CosetTableFpHom does not set one, useAddition expected by NEWTC_Rewrite

[clnbr]

I ran into a bug in NEWTC_Rewrite with the attached input. The test case could probably be made more minimal, but I don't really know may waya round the FpGroups functionality very well yet. It's a bug that I've run into a couple of times recently, and this is the only reasonably self-contained test case I've managed to come up with. I hope it's still helpful.

The offending rec is returned from CosetTableFpHom. I've included code that resolves the break loop in this particular case. The transcript is below and the input is a attached
NEWTC_Rewrite_bug.g.txt

 ┌───────┐   GAP 4.8.8-4401-g5f25772-dirty of today
 │  GAP  │   https://www.gap-system.org
 └───────┘   Architecture: x86_64-apple-darwin15.6.0-gcc-default64
 Configuration:  gmp 6.1.2
 Loading the library and packages ...
 Components: trans 1.0, prim 3.0, small* 1.0, id* 1.0
 Packages:   AClib 1.2, Alnuth 3.0.0, AtlasRep 1.5.1, AutPGrp 1.8, CRISP 1.4.4, Cryst 4.1.12, CrystCat 1.1.6, CTblLib 1.2.2, FactInt 1.5.4, 
             FGA 1.3.1, GAPDoc 1.6, IO 4.4.6, IRREDSOL 1.4, LAGUNA 3.7.0, Polenta 1.3.7, Polycyclic 2.11, RadiRoot 2.7, ResClasses 4.6.0, 
             Sophus 1.23, SpinSym 1.5, TomLib 1.2.6, Utils 0.46
 Try '??help' for help. See also '?copyright', '?cite' and '?authors'
gap> p := 5;
5
gap> gpAfp := (function(gpF)
>              return gpF / [gpF.a^(p^2), gpF.b^(p^2), Comm(gpF.a, gpF.b)];
>          end)(FreeGroup("a", "b"));
<fp group on the generators [ a, b ]>
gap> a := gpAfp.1;
a
gap> b := gpAfp.2;
b
gap> 
gap> # make a constructor for automorphisms from lists of images
gap> # need to use Group...ByImagesNC since there is no method to compute
gap> # IsSingleValued
gap> AutomorphismCtor := gpG -> imgs -> GroupHomomorphismByImagesNC(gpG, gpG, GeneratorsOfGroup(gpG), imgs);
function( gpG ) ... end
gap> AutForAImgs := AutomorphismCtor(gpAfp);
function( imgs ) ... end
gap> gpHgens_as_auts := [ AutForAImgs([ a^(p+1), b^(-p+1) ]), AutForAImgs( [ b^(-p)*a, a^(-p)*b ]) ];
[ [ a, b ] -> [ a^6, b^-4 ], [ a, b ] -> [ b^-5*a, a^-5*b ] ]
gap> # are they really automorphisms?
gap> List(gpHgens_as_auts, IsBijective);
[ true, true ]
gap> gpH_as_auts := GroupWithGenerators(gpHgens_as_auts, IdentityMapping(gpAfp));
<group with 2 generators>
gap> Size(gpH_as_auts);
Error, Record: '<rec>.one' must have an assigned value in
  c := DATA.one; at /Users/calin/prj/gap-head/lib/sgpres.gi:3264 called from 
NEWTC_Rewrite( aug, 1, LetterRepAssocWord( word ) ) at /Users/calin/prj/gap-head/lib/ghomfp.gi:269 called from
ImageElm( map, elm ) at /Users/calin/prj/gap-head/lib/mapping.gi:191 called from
Image( a, i ) at /Users/calin/prj/gap-head/lib/ghom.gi:594 called from
func( C[i] ) at /Users/calin/prj/gap-head/lib/coll.gi:746 called from
List( GeneratorsSmallest( Source( a ) ), function ( i )
      return Image( a, i );
  end ) at /Users/calin/prj/gap-head/lib/ghom.gi:594 called from
...  at *stdin*:17
you can 'return;' after assigning a value
brk> 
brk> DATA.one := One(DATA.homgens[1]);
<identity ...>
brk> return;
Error, Record: '<rec>.useAddition' must have an assigned value in
  if DATA.useAddition then
    c := c + DATA.aug[(j + offset)][i];
else
    c := WordProductLetterRep( c, DATA.aug[j + offset][i] );
fi; at /Users/calin/prj/gap-head/lib/sgpres.gi:3271 called from 
NEWTC_Rewrite( aug, 1, LetterRepAssocWord( word ) ) at /Users/calin/prj/gap-head/lib/ghomfp.gi:269 called from
ImageElm( map, elm ) at /Users/calin/prj/gap-head/lib/mapping.gi:191 called from
Image( a, i ) at /Users/calin/prj/gap-head/lib/ghom.gi:594 called from
func( C[i] ) at /Users/calin/prj/gap-head/lib/coll.gi:746 called from
List( GeneratorsSmallest( Source( a ) ), function ( i )
      return Image( a, i );
  end ) at /Users/calin/prj/gap-head/lib/ghom.gi:594 called from
...  at *stdin*:17
you can 'return;' after assigning a value
brk> DATA.useAddition := false;
false
brk> return;
25

[fingolfin]

@hulpke wrote the new MTC code, so hopefully he has some insights on this.

[fingolfin]

To ease debugging, here is the input, in a form that also works in older GAP versions:

p:=5;
f:=gpF -> gpF / [gpF.a^(p^2), gpF.b^(p^2), Comm(gpF.a, gpF.b)];
gpAfp := f(FreeGroup("a", "b"));
a := gpAfp.1;
b := gpAfp.2;
AutomorphismCtor := gpG -> imgs -> GroupHomomorphismByImagesNC(gpG, gpG, GeneratorsOfGroup(gpG), imgs);

AutForAImgs := AutomorphismCtor(gpAfp);
gpHgens_as_auts := [ AutForAImgs([ a^(p+1), b^(-p+1) ]), AutForAImgs( [ b^(-p)*a, a^(-p)*b ]) ];
List(gpHgens_as_auts, IsBijective);
gpH_as_auts := GroupWithGenerators(gpHgens_as_auts, IdentityMapping(gpAfp));
Size(gpH_as_auts);

In GAP 4.8.7 and older, the last command returns 25.

[hulpke]

Thank you, @fingolfin for isolating out the example. The issue is simply a forgotten component copy. I will fix it.