ConjugatorSpaceGroups fails to compute the conjugator.

[hongyi-zhao]

See my following example:

gap> Sgen:=[ [ [ -1, 0, 0, -15/2 ], [ 0, -1, 0, 1/2 ], [ 3/2, 5/2, 1, 11/2 ], [ 0, 0, 0, 1 ] ], [ [ 1, 18, 0, 13/2 ], [ 0, -1, 0, -1/2 ], [ -3/2, -27/2, -1, -17/4 ], [ 0, 0, 0, 1 ] ]
>     , [ [ -27/2, -41/2, -18, -13/4 ], [ 3/2, 5/2, 2, 1/4 ], [ 17/2, 29/2, 11, 9/4 ], [ 0, 0, 0, 1 ] ], 
>   [ [ -9/2, -77/2, 0, -18 ], [ 1/2, 9/2, 0, 2 ], [ 2, 22, -1, 43/4 ], [ 0, 0, 0, 1 ] ], [ [ -1, 0, 0, 5 ], [ 0, -1, 0, -1 ], [ 0, 0, -1, -13/4 ], [ 0, 0, 0, 1 ] ], 
>   [ [ 1, 0, 0, -9 ], [ 0, 1, 0, 1 ], [ 0, 0, 1, 6 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 2 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, -1 ], [ 0, 0, 0, 1 ] ], 
>   [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ] ];
[ [ [ -1, 0, 0, -15/2 ], [ 0, -1, 0, 1/2 ], [ 3/2, 5/2, 1, 11/2 ], [ 0, 0, 0, 1 ] ], [ [ 1, 18, 0, 13/2 ], [ 0, -1, 0, -1/2 ], [ -3/2, -27/2, -1, -17/4 ], [ 0, 0, 0, 1 ] ]
    , [ [ -27/2, -41/2, -18, -13/4 ], [ 3/2, 5/2, 2, 1/4 ], [ 17/2, 29/2, 11, 9/4 ], [ 0, 0, 0, 1 ] ], 
  [ [ -9/2, -77/2, 0, -18 ], [ 1/2, 9/2, 0, 2 ], [ 2, 22, -1, 43/4 ], [ 0, 0, 0, 1 ] ], [ [ -1, 0, 0, 5 ], [ 0, -1, 0, -1 ], [ 0, 0, -1, -13/4 ], [ 0, 0, 0, 1 ] ], 
  [ [ 1, 0, 0, -9 ], [ 0, 1, 0, 1 ], [ 0, 0, 1, 6 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 2 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, -1 ], [ 0, 0, 0, 1 ] ], 
  [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ] ]
gap> S:=AffineCrystGroupOnLeft(Sgen);
<matrix group with 8 generators>
gap> cc:=[
>   [18,    0,   -4,       1],
>   [-10,    0,    2,    -1/2],
>   [-11,    1,    3,    -1/8],
>   [0,0,0,1]
> ];
[ [ 18, 0, -4, 1 ], [ -10, 0, 2, -1/2 ], [ -11, 1, 3, -1/8 ], [ 0, 0, 0, 1 ] ]
gap> # My method works:
gap> AffineIsomorphismSpaceGroups(SpaceGroupOnLeftIT(3,227,'2'), S^cc);
[ [ 35/8, 43/8, 9/4, 3/32 ], [ -3/8, -17/8, 5/4, -5/32 ], [ 1, 5/4, 1/2, -1/16 ], [ 0, 0, 0, 1 ] ]
gap> SpaceGroupOnLeftIT(3,227,'2')^(last^-1)=S^cc;
true
gap> # ConjugatorSpaceGroups fails:
gap> ConjugatorSpaceGroups(SpaceGroupOnLeftIT(3,227,'2'),S^cc);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `Length' on 1 arguments
The 1st argument is 'fail' which might point to an earlier problem
 at /home/werner/Public/repo/github.com/gap-system/gap.git/lib/methsel2.g:250 called from
Length( str ) at /home/werner/Public/repo/github.com/gap-system/gap.git/pkg/caratinterface/gap/carat.gi:57 called from
CaratNextNumber( str, 1 ) at /home/werner/Public/repo/github.com/gap-system/gap.git/pkg/caratinterface/gap/carat.gi:93 called from
CaratReadNumbers( input, n * m ) at /home/werner/Public/repo/github.com/gap-system/gap.git/pkg/caratinterface/gap/carat.gi:160 called from
CaratReadMatrixFull( input, n, n ) at /home/werner/Public/repo/github.com/gap-system/gap.git/pkg/caratinterface/gap/carat.gi:207 called from
CaratReadMatrix( input, line ) at /home/werner/Public/repo/github.com/gap-system/gap.git/pkg/caratinterface/gap/methods.gi:299 called from
...  at *stdin*:181
type 'quit;' to quit to outer loop
brk> 

As you can see, my method works, but ConjugatorSpaceGroups fails.

