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###############################################################################
##
#F ppowerpolypcpgroups.gi The SymbCompCC package Dörte Feichtenschlager
##
###############################################################################
##
## Declare a new category to be able to handle the groups elements of the Schur
## Extension with p-power-poly exponents
##
###############################################################################
##
#M PPPPcpGroups( rel, n, d, m, expo, expo_vec, prime )
##
## Input: a list of relations rel, the numbers of the different generators n,
## m, d, the exponend of the t_i's expo, the list of exponents of the
## c_i's and a prime p
##
## Output: p-power-poly-pcp-groups (including checks)
##
InstallGlobalFunction( PPPPcpGroups,
function( arg )
# function( rel, n, d, m, expo, expo_vec, prime, cc, name )
local prime, n, d, m, rel, expo, expo_vec, name, cc, i, j, k, obj;
if Length( arg ) = 1 then
prime := arg[1]!.prime;
n := arg[1]!.n;
d := arg[1]!.d;
m := arg[1]!.m;
rel := arg[1]!.rel;
expo := arg[1]!.expo;
expo_vec := arg[1]!.expo_vec;
cc := arg[1]!.cc;
name := arg[1]!.name;
else rel := arg[1];
n := arg[2];
d := arg[3];
m := arg[4];
expo := arg[5];
expo_vec := arg[6];
prime := arg[7];
cc := arg[8];
name := arg[9];
fi;
if not IsPrime( prime ) then
Error( "Wrong input. The seventh input has to be a prime." );
elif Length( expo_vec ) <> m then
Error( "Wrong input. The sixth input has to be a list of length the fourth input." );
elif Length( rel ) <> n+d+m then
Error( "Wrong input. See the manual for more information." );
else i := 1;
while i <= m do
if not IsList( expo_vec[i] ) then
Error( "Wrong input. See the manual for more information." );
fi;
i := i + 1;
od;
fi;
i := 1;
while i <= n+d+m do
j := 1;
if Length( rel[i] ) <> i then
Error( "Wrong input. See the manual for more information." );
fi;
while j <= i do
k := 1;
while k <= Length( rel[i][j] ) do
if rel[i][j][k][1] <= n then
if not IsInt( rel[i][j][k][2] ) then
Error( "Wrong input. See the manual for more information." );
fi;
else
if not IsList( rel[i][j][k][2] ) then
Error( "Wrong input. See the manual for more information." );
fi;
fi;
k := k + 1;
od;
j := j + 1;
od;
i := i + 1;
od;
obj := Objectify( NewType( PPPPcpGroupsFamily, IsPPPPcpGroupsRep ), rec(rel:=StructuralCopy(rel),n:=n,d:=d,m:=m,expo:=ShallowCopy(expo),expo_vec:=StructuralCopy(expo_vec),prime:=prime,cc:=cc,name:=name ) );
if IsConsistentPPPPcp( obj ) then
return obj;
else Error( "The pp-presentation has to be consistent." );
fi;
end);
###############################################################################
##
#M PPPPcpGroupsNC( rel, n, d, m, expo, expo_vec, prime )
##
## "for Schur extension with p-power-poly exponents",
## [ IsList,IsPosInt,IsPosInt,IsPosInt,IsPPowerPoly,IsList,IsPosInt ],
##
## Input: a list of relations rel, the numbers of the different generators n,
## m, d, the exponend of the t_i's expo, the list of exponents of the
## c_i's and a prime p
##
## Output: p-power-poly-pcp-groups (no checks)
##
InstallGlobalFunction( PPPPcpGroupsNC,
function( arg )
# function( rel, n, d, m, expo, expo_vec, primen cc, name )
local prime, n, d, m, rel, expo, expo_vec, cc, name, i, j, k, obj;
if Length( arg ) = 1 then
prime := arg[1]!.prime;
n := arg[1]!.n;
