Home
last modified time | relevance | path

Searched refs:pcgs (Results 1 – 25 of 272) sorted by relevance

1234567891011

/dports/math/gap/gap-4.11.0/pkg/polycyclic-2.15.1/gap/action/
H A Dbasepcgs.gi5 #W A base pcgs is a pcgs with attached base and strong generating set.
82 if IsBound( pcgs.rels ) then return pcgs.rels; fi;
85 Add( pcgs.rels, pcgs.trels[t[1]][t[2]] );
96 if IsBound( pcgs.pcgs ) then return pcgs.pcgs; fi;
97 pcgs.pcgs := [];
99 Add( pcgs.pcgs, pcgs.trans[t[1]][t[2]] );
101 return pcgs.pcgs;
133 j := Position( pcgs.orbit[i], pcgs.oper( pcgs.orbit[i][1], h ) );
153 j := Position( pcgs.orbit[i], pcgs.oper( pcgs.orbit[i][1], h ) );
186 return pcgs.trivl( SiftByBasePcgs( pcgs,g ) );
[all …]
H A Dextend.gi116 #F SmallOrbitPoint( pcgs, g )
121 b := Random(pcgs.acton);
122 until pcgs.oper( b, g ) <> b;
128 #F ExtendedBasePcgs( pcgs, g, d ) . . . . . . . . . . . . extend a base pcgs
130 ## g normalizes <pcgs> and we compute a new pcgs for <pcgs, g>.
136 Unbind(pcgs.pcgs);
137 Unbind(pcgs.rels);
145 while not pcgs.trivl( h ) do
161 c := pcgs.oper( b, h );
173 EnlargeOrbit( pcgs.orbit[i], h, m, pcgs.oper );
[all …]
/dports/math/gap/gap-4.11.0/lib/
H A Dpcgsmodu.gi96 pcgs -> Length(pcgs!.pcSequence) );
242 pcgs := List(pcgs);
284 pcgs!.depthsInParent:=List(pcgs,i->DepthOfPcElement(Parent(pcgs),i));
424 InstallMethod( MOD,"parent pcgs mod induced pcgs",
512 "pcgs modulo pcgs, ignoring <min>",
672 "pcgs modulo pcgs",
693 "pcgs modulo pcgs",
716 "pcgs modulo pcgs",
1030 if IsModuloPcgs(pcgs) and not IsPcgs(pcgs) then
1043 if IsModuloPcgs(pcgs) and not IsPcgs(pcgs) then
[all …]
H A Dpcgs.gi97 pcgs -> Length(pcgs!.pcSequence) );
105 pcgs -> pcgs!.pcSequence );
385 "pcgs modulo pcgs, ignoring <min>",
462 pcgs!.conjugates[i][j]:=ExponentsOfPcElement(pcgs,pcgs[i]^pcgs[j]);
474 return ExponentsOfPcElement(pcgs,pcgs[i]^RelativeOrders(pcgs)[i]);
484 return ExponentsOfPcElement(pcgs,Comm(pcgs[i],pcgs[j]));
1184 #tmp := pcgs[i]^RelativeOrderOfPcElement(pcgs,pcgs[i]);
1265 rec( pcgs := pcgs, sublist := [ 1 .. Length(pcgs) ],
1308 pcgs := enum!.pcgs;
1334 pcgs := enum!.pcgs;
[all …]
H A Dpcgspcg.gi152 return pcgs;
193 return pcgs;
224 return pcgs;
276 "family pcgs",
300 "family pcgs",
324 "family pcgs",
839 pcgs!.conjugates[i][j]:=ExponentsOfPcElement(pcgs,pcgs[i]^pcgs[j]);
850 function( pcgs, i )
853 return ExponentsOfPcElement(pcgs,pcgs[i]^RelativeOrders(pcgs)[i]);
1213 function(pcgs,elm)
[all …]
H A Dpcgsind.gi74 if HasIsSpecialPcgs( pcgs ) and IsSpecialPcgs( pcgs ) then