Regards,
Zhao

[kiryph]

FYI, I get following Carat error but still no result:

 ┌───────┐   GAP 4.12.2 of 2022-12-18
 │  GAP  │   https://www.gap-system.org
 └───────┘   Architecture: x86_64-apple-darwin22-default64-kv8
 Configuration:  gmp 6.3.0, GASMAN, readline
 Loaded workspace: /Users/kiryph/.cache/gap/workspace
 Packages:   AClib 1.3.2, Alnuth 3.2.1, AtlasRep 2.1.6, AutPGrp 1.11, Browse 1.8.19, CaratInterface 2.3.6,
             CRISP 1.4.6, crypting 0.10.4, Cryst 4.1.27, CrystCat 1.1.10, CTblLib 1.3.4, curlInterface 2.3.1,
             datastructures 0.3.0, debugger 0.4, Digraphs 1.6.1, FactInt 1.6.3, FGA 1.4.0, float 1.0.3,
             Forms 1.2.9, GAPDoc 1.6.6, genss 1.6.8, GRAPE 4.9.0, IO 4.8.0, IRREDSOL 1.4.4, json 2.1.1,
             LAGUNA 3.9.5, Memoisation 1.0, orb 4.9.0, PackageManager 1.3.2, Polenta 1.3.10, Polycyclic 2.16,
             polymaking 0.8.6, PrimGrp 3.4.3, RadiRoot 2.9, recog 1.4.2, ResClasses 4.7.3, SmallGrp 1.5.1,
             Sophus 1.27, SpinSym 1.5.2, TomLib 1.2.9, TransGrp 3.6.3, typeset 1.1, utils 0.81
 Try '??help' for help. See also '?copyright', '?cite' and '?authors'

gap> Sgen:=[ [ [ -1, 0, 0, -15/2 ], [ 0, -1, 0, 1/2 ], [ 3/2, 5/2, 1, 11/2 ], [ 0, 0, 0, 1 ] ], [ [ 1, 18, 0, 13/2 ], [ 0, -1, 0, -1/2 ], [ -3/2, -27/2, -1, -17/4 ], [ 0, 0, 0, 1 ] ]
>     , [ [ -27/2, -41/2, -18, -13/4 ], [ 3/2, 5/2, 2, 1/4 ], [ 17/2, 29/2, 11, 9/4 ], [ 0, 0, 0, 1 ] ],
>   [ [ -9/2, -77/2, 0, -18 ], [ 1/2, 9/2, 0, 2 ], [ 2, 22, -1, 43/4 ], [ 0, 0, 0, 1 ] ], [ [ -1, 0, 0, 5 ], [ 0, -1, 0, -1 ], [ 0, 0, -1, -13/4 ], [ 0, 0, 0, 1 ] ],
>   [ [ 1, 0, 0, -9 ], [ 0, 1, 0, 1 ], [ 0, 0, 1, 6 ], [ 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 2 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, -1 ], [ 0, 0, 0, 1 ] ],
>   [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ] ];;
gap> S:=AffineCrystGroupOnLeft(Sgen);;
gap> cc:=[
>   [18,    0,   -4,       1],
>   [-10,    0,    2,    -1/2],
>   [-11,    1,    3,    -1/8],
>   [0,0,0,1]
> ];;
gap> ConjugatorSpaceGroups(SpaceGroupOnLeftIT(3,227,'2'),S^cc);
Verfahren hat nach 10000 Schritten nicht konvergiert !
Error, Carat program Z_equiv failed with error code 3 and the above output at /Users/kiryh/Library/Preferences/GAP/pkg/CaratInterface-2.3.6/gap/carat.gi:634 called from
CaratCommand( "Z_equiv", args, resfile
 ); at /Users/kiryh/Library/Preferences/GAP/pkg/CaratInterface-2.3.6/gap/methods.gi:291 called from
RepresentativeActionOp( G, d, e, act ) at /usr/local/Cellar/gap/4.12.2/libexec/lib/oprt.gi:2893 called from
RepresentativeAction( GL( d, Integers ), P2std, P1std
 ) at /Users/kiryh/Library/Preferences/GAP/pkg/cryst-4.1.27/gap/equiv.gi:134 called from
<<compiled GAP code>> from GAPROOT/lib/oper1.g:1105 in function ConjugatorSpaceGroups  fallback method to test cond\
itions called from
<<compiled GAP code>> from GAPROOT/lib/oper1.g:1105 in function ConjugatorSpaceGroups  fallback method to test cond\
itions called from
...  at *stdin*:323
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk>

The message is in German and translates to:

Procedure has not converged after 10'000 steps !

I would guess that Carat is not properly installed.

But as you can see it still does not solve it in your case.

The 10'000 seems to be a compile time constant which you can change in source and recompile:
https://github.com/lbfm-rwth/carat/blob/21bfdb516cc21c8e634a9fc99c469a07b8c7490c/functions/Bravais/rform.c#L17