d := arg[1]!.d;
m := arg[1]!.m;
rel := arg[1]!.rel;
expo := arg[1]!.expo;
expo_vec := arg[1]!.expo_vec;
cc := arg[1]!.cc;
name := arg[1]!.name;
else rel := arg[1];
n := arg[2];
d := arg[3];
m := arg[4];
expo := arg[5];
expo_vec := arg[6];
prime := arg[7];
cc := arg[8];
name := arg[9];
fi;
if not IsPrime( prime ) then
Error( "Wrong input. The seventh input has to be a prime." );
elif Length( expo_vec ) <> m then
Error( "Wrong input. The sixth input has to be a list of length the fourth input." );
elif Length( rel ) <> n+d+m then
Error( "Wrong input. See the manual for more information." );
else i := 1;
while i <= m do
if not IsList( expo_vec[i] ) then
Error( "Wrong input. See the manual for more information." );
fi;
i := i + 1;
od;
fi;
i := 1;
while i <= n+d+m do
j := 1;
if Length( rel[i] ) <> i then
Error( "Wrong input. See the manual for more information." );
fi;
while j <= i do
k := 1;
while k <= Length( rel[i][j] ) do
if rel[i][j][k][1] <= n then
if not IsInt( rel[i][j][k][2] ) then
Error( "Wrong input. See the manual for more information." );
fi;
else
if not IsList( rel[i][j][k][2] ) then
Error( "Wrong input. See the manual for more information." );
fi;
fi;
k := k + 1;
od;
j := j + 1;
od;
i := i + 1;
od;
obj := Objectify( NewType( PPPPcpGroupsFamily, IsPPPPcpGroupsRep ), rec(rel:=StructuralCopy(rel),n:=n,d:=d,m:=m,expo:=ShallowCopy(expo),expo_vec:=StructuralCopy(expo_vec),prime:=prime,cc:=cc,name:=name ) );
return obj;
end);
###############################################################################
##
#M PPPPcpGroupsElement( grp_pres, word )
##
## Input: a list word that represents a word and p-power-poly-pcp-groups
## grp_pres (accepts collected or uncollected words)
##
## Output: word as an element of grp_pres (including checks)
##
InstallMethod(PPPPcpGroupsElement,[IsPPPPcpGroups,IsList],0,
function( grp_pres, word )
local m, div;
m := grp_pres!.m;
div := List( [1..m], x -> 1 );
return PPPPcpGroupsElement( grp_pres, word, div );
end);
###############################################################################
##
#M PPPPcpGroupsElementNC( grp_pres, word )
##
## Input: a list word that represents a word and p-power-poly-pcp-groups
## grp_pres (accepts collected or uncollected words)
##
## Output: word as an element of grp_pres (no checks)
##
InstallMethod(PPPPcpGroupsElementNC,[IsPPPPcpGroups,IsList],0,
function( grp_pres, word )
local m, div;
m := grp_pres!.m;
div := List( [1..m], x -> 1 );
return PPPPcpGroupsElementNC( grp_pres, word, div );
end);
###############################################################################
##
#M PPPPcpGroupsElementNC( grp_pres, word, div )
##
## Input: a list word that represents a word together with a list div and
## p-power-poly-pcp-groups grp_pres (accepts collected or uncollected
## words)
##
## Output: word as an element of grp_pres (no checks)
##
InstallMethod(PPPPcpGroupsElementNC,[IsPPPPcpGroups,IsList,IsList],0,
function( grp_pres, word, div )
local i, obj;
if Length( div ) <> grp_pres!.m then
Error( "The input has to be of the correct form, see the manual for more information." );
elif word <> [] then
i := 1;
while i <= Length( word ) do
if not IsList( word[i] ) then
Error( "The second input has to be a list of lists of length two, see the manual for more information." );
elif Length( word[i] ) <> 2 then