135 if 0 < Length(pcgs) and pcgs[Length(pcgs)-Length(pcs)+1]=pcs[1] then
141 if HasIsFamilyPcgs(pcgs) and IsFamilyPcgs(pcgs) then
432 pcgs:=InducedPcgsByPcSequenceNC( pcgs, igs );
1039 y -> DepthOfPcElement( pcgs, Comm(pcgs[x],pcgs[y])) ) );
1106 "prime orders pcgs, tail-pcgs, list",IsFamFamFam,
1150 "prime orders pcgs, tail-pcgs, list",IsFamFamFam,
1189 #M NormalIntersectionPcgs( <parent-pcgs>, <tail-pcgs>, <induced-pcgs> )
1192 "prime orders pcgs, tail-pcgs, induced-pcgs",IsFamFamFam,
1202 if pcgs <> ParentPcgs(n) or pcgs <> ParentPcgs(u)
[all …]
H A Dpcgscomp.gi27 local pcgs;
42 return pcgs;
52 local pcgs;
59 return pcgs;
115 pcgs := [];
128 pcgs := PcgsByPcSequenceNC( FamilyObj(One(grp)), pcgs );
133 return pcgs;
178 function( pcgs )
195 function( pcgs )
200 #T grp := GroupByGenerators( pcgs, One(pcgs) );
[all …]
H A Dpcgsind.gd17 #C IsInducedPcgs(<pcgs>)
24 ## The category of induced pcgs. This a subcategory of pcgs.
44 ## with respect to <A>pcgs</A> this operation returns an induced pcgs
89 ## returns an induced pcgs with respect to <A>pcgs</A> of the subgroup
122 ## returns an induced pcgs with respect to <A>pcgs</A>
156 ## computes a canonical, <A>pcgs</A>-induced pcgs for the span of
198 ## returns the pcgs by which <A>pcgs</A> was induced.
199 ## If <A>pcgs</A> was not induced, it simply returns <A>pcgs</A>.
226 ## returns the canonical pcgs corresponding to the induced pcgs <A>pcgs</A>.
257 ## induced pcgs with respect to a parent pcgs a canonical pcgs is unique.
[all …]
H A Dpcgsnice.gi19 local nice, npcgs, pcgs;
27 pcgs := PcgsByPcSequenceNC( ElementsFamily( FamilyObj( G ) ), pcgs );
31 SetNiceMonomorphism( pcgs, nice );
32 SetNiceObject ( pcgs, npcgs );
33 SetGroupOfPcgs ( pcgs, G );
34 SetOneOfPcgs(pcgs,One(G));
36 return pcgs;
50 function( pcgs, g, depth )
74 function( pcgs, g, poss )
84 function( pcgs, g, poss )
[all …]
H A Dpcgs.gd22 ## The category of general pcgs. Each modulo pcgs is a general pcgs.
44 ## The category of modulo pcgs. Note that each pcgs is a modulo pcgs for
127 ## create a new pcgs which is not induced by any other pcgs
786 ## whose family pcgs is a prime order pcgs.
804 ## returns the list of relative orders of the pcgs <A>pcgs</A>.
850 ## <A>pcgs</A>.
888 ## <A>pcgs</A>. For the family pcgs or pcgs induced by it (see section
911 ## For the family pcgs or pcgs induced by it (see section
933 ## with respect to <A>pcgs</A>. For the family pcgs or pcgs induced by it,
1124 ## <A>pcgs</A>.
[all …]
H A Dpcgsspec.gi289 w := Comm( pcgssys.pcgs[ j ], pcgssys.pcgs[ i ] );
393 g := Comm( pcgssys.pcgs[j], pcgssys.pcgs[i] );
398 aij := pcgssys.pcgs[j] ^ pcgssys.pcgs[i];
445 w := Comm( pcgssys.pcgs[j], pcgssys.pcgs[i] );
526 g := Comm( pcgssys.pcgs[j], pcgssys.pcgs[i] );
531 aij := pcgssys.pcgs[j] ^ pcgssys.pcgs[i];
578 function( pcgs )
603 pcgssys.pcgs:=PcgsByPcSequence(FamilyObj(OneOfPcgs(pcgs)),
639 function( pcgs )
660 function( pcgs )
[all …]
H A Dpcgsperm.gi578 return pcgs;
873 ( pcgs, pcgs[ n ] ^ p ) ) );
905 ( pcgs[ n ], pcgs[ n2 ] ) ) ) );
973 pcgs -> Pcgs( GroupOfPcgs( pcgs ) ) );
981 pcgs -> Pcgs( pcgs!.denominator ) );
1117 pcgs{[pins[i]..Length(pcgs)]},
1174 pcgs!.depthMapFromParent{ran}:=[1..Length(pcgs)];
1330 =ExponentsOfPcElement(pcgs,pcgs[x]^r[x])) and
1333 =ExponentsOfPcElement(pcgs,pcgs[y]^pcgs[x]))) then
1383 local pcgs;
[all …]
H A Dgrppcint.gi85 # the pcgs of this group will be compatible with the pcgs wrt. which we
112 firsts := LGFirst( pcgs );
154 G := GroupOfPcgs( pcgs );
155 m := Length( pcgs );
157 # use the special pcgs
158 first := LGFirst( pcgs );
175 #pcgsN := InducedPcgsByPcSequenceNC( pcgs, pcgs{depthN} );
207 pcgsS := InducedPcgsByPcSequenceNC( pcgs, pcgs{depthS} );
252 m := Length( pcgs );
277 "groups with pcgs",
[all …]
H A Dpcgsspec.gd47 ## <Attr Name="SpecialPcgs" Arg='pcgs' Label="for a pcgs"/>
51 ## computes a special pcgs for the group defined by <A>pcgs</A> or for
63 #A LGHeads( <pcgs> )
69 ## returns the LGHeads of the special pcgs <A>pcgs</A>.
77 #A LGTails( <pcgs> )
83 ## returns the LGTails of the special pcgs <A>pcgs</A>.
98 ## returns the LGWeights of the special pcgs <A>pcgs</A>.
108 #A LGLayers( <pcgs> )
115 ## returns the layers of the special pcgs <A>pcgs</A>.
125 #A LGFirst( <pcgs> )
[all …]
H A Doprtpcgs.gi15 local pcgs,D,pnt,acts,act,
19 S, rel, # stabilizer and induced pcgs
95 if not IsIdenticalObj(pcgs,ParentPcgs(pcgs)) then
97 dep:=pcgs!.depthsInParent{dep};
120 ## with <pcgs>.
158 #M OrbitStabilizerOp( <G>, <D>, <pnt>, <pcgs>, <acts>, <act> ) . . . by pcgs
171 function( G, pnt, pcgs, acts, act )
225 pcgs := Pcgs( G );
226 acts := pcgs;
229 pcgs := xset!.generators;
[all …]
H A Dgrppc.gd144 ## returns the pcgs which induced with respect to a family pcgs
155 #O InducedPcgs( <pcgs>, <grp> )
162 ## computes a pcgs for <A>grp</A> which is induced by <A>pcgs</A>.
163 ## If <A>pcgs</A> has a parent pcgs,
183 ## computes a pcgs for <A>grp</A> which is induced by <A>pcgs</A>. <A>pcgs</A> must not
199 ## This function sets <A>pcgs</A> to be a <A>home</A>-induced pcgs for
208 ## home pcgs of the calculation.
240 ## returns an induced pcgs for <A>grp</A> with respect to the home pcgs.
297 ## pcgs at low costs.
402 ## corresponding to the modulo pcgs <A>pcgs</A> with translation
[all …]
H A Dgrppc.gi110 pcgs := ParentPcgs (pcgs);
168 pcgs := ParentPcgs (pcgs);
340 ## automatically set family pcgs and home pcgs.
365 FamilyPcgs,pcgs,HomePcgs,pcgs,GeneralizedPcgs,pcgs);
366 #SetGroupOfPcgs (pcgs, G); That cannot be true, as pcgs is the family pcgs
395 FamilyPcgs,pcgs,HomePcgs,pcgs,GeneralizedPcgs,pcgs);
425 FamilyPcgs,pcgs,HomePcgs,pcgs,GeneralizedPcgs,pcgs);
510 "pcgs computable groups using home pcgs",
529 "pcgs computable groups using family pcgs",
1893 if pcgs[j] * pcgs[i] = pcgs[i] * pcgs[j] then
[all …]
H A Dghompcgs.gi163 pcgs:=map!.sourcePcgs;
165 r:=RelativeOrders(pcgs);
169 elm:=pcgs[i]^r[i];
182 elm:=pcgs[j]^pcgs[i];
227 pcgs:=map!.sourcePcgs;
233 elm:=pcgs[i]^r[i];
245 elm:=pcgs[j]^pcgs[i];
284 local pcgs, new,
514 # precompute pcgs
666 #M NaturalIsomorphismByPcgs( <grp>, <pcgs> ) . . presentation through <pcgs>
[all …]
H A Dgrppcatr.gi151 "pcgs computable groups using special pcgs",
180 "pcgs computable groups using special pcgs",
260 "pcgs computable groups using special pcgs",
300 "pcgs computable groups using special pcgs",
348 pcgsN := InducedPcgsByPcSequenceNC( pcgs, pcgs{[next..m]} );
389 "pcgs computable groups using special pcgs",
397 "pcgs computable groups using special pcgs",
408 "pcgs computable groups using special pcgs",
457 "pcgs computable groups using special pcgs",
615 "pcgs computable groups using special pcgs",
[all …]
/dports/math/gap/gap-4.11.0/pkg/polenta-1.3.9/lib/
H A Dfinite.gi45 #Print( "pcgs.suitableOrbitPoints", pcgs.suitableOrbitPoints, "\n" );
59 #Print( "pcgs.suitableOrbitPoints", pcgs.suitableOrbitPoints, "\n" );
279 #F ExtendedBasePcgsMod( pcgs, g, d ) . . . . . .. . . . . extend a base pcgs
281 ## g normalizes <pcgs> and we compute a new pcgs for <pcgs, g>.
287 Unbind(pcgs.pcgs);
288 Unbind(pcgs.rels);
326 EnlargeOrbit( pcgs.orbit[i], h, m, pcgs.oper );
328 Add( pcgs.pcref, [i, Length(pcgs.trans[i]),g] );
361 g := pcgs.pcref[Length(pcgs.pcref)][3];
522 ## by pcgs
[all …]
H A Dfinite.gd63 #F ExtendedBasePcgsMod( pcgs, g, d ) . . . . . .. . . . . extend a base pcgs
65 ## g normalizes <pcgs> and we compute a new pcgs for <pcgs, g>.
71 #F RelativeOrdersPcgs_finite( pcgs )
77 #F ExponentvectorPcgs_finite( pcgs, g )
83 #F ExponentvectorPartPcgs( pcgs, g , index)
85 ## g = ...* pcgs.gens[index]^ExponentvectorPartPcgs * ...
97 #F POL_SetPcPresentation(pcgs)
99 ## pcgs is a constructive pc-sequence, calculated
102 ## by pcgs
108 #F POL_TestExpVector_finite( pcgs, g )
/dports/math/gap/gap-4.11.0/pkg/crisp-1.4.5/lib/
H A Dutil.gi77 return rec(primes := primes, generators := gens, pcgs := pcgs);
108 return rec(primes := primes, generators := gens, pcgs := pcgs);
227 p := RelativeOrderOfPcElement(pcgs, pcgs[1]);
299 i -> InducedPcgsByPcSequence(pcgs, pcgs{[i..Length(pcgs)]}));
377 function(pcgs)
394 n := DepthOfPcElement(pcgs, pcgs[i]^p);
400 d := DepthOfPcElement(pcgs, pcgs[j]^p);
407 DepthOfPcElement(pcgs, Comm(pcgs[j], pcgs[k]))));
426 d := DepthOfPcElement(pcgs, Comm(pcgs[k], pcgs[j]));
439 npcgs := InducedPