, 4, 32, 93, 18, 13, 55, 94, 49, 42,
> 99, 46, 35, 84, 52, 79, 80, 7, 85, 53, 89, 70, 79, 27, 84, 99, 9, 73, 33, 70,
> 77, 69, 41, 18, 63, 29, 42, 33, 75, 56, 79, 63, 89, 90, 64, 98, 49, 35, 100,
> 89, 71, 3, 70, 20, 2, 26, 11, 39, 9, 7, 89, 90, 48, 89, 85, 8, 56, 42, 10,
> 61, 25, 98, 55, 39]);;
gap> NR_COMPONENTS_TRANS(f);
3
gap> f := Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1)
> * (14918, 184, 141)(14140, 124);;
gap> NR_COMPONENTS_TRANS(f);
65533
gap> NR_COMPONENTS_TRANS("a");
Error, NR_COMPONENTS_TRANS: <f> must be a transformation (not a list (string))
# COMPONENTS_TRANS
gap> COMPONENTS_TRANS(Transformation([1, 2, 1]));
[ [ 1, 3 ], [ 2 ] ]
gap> COMPONENTS_TRANS(Transformation([1, 1, 1]));
[ [ 1, 2, 3 ] ]
gap> COMPONENTS_TRANS(Transformation([1, 1, 2]));
[ [ 1, 2, 3 ] ]
gap> COMPONENTS_TRANS(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]));
[ [ 1, 2, 6, 9, 3, 7, 4, 5, 8, 10 ] ]
gap> COMPONENTS_TRANS(Transformation([3, 8, 1, 9, 9, 4, 10, 5, 10, 6, 12, 11,
> 14, 13, 15, 16, 17, 18, 19, 20, 21, 22,
> 23, 24, 25, 26, 27, 28, 31, 30, 29]));;
gap> COMPONENTS_TRANS(IdentityTransformation);
[ ]
gap> COMPONENTS_TRANS(Transformation([9, 45, 53, 15, 42, 97, 71, 66, 7, 88, 6,
> 98, 95, 36, 20, 59, 94, 6, 81, 70, 65,
> 29, 78, 37, 74, 48, 52, 4, 32, 93, 18,
> 13, 55, 94, 49, 42, 99, 46, 35, 84, 52,
> 79, 80, 7, 85, 53, 89, 70, 79, 27, 84,
> 99, 9, 73, 33, 70, 77, 69, 41, 18, 63,
> 29, 42, 33, 75, 56, 79, 63, 89, 90, 64,
> 98, 49, 35, 100, 89, 71, 3, 70, 20, 2,
> 26, 11, 39, 9, 7, 89, 90, 48, 89, 85, 8,
> 56, 42, 10, 61, 25, 98, 55, 39]));
[ [ 1, 9, 7, 71, 64, 33, 55, 2, 45, 85, 3, 53, 16, 59, 41, 52, 99, 19, 81,
23, 78, 24, 37, 27, 38, 46, 44, 50, 57, 77, 86, 91 ],
[ 4, 15, 20, 70, 90, 89, 48, 5, 42, 79, 6, 97, 25, 74, 35, 49, 8, 66, 56,
10, 88, 11, 13, 95, 14, 36, 17, 94, 18, 21, 65, 75, 100, 39, 22, 29,
32, 26, 28, 30, 93, 31, 34, 40, 84, 43, 80, 47, 51, 54, 73, 58, 69, 60,
61, 63, 62, 67, 68, 76, 82, 83, 87, 92, 96 ], [ 12, 98, 72 ] ]
gap> comps := COMPONENTS_TRANS(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1)
> * (14918, 184, 141)(14140, 124));;
gap> Length(comps);
65533
gap> Union(comps) = [1 .. 70000];
true
gap> COMPONENTS_TRANS("a");
Error, COMPONENTS_TRANS: <f> must be a transformation (not a list (string))
# COMPONENT_TRANS_INT
gap> COMPONENT_TRANS_INT(Transformation([1, 2, 1]), 1);
[ 1 ]
gap> COMPONENT_TRANS_INT(Transformation([1, 2, 1]), 2);
[ 2 ]
gap> COMPONENT_TRANS_INT(Transformation([1, 2, 1]), 3);
[ 3, 1 ]
gap> COMPONENT_TRANS_INT(Transformation([1, 2, 1]), 5);
[ 5 ]
gap> COMPONENT_TRANS_INT(Transformation([1, 1, 1]), 1);
[ 1 ]
gap> COMPONENT_TRANS_INT(Transformation([1, 1, 1]), 2);
[ 2, 1 ]
gap> COMPONENT_TRANS_INT(Transformation([1, 1, 1]), 3);
[ 3, 1 ]
gap> COMPONENT_TRANS_INT(Transformation([1, 1, 1]), 5);
[ 5 ]
gap> COMPONENT_TRANS_INT(Transformation([1, 1, 2]), 1);
[ 1 ]
gap> COMPONENT_TRANS_INT(Transformation([1, 1, 2]), 2);
[ 2, 1 ]
gap> COMPONENT_TRANS_INT(Transformation([1, 1, 2]), 3);
[ 3, 2, 1 ]
gap> COMPONENT_TRANS_INT(Transformation([1, 1, 2]), 5);
[ 5 ]
gap> COMPONENT_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 1);
[ 1, 2, 6, 9 ]
gap> COMPONENT_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 2);
[ 2, 6, 9, 1 ]
gap> COMPONENT_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 3);
[ 3, 7, 9, 1, 2, 6 ]
gap> COMPONENT_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 4);
[ 4, 2, 6, 9, 1 ]
gap> COMPONENT_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 5);
[ 5, 6, 9, 1, 2 ]
gap> COMPONENT_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 6);
[ 6, 9, 1, 2 ]
gap> COMPONENT_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 7);
[ 7, 9, 1, 2, 6 ]
gap> COMPONENT_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 8);
[ 8, 1, 2, 6, 9 ]
gap> COMPONENT_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 9);
[ 9, 1, 2, 6 ]
gap> COMPONENT_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 10);
[ 10, 5, 6, 9, 1, 2 ]
gap> COMPONENT_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 20);
[ 20 ]
gap> COMPONENT_TRANS_INT(Transformation([3, 8, 1, 9, 9, 4, 10, 5, 10, 6, 12,
> 11, 14, 13, 15, 16, 17, 18, 19, 20,
> 21, 22, 23, 24, 25, 26, 27, 28, 31,
> 30, 29]), 10);
[ 10, 6, 4, 9 ]
gap> COMPONENT_TRANS_INT(Transformation([3, 8, 1, 9, 9, 4, 10, 5, 10, 6, 12,
> 11, 14, 13, 15, 16, 17, 18, 19, 20,
> 21, 22, 23, 24, 25, 26, 27, 28, 31,
> 30, 29]), 40);
[ 40 ]
gap> COMPONENT_TRANS_INT(Transformation([3, 8, 1, 9, 9, 4, 10, 5, 10, 6, 12,
> 11, 14, 13, 15, 16, 17, 18, 19, 20,
> 21, 22, 23, 24, 25, 26, 27, 28, 31,
> 30, 29]), 1);
[ 1, 3 ]
gap> COMPONENT_TRANS_INT(IdentityTransformation, 10);
[ 10 ]
gap> COMPONENT_TRANS_INT(IdentityTransformation, 0);
Error, COMPONENT_TRANS_INT: <pt> must be a positive small integer (not the int\
eger 0)
gap> COMPONENT_TRANS_INT(IdentityTransformation, "a");
Error, COMPONENT_TRANS_INT: <pt> must be a positive small integer (not a list \
(string))
gap> COMPONENT_TRANS_INT((), 1);
Error, COMPONENT_TRANS_INT: <f> must be a transformation (not a permutation (s\
mall))
gap> COMPONENT_TRANS_INT(Transformation([9, 45, 53, 15, 42, 97, 71, 66, 7, 88, 6,
> 98, 95, 36, 20, 59, 94, 6, 81, 70, 65,
> 29, 78, 37, 74, 48, 52, 4, 32, 93, 18,
> 13, 55, 94, 49, 42, 99, 46, 35, 84, 52,
> 79, 80, 7, 85, 53, 89, 70, 79, 27, 84,
> 99, 9, 73, 33, 70, 77, 69, 41, 18, 63,
> 29, 42, 33, 75, 56, 79, 63, 89, 90, 64,
> 98, 49, 35, 100, 89, 71, 3, 70, 20, 2,
> 26, 11, 39, 9, 7, 89, 90, 48, 89, 85, 8,
> 56, 42, 10, 61, 25, 98, 55, 39]), 1);
[ 1, 9, 7, 71, 64, 33, 55 ]
gap> COMPONENT_TRANS_INT(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1)
> * (14918, 184, 141)(14140, 124), 1);
[ 1 ]
gap> COMPONENT_TRANS_INT(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1)
> * (14918, 184, 141)(14140, 124), 14918);
[ 14918, 184, 141 ]
gap> COMPONENT_TRANS_INT(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1)
> * (14918, 184, 141)(14140, 124), 69999);
[ 69999, 1 ]
# CYCLE_TRANS_INT
gap> CYCLE_TRANS_INT(Transformation([1, 2, 1]), 1);
[ 1 ]
gap> CYCLE_TRANS_INT(Transformation([1, 2, 1]), 2);
[ 2 ]
gap> CYCLE_TRANS_INT(Transformation([1, 2, 1]), 3);
[ 1 ]
gap> CYCLE_TRANS_INT(Transformation([1, 2, 1]), 5);
[ 5 ]
gap> CYCLE_TRANS_INT(Transformation([1, 1, 1]), 1);
[ 1 ]
gap> CYCLE_TRANS_INT(Transformation([1, 1, 1]), 2);
[ 1 ]
gap> CYCLE_TRANS_INT(Transformation([1, 1, 1]), 3);
[ 1 ]
gap> CYCLE_TRANS_INT(Transformation([1, 1, 1]), 5);
[ 5 ]
gap> CYCLE_TRANS_INT(Transformation([1, 1, 2]), 1);
[ 1 ]
gap> CYCLE_TRANS_INT(Transformation([1, 1, 2]), 2);
[ 1 ]
gap> CYCLE_TRANS_INT(Transformation([1, 1, 2]), 3);
[ 1 ]
gap> CYCLE_TRANS_INT(Transformation([1, 1, 2]), 5);
[ 5 ]
gap> CYCLE_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 1);
[ 1, 2, 6, 9 ]
gap> CYCLE_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 2);
[ 2, 6, 9, 1 ]
gap> CYCLE_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 3);
[ 9, 1, 2, 6 ]
gap> CYCLE_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 4);
[ 2, 6, 9, 1 ]
gap> CYCLE_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 5);
[ 6, 9, 1, 2 ]
gap> CYCLE_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 6);
[ 6, 9, 1, 2 ]
gap> CYCLE_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 7);
[ 9, 1, 2, 6 ]
gap> CYCLE_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 8);
[ 1, 2, 6, 9 ]
gap> CYCLE_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 9);
[ 9, 1, 2, 6 ]
gap> CYCLE_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 10);
[ 6, 9, 1, 2 ]
gap> CYCLE_TRANS_INT(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]), 20);
[ 20 ]
gap> CYCLE_TRANS_INT(Transformation([3, 8, 1, 9, 9, 4, 10, 5, 10, 6, 12,
> 11, 14, 13, 15, 16, 17, 18, 19, 20,
> 21, 22, 23, 24, 25, 26, 27, 28, 31,
> 30, 29]), 10);
[ 10, 6, 4, 9 ]
gap> CYCLE_TRANS_INT(Transformation([3, 8, 1, 9, 9, 4, 10, 5, 10, 6, 12,
> 11, 14, 13, 15, 16, 17, 18, 19, 20,
> 21, 22, 23, 24, 25, 26, 27, 28, 31,
> 30, 29]), 40);
[ 40 ]
gap> CYCLE_TRANS_INT(Transformation([3, 8, 1, 9, 9, 4, 10, 5, 10, 6, 12,
> 11, 14, 13, 15, 16, 17, 18, 19, 20,
> 21, 22, 23, 24, 25, 26, 27, 28, 31,
> 30, 29]), 1);
[ 1, 3 ]
gap> CYCLE_TRANS_INT(IdentityTransformation, 10);
[ 10 ]
gap> CYCLE_TRANS_INT(IdentityTransformation, 0);
Error, CYCLE_TRANS_INT: <pt> must be a positive small integer (not the integer\
0)
gap> CYCLE_TRANS_INT(IdentityTransformation, "a");
Error, CYCLE_TRANS_INT: <pt> must be a positive small integer (not a list (str\
ing))
gap> CYCLE_TRANS_INT((), 1);
Error, CYCLE_TRANS_INT: <f> must be a transformation (not a permutation (small\
))
gap> CYCLE_TRANS_INT(Transformation([9, 45, 53, 15, 42, 97, 71, 66, 7, 88, 6,
> 98, 95, 36, 20, 59, 94, 6, 81, 70, 65,
> 29, 78, 37, 74, 48, 52, 4, 32, 93, 18,
> 13, 55, 94, 49, 42, 99, 46, 35, 84, 52,
> 79, 80, 7, 85, 53, 89, 70, 79, 27, 84,
> 99, 9, 73, 33, 70, 77, 69, 41, 18, 63,
> 29, 42, 33, 75, 56, 79, 63, 89, 90, 64,
> 98, 49, 35, 100, 89, 71, 3, 70, 20, 2,
> 26, 11, 39, 9, 7, 89, 90, 48, 89, 85, 8,
> 56, 42, 10, 61, 25, 98, 55, 39]), 1);
[ 33, 55 ]
gap> CYCLE_TRANS_INT(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1)
> * (14918, 184, 141)(14140, 124), 1);
[ 1 ]
gap> CYCLE_TRANS_INT(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1)
> * (14918, 184, 141)(14140, 124), 14918);
[ 14918, 184, 141 ]
gap> CYCLE_TRANS_INT(Transformation([65537 .. 70000],
> [65537 .. 70000] * 0 + 1)
> * (14918, 184, 141)(14140, 124), 69999);
[ 1 ]
# CYCLES_TRANS
gap> CYCLES_TRANS(Transformation([1, 2, 1]));
[ [ 1 ], [ 2 ] ]
gap> CYCLES_TRANS(Transformation([1, 1, 1]));
[ [ 1 ] ]
gap> CYCLES_TRANS(Transformation([1, 1, 2]));
[ [ 1 ] ]
gap> CYCLES_TRANS(Transformation([2, 6, 7, 2, 6, 9, 9, 1, 1, 5]));
[ [ 1, 2, 6, 9 ] ]
gap> CYCLES_TRANS(Transformation([3, 8, 1, 9, 9, 4, 10, 5, 10, 6, 12,
> 11, 14, 13, 15, 16, 17, 18, 19, 20,
> 21, 22, 23, 24, 25, 26, 27, 28, 31,
> 30, 29]));
[ [ 1, 3 ], [ 9, 10, 6, 4 ], [ 11, 12 ], [ 13, 14 ], [ 15 ], [ 16 ], [ 17 ],
[ 18 ], [ 19 ], [ 20 ], [ 21 ], [ 22 ], [ 23 ], [ 24 ], [ 25 ], [ 26 ],
[ 27 ], [ 28 ], [ 29, 31 ], [ 30 ] ]
gap> CYCLES_TRANS(IdentityTransformation);
[ ]
gap> CYCLES_TRANS(Transformation([9, 45, 53, 15, 42, 97, 71, 66, 7, 88, 6,
> 98, 95, 36, 20, 59, 94, 6, 81, 70, 65,
> 29, 78, 37, 74, 48, 52, 4, 32, 93, 18,
--> --------------------
--> maximum size reached
--> --------------------
[ Dauer der Verarbeitung: 0.21 Sekunden
(vorverarbeitet)
]
|