Error( "The second input has to be a list of lists of length two, see the manual for more information." );
elif word[i][1] > grp_pres!.n + grp_pres!.d + grp_pres!.m then
Error( "The number of the generator has to be smaller then or equal to the total number of generators, see the manual for more information." );
elif word[i][1] <= grp_pres!.n then
if not IsInt( word[i][2] ) then
Error( "The method can only handle exponents with integers as constant term, see the manual for more information." );
fi;
else
if not IsList(word[i][2]) and not IsInt(word[i][2]) then
Error( "The input has to be of the correct form, see the manual for more information." );
elif IsList(word[i][2]) and not grp_pres!.prime=word[i][2][1] then
Error( "The underlying primes are different, see the manual for more information." );
elif IsInt( word[i][2] ) then
word[i][2] := Int2PPowerPoly( grp_pres!.prime, word[i][2] );
fi;
fi;
i := i + 1;
od;
fi;
i := 1;
while i <= grp_pres!.m do
if not IsPosInt( div[i] ) then
Error( "The input has to be of the correct form, see the manual for more information." );
else i := i + 1;
fi;
od;
obj := Objectify( NewType( PPPPcpGroupsElementFamily, IsPPPPcpGroupsElementRep ), rec(word:=StructuralCopy(word),div:=StructuralCopy(div),grp_pres:=StructuralCopy(grp_pres) ) );
return obj;
end);
###############################################################################
##
#M PPPPcpGroupsElement( grp_pres, word, div )
##
## Input: a list word that represents a word together with a list div and
## p-power-poly-pcp-groups grp_pres (accepts collected or uncollected
## words)
##
## Output: word as an element of grp_pres (including checks)
##
InstallMethod(PPPPcpGroupsElement,[IsPPPPcpGroups,IsList,IsList],0,
function( grp_pres, word, div )
local obj;
obj := PPPPcpGroupsElementNC( grp_pres, word, div );
if COLLECT_PPOWERPOLY_PCP then
obj := CollectPPPPcp( obj );
fi;
return obj;
end);
###############################################################################
##
#M PrintObj( obj )
##
## Input: p-power-poly-pcp-groups obj
##
## Output: the method prints obj
##
InstallMethod( PrintObj, [ IsPPPPcpGroups ],
function( obj )
local i, p, expo, expo_vec;
Print( "< P-Power-Poly-pcp-groups with ", obj!.n+obj!.d+ obj!.m );
Print( " generators of relative orders [ " );
p := obj!.prime;
expo := obj!.expo;
expo_vec := obj!.expo_vec;
## first n-part
if obj!.n > 0 then
Print( p );
fi;
for i in [2..obj!.n] do
Print( ",", p );
od;
## then d-part
if obj!.n = 0 and obj!.d > 0 then
Print( expo );
elif obj!.d > 0 then
Print( "," );
PPP_Print( expo );
fi;
for i in [2..obj!.d] do
Print( "," );
PPP_Print( expo );
od;
## finally m-part
if obj!.n = 0 and obj!.d = 0 and obj!.m > 0 then
PPP_Print( expo_vec[1] );
elif obj!.m > 0 then
Print( "," );
PPP_Print( expo_vec[1] );
fi;
for i in [2..obj!.m] do
Print( "," );
PPP_Print( expo_vec[i] );
od;
Print( " ] >\n" );
end);
###############################################################################
##
#M ViewObj( obj )
##
## Input: p-power-poly-pcp-groups obj
##
## Output: the method prints obj
##
InstallMethod( ViewObj, [ IsPPPPcpGroups ],
function( obj )
local strg, i, p, expo, expo_vec;
Print( "< P-Power-Poly-pcp-groups with ", obj!.n+obj!.d+ obj!.m );
Print( " generators of relative orders [ " );
p := obj!.prime;
expo := obj!.expo;
expo_vec := obj!.expo_vec;
## first n-part
if obj!.n > 0 then
Print( p );
fi;
for i in [2..obj!.n] do
Print( ",", p );
od;
## then d-part
if obj!.n = 0 and obj!.d > 0 then
PPP_Print( expo );
elif obj!.d > 0 then
Print( "," );
PPP_Print( expo );
fi;
for i in [2..obj!.d] do
Print( "," );
PPP_Print( expo );
od;
## finally m-part
if obj!.n = 0 and obj!.d = 0 and obj!.m > 0 then
PPP_Print( expo_vec[1] );
elif obj!.m > 0 then
Print( "," );
PPP_Print( expo_vec[1] );
fi;
for i in [2..obj!.m] do
Print( "," );
PPP_Print( expo_vec[i] );
od;
Print( " ] >" );
end);
###############################################################################
##
#M Order( obj )
##
## Input: p-power-poly-pcp-groups obj
##
## Output: the orders of obj
##
InstallImmediateMethod( Order, IsPPPPcpGroups, 0,
function( obj )
local i, ord, expo_vec;
## p is the relative order of g_1, ..., g_n
ord := obj!.prime^obj!.n;
## expo is the relative order of t_1, ..., t_d
for i in [1..obj!.d] do
ord := PPP_Mult( ord, obj!.expo );
od;
## expo_vec[i] is the relative order of c_i
expo_vec := obj!.expo_vec;
for i in [1..obj!.m] do
ord := PPP_Mult( ord, expo_vec[i] );
od;
# Print( "Order of the p-power-poly-pcp-groups: " );
# PPP_Print( ord );
# Print( "\n" );
return ord;
end);
###############################################################################
##
#M PrintObj
##
## Input: a p-power-poly-pcp-groups element obj
##
## Output: the method prints obj
##
InstallMethod( PrintObj, [ IsPPPPcpGroupsElement ],
function( obj )
local word, div, n, d, m, p, One1, Zero0, i;
if COLLECT_PPOWERPOLY_PCP then
obj := CollectPPPPcp( obj );
fi;
word := obj!.word;
div := obj!.div;
if word = [] then
Print( "<identity>" );
else n := obj!.grp_pres!.n;
d := obj!.grp_pres!.d;
m := obj!.grp_pres!.m;
p := obj!.grp_pres!.prime;
One1 := Int2PPowerPoly( p, 1 );
Zero0 := Int2PPowerPoly( p, 0 );
for i in [1..Length( word )] do
if word[i][1] <= n then
if word[i][2] > 0 then
Print( "g", word[i][1] );
if word[i][2] > 1 then
Print( "^", word[i][2] );
fi;
fi;
elif word[i][1] <= n+d then
if not PPP_Equal( word[i][2], Zero0 ) then
Print( "t", word[i][1]-n );
if PPP_Greater( word[i][2], One1 ) then
Print( "^(" );
PPP_Print( word[i][2] );
Print( ")" );
fi;
fi;
else Print( "c", word[i][1]-(n+d) );
if div[word[i][1]-n-d] <> 1 then
if not PPP_Equal( word[i][2], One1 ) then
Print( "^(" );
PPP_Print( word[i][2] );
else Print( "^(1" );
fi;
Print( "/", div[word[i][1]-n-d], ")" );
elif not PPP_Equal( word[i][2], One1 ) then
Print( "^(" );
PPP_Print( word[i][2] );
Print( ")" );
fi;
fi;
if i < Length( word ) then
Print( "*" );
fi;
od;
fi;
end);
###############################################################################
##
## \in
##
## Input: a p-power-poly-pcp-groups element obj and p-power-poly-pcp-groups G
##
## Output: a boolean that indicates whether obj is an element of G
##
InstallMethod( \in, true, [ IsPPPPcpGroupsElement, IsPPPPcpGroups ], 1974,
function( obj, G )
local word, n, d, m, i;
if obj!.grp_pres <> G then return false; fi;
word := obj!.word;
n := obj!.grp_pres!.n;
d := obj!.grp_pres!.d;
m := obj!.grp_pres!.m;
for i in [1..Length( word )] do
if word[i][1] > n+d+m then return false; fi;
if word[i][1] <= n and not IsInt( word[i][2] ) then return false; fi;
od;
return true;
end);
###############################################################################
##
## ShallowCopy
##
## Input: a p-power-poly-pcp-groups element obj
##
## Output: a shallow copy of obj
##
InstallMethod( ShallowCopy, [ IsPPPPcpGroupsElement ],
function( obj )
local word, div, grp_pres;
word := StructuralCopy( obj!.word );
div := StructuralCopy( obj!.div );
grp_pres := StructuralCopy( obj!.grp_pres );
return PPPPcpGroupsElement( grp_pres, word );
end);
#############################################################################
##
#M PPP_Words_Equal( word1, word2, group_pres )
##
## Input: lists word1 and word2 and the corresponding p-power-poly-pcp-groups
## group_pres
##
## Output: a boolean, indicating whether word1 and word2 are equal
##
InstallGlobalFunction( "PPP_Words_Equal",
function( word1, word2, group_pres )
local n, i;
if Length( word1 ) <> Length( word2 ) then return false; fi;
n := group_pres!.n;
for i in [1..Length( word1 )] do
if word1[i][1] <> word2[i][1] then return false; fi;
if word1[i][1] <= n and word1[i][2] <> word2[i][2] then return false; fi;
if i > n and not PPP_Equal( word1[i][2], word2[i][2] ) then
return false;
fi;
od;
return true;
end);
#############################################################################
##
#M \=( objj1, objj2 )
##
## Input: p-power-poly-pcp-groups elements objj1 and objj2
##
##Output: a boolean indicating whether objj1 equals objj2
##
InstallMethod( \=, [ IsPPPPcpGroupsElement, IsPPPPcpGroupsElement ],
function( objj1, objj2 )
local obj1, obj2, p, n, d, m, group_pres, div1, div2, word1, word2,
expo_vec, vec, i, mult, test1, test2;
obj1 := CollectPPPPcp( objj1 );;
obj2 := CollectPPPPcp( objj2 );;
if obj1!.grp_pres = obj1!.grp_pres then
if PPP_Words_Equal( obj1!.word, obj2!.word, obj1!.grp_pres ) and obj1!.div = obj2!.div then
return true;
elif ForAny(obj1!.div,x->x<>1) or ForAny(obj2!.div,x->x<>1) then
div1 := obj1!.div;
div2 := obj2!.div;
word1 := StructuralCopy( obj1!.word );;
word2 := StructuralCopy( obj2!.word );;
group_pres := obj1!.grp_pres;
p := group_pres!.prime;
n := group_pres!.n;
d := group_pres!.d;
m := group_pres!.m;
expo_vec := group_pres!.expo_vec;
for i in [1..Length( word1 )] do
if word1[i][1] > n+d and div2[word1[i][1]-n-d] <> 1 then
mult := Int2PPowerPoly( p, div2[word1[i][1]-n-d] );
word1[i][2] := Reduce_ci_ppowerpolypcp( PPP_Mult( word1[i][2], mult ), div1[word1[i][1]-n-d], word1[i][1]-n-d, expo_vec )[1];
fi;
od;
for i in [1..Length( word2 )] do
if word2[i][1] >= n+d and div1[word2[i][1]-n-d] <> 1 then
mult := Int2PPowerPoly( p, div1[word1[i][1]-n-d] );
word2[i][2] := Reduce_ci_ppowerpolypcp( PPP_Mult( word2[i][2], mult ), div2[word2[i][1]-n-d], word2[i][1]-n-d, expo_vec )[1];
fi;
od;
## initialize div-vec
vec := [];
for i in [1..m] do
vec[i] := div1[i]*div2[i];
od;
test1 := PPPPcpGroupsElement( group_pres, word1, vec );;
test2 := PPPPcpGroupsElement( group_pres, word2, vec );;
return test1=test2;
fi;
else Error( "The underlying PPPPcpGroups are different." );
fi;
end);
#############################################################################
##
#M \*( obj1, obj2 )
##
## Input: p-power-poly-pcp-groups elements obj1 and obj2
##
## Output: the product of obj1 and obj2
##
InstallMethod( \*, [ IsPPPPcpGroupsElement, IsPPPPcpGroupsElement ],
function( obj1, obj2 )
local p, n, d, word1, word2, div1, div2, l1, l2, i, obj;
p := obj1!.grp_pres!.prime;
n := obj1!.grp_pres!.n;
d := obj1!.grp_pres!.d;
if obj1!.grp_pres = obj2!.grp_pres then
word1 := StructuralCopy( obj1!.word );
div1 := StructuralCopy( obj1!.div );
word2 := obj2!.word;
div2 := obj2!.div;
l1 := Length( word1 );
l2 := Length( word2 );
if div1 <> div2 then
## if div is not trivial then act accordingly
for i in [1..l2] do
if word2[i][1] > n+d then
word2[i][2] := PPP_Mult( word2[i][2], Int2PPowerPoly( p, div1[word2[i][1]-n-d] ) );
fi;
od;
for i in [1..l1] do
if word1[i][1] > n+d then
word1[i][2] := PPP_Mult( word1[i][2], Int2PPowerPoly(p,div2[word1[i][1]-n-d] ) );
fi;
od;
fi;
for i in [l2, l2-1..1] do
word1[l1+i] := word2[i];
od;
for i in [1..obj1!.grp_pres!.m] do
div1[i] := div1[i]*div2[i];
od;
obj := PPPPcpGroupsElement( obj1!.grp_pres, word1, div1 );
if COLLECT_PPOWERPOLY_PCP then
obj := CollectPPPPcp( obj );
fi;
return obj;
else Error( "The underlying PPPPcpGroups are different." );
fi;
end);
#############################################################################
##
#M Inverse( obj )
##
## Input: a p-power-poly-pcp-groups elements obj
##
## Output: the inverse of obj
##
InstallMethod( Inverse, [ IsPPPPcpGroupsElement ],
function( obj )
return obj^-1;
end);
#############################################################################
##
#M \^-1( obj )
##
## Input: a p-power-poly-pcp-groups elements obj
##
## Output: the inverse of obj
##
InstallMethod( InverseMutable, [ IsPPPPcpGroupsElement ],
function( obj )
local word, l, i, n;
n := obj!.grp_pres!.n;
word := [];
l := Length( obj!.word );
for i in [1..l] do
word[i] := [];
word[i][1] := obj!.word[l+1-i][1];
if word[i][1] <= n then
word[i][2] := - StructuralCopy( obj!.word[l+1-i][2] );
else word[i][2] := [];
word[i][2][1] := obj!.word[l+1-i][2][1];
word[i][2][2] := - obj!.word[l+1-i][2][2];
fi;
od;
return PPPPcpGroupsElement( obj!.grp_pres, word, obj!.div );
end);
InstallMethod( \/, [ IsPPPPcpGroupsElement, IsPPPPcpGroupsElement ],
function( obj1, obj2 )
return obj1 * obj2^-1;
end);
#############################################################################
##
#M One( obj )
##
## Input: a p-power-poly-pcp-groups elements obj
##
## Output: the one corresponding to obj
##
InstallMethod( OneOp, [ IsPPPPcpGroupsElement ],
elm -> PPPPcpGroupsElement( elm!.grp_pres, [] )
);
###############################################################################
##
## One( G )
##
## Input: p-power-poly-pcp-groups G
##
## Output: the one in G
##
InstallOtherMethod( One, true, [IsPPPPcpGroups], 102,
function( G )
return PPPPcpGroupsElement( G, [] );
end);
###############################################################################
##
## GeneratorsOfGroup
##
## Input: p-power-poly-pcp-groups G
##
## Output: the generators of G
##
InstallMethod( GeneratorsOfGroup, [ IsPPPPcpGroups ],
function( G )
local i, n, d, list;
n := G!.n;
d := G!.d;
list := [];
for i in [1..n] do
list[i] := PPPPcpGroupsElement( G, [[i,1]] );
od;
for i in [1..d] do
list[n+i] := PPPPcpGroupsElement( G, [[n+i,1]] );
od;
for i in [1..G!.m] do
list[n+d+i] := PPPPcpGroupsElement( G, [[n+d+i,1]] );
od;
return list;
end);
###############################################################################
##
#M IsConsistentPPPPcp( group_pres )
##
## Input: p-power-poly-pcp-groups group_pres
##
## Output: a boolean indicating whether group_pres is consistent
##
InstallMethod( IsConsistentPPPPcp, [ IsPPPPcpGroups ],
function( group_pres )
local n, d, m, p, test, One1, Zero0, i, f_i, f_im, j, f_j, k, f_k,
help1, help2, help, exp1, exp2;
n := group_pres!.n;
d := group_pres!.d;
m := group_pres!.m;
p := group_pres!.prime;
test := true;
One1 := Int2PPowerPoly( p, 1 );
Zero0 := Int2PPowerPoly( p, 0 );
## check consistency
## f_k(f_jf_i) = (f_kf_j)f_i, k>j>i
i := 1;
while test and i <= n+d+m-2 do
if i <= n then
f_i := PPPPcpGroupsElement( group_pres, [[i,1]] );
else f_i := PPPPcpGroupsElement( group_pres, [[i,One1]] );
fi;
j := i + 1;
while test and j <= n+d+m-1 do
if j <= n then
f_j := PPPPcpGroupsElement( group_pres, [[j,1]] );
else f_j := PPPPcpGroupsElement( group_pres, [[j,One1]] );
fi;
k := j + 1;
while test and k <= n+d+m do
if k <= n then
f_k := PPPPcpGroupsElement( group_pres, [[k,1]] );
else
f_k := PPPPcpGroupsElement( group_pres, [[k,One1]] );
fi;
help1 := StructuralCopy( CollectPPPPcp( f_j*f_i ) );
help1 := StructuralCopy( CollectPPPPcp( f_k*help1 ) );
help2 := StructuralCopy( CollectPPPPcp( (f_k*f_j)*f_i ) );
if not help1 = help2 then
test := false;
fi;
if InfoLevel( InfoConsistencyPPPPcp ) > 0 and not test then
Print( "Failing consistency relation: (", k, "*", j, ")*", i, " = ", k, "*(", j, "*", i, ")\n" );
fi;
if InfoLevel( InfoConsistencyPPPPcp ) = 2 and test then
Print( "Checked relation: (", k, "*", j, ")*", i, " = ", k, "*(", j, "*", i, ")\n" );
fi;
k := k + 1;
od;
j := j + 1;
od;
i := i + 1;
od;
## g_j^e_j g_i = g_j^(e_j-1)(g_jg_i), j>i
i := 1;
while i <= n+d+m-1 and test do
if i <= n then
f_i := PPPPcpGroupsElement( group_pres, [[i,1]] );
else f_i := PPPPcpGroupsElement( group_pres, [[i,One1]] );
fi;
j := i + 1;
while j <= n+d+m and test do
if j <= n then
f_j := PPPPcpGroupsElement( group_pres, [[j,1]] );
exp1 := p;
exp2 := exp1 - 1;
elif j <= n+d then
f_j := PPPPcpGroupsElement( group_pres, [[j,One1]] );
exp1 := group_pres!.expo;
exp2 := PPP_Subtract( exp1, One1 );
else f_j := PPPPcpGroupsElement( group_pres, [[j,One1]] );
exp1 := group_pres!.expo_vec[j-n-d];
exp2 := PPP_Subtract( exp1, One1 );
fi;
if exp1 = p or ( not PPP_Equal( exp1, Zero0 ) ) then
help1 := PPPPcpGroupsElement( group_pres, [[j,exp1]] );
if not COLLECT_PPOWERPOLY_PCP then
help1 := StructuralCopy( CollectPPPPcp( help1 ) );
fi;
help1 := StructuralCopy( CollectPPPPcp( help1*f_i ) );
help2 := StructuralCopy( CollectPPPPcp( f_j*f_i ) );
help2 := StructuralCopy( CollectPPPPcp( PPPPcpGroupsElement( group_pres, [[j,exp2]] )*help2 ) );
if not help1 = help2 then
test := false;
fi;
if InfoLevel( InfoConsistencyPPPPcp ) > 0 and not test then
Print( "Failing consistency relation: ", j, "^exp*", i, " = ", j, "^(exp-1)*(", j, "*", i, ")\n" );
fi;
if InfoLevel( InfoConsistencyPPPPcp ) = 2 and test then
Print( "Checked relation: ", j, "^exp*", i, " = ", j, "^(exp-1)*(", j, "*", i, ")\n" );
fi;
fi;
j := j + 1;
od;
i := i + 1;
od;
## g_jg_i^e_i = (g_jg_i)g_i^(e_i-1), j>i
i := 1;
while i <= n+d+m-1 and test do
if i <= n then
f_i := PPPPcpGroupsElement( group_pres, [[i,1]] );
exp1 := p;
exp2 := exp1 - 1;
elif i <= n+d then
f_i := PPPPcpGroupsElement( group_pres, [[i,One1]] );
exp1 := group_pres!.expo;
exp2 := PPP_Subtract( exp1, One1 );
else f_i := PPPPcpGroupsElement( group_pres, [[i,One1]] );
exp1 := group_pres!.expo_vec[i-n-d];
exp2 := PPP_Subtract( exp1, One1 );
fi;
if exp1 = p or (not PPP_Equal( exp1, Zero0 ) ) then
j := i + 1;
while j <= n+d+m and test do
if j <= n then
f_j := PPPPcpGroupsElement( group_pres, [[j,1]] );
else f_j := PPPPcpGroupsElement( group_pres, [[j,One1]] );
fi;
help1 := CollectPPPPcp( PPPPcpGroupsElement( group_pres, [[i,exp1]] ) );
if not COLLECT_PPOWERPOLY_PCP then
help1 := StructuralCopy( CollectPPPPcp( help1 ) );
fi;
help1 := StructuralCopy( CollectPPPPcp( f_j*help1 ) );
help2 := StructuralCopy( CollectPPPPcp( f_j*f_i ) );
help2 := StructuralCopy( CollectPPPPcp( help2*PPPPcpGroupsElement( group_pres, [[i,exp2]] ) ) );
if help1 <> help2 then
test := false;
fi;
if InfoLevel( InfoConsistencyPPPPcp ) > 0 and not test then
Print( "Failing consistency relation: ", j, "*", i, "^exp = (", j, "*", i, ")*", i, "^(exp-1))\n" );
fi;
if InfoLevel( InfoConsistencyPPPPcp ) = 2 and test then
Print( "Checked relation: ", j, "*", i, "^exp = (", j, "*", i, ")*", i, "^(exp-1))\n" );
fi;
j := j + 1;
od;
fi;
i := i + 1;
od;
## g_i^e_ig_i = g_ig_i^e_i
i := 1;
while i <= n+d+m and test do
if i <= n then
f_i := PPPPcpGroupsElement( group_pres, [[i,1]] );
exp1 := p;
elif i <= n+d then
f_i := PPPPcpGroupsElement( group_pres, [[i,One1]] );
exp1 := group_pres!.expo;
else f_i := PPPPcpGroupsElement( group_pres, [[i,One1]] );
exp1 := group_pres!.expo_vec[i-n-d];
fi;
if exp1 = p or (not PPP_Equal( exp1, Zero0 ) ) then
help := CollectPPPPcp( PPPPcpGroupsElement( group_pres, [[i,exp1]] ) );
if not COLLECT_PPOWERPOLY_PCP then
help := StructuralCopy( CollectPPPPcp( help ) );
fi;
help1 := StructuralCopy( CollectPPPPcp( help*f_i ) );
help2 := StructuralCopy( CollectPPPPcp( f_i*help ) );
if help1 <> help2 then
test := false;
fi;
if InfoLevel( InfoConsistencyPPPPcp ) > 0 and not test then
Print( "Failing consistency relation: (", i, "^exp)*", i, " = ", i, "*(", i, "^exp)\n" );
fi;
if InfoLevel( InfoConsistencyPPPPcp ) = 2 and test then
Print( "Checked relation: (", i, "^exp)*", i, " = ", i, "*(", i, "^exp)\n" );
fi;
fi;
i := i + 1;
od;
## g_j = (g_jg_i^-1)g_i
i := n+d+1;
while i <= n+d+m-1 and test do
if not PPP_Equal( group_pres!.expo_vec[i-n-d], Zero0 ) then
f_i := PPPPcpGroupsElement( group_pres, [[i,One1]] );
f_im := PPPPcpGroupsElement( group_pres, [[i,PPP_AdditiveInverse( One1 )]] );
j := i + 1;
while j <= n+d+m and test do
help1 := PPPPcpGroupsElement( group_pres, [[j,One1]] );
help2 := StructuralCopy( CollectPPPPcp( help1*f_im ) );
help2 := StructuralCopy( CollectPPPPcp( help2*f_i ) );
if help1 <> help2 then
test := false;
fi;
if InfoLevel( InfoConsistencyPPPPcp ) > 0 and not test then
Print( "Failing consistency relation: ", j, " = (", j, "*", i, "^-1)*", i, "\n" );
fi;
if InfoLevel( InfoConsistencyPPPPcp ) = 2 and test then
Print( "Checked relation: ", j, " = (", j, "*", i, "^-1)*", i, "\n" );
fi;
j := j + 1;
od;
fi;
i := i + 1;
od;
return test;
end);
###############################################################################
##
#M IsConsistentPPPPcp( ParPres )
##
## Input: a record ParPres presenting p-power-poly-pcp-groups
##
## Output: a boolean indicating whether ParPres is consistent
##
InstallMethod( IsConsistentPPPPcp, [ IsRecord ],
function( ParPres )
local G;
G := PPPPcpGroups( ParPres );
return IsConsistentPPPPcp( G );
end);
#E ppowerpolypcpgroups.gi . . . . . . . . . . . . . . . . . . . . . ends here
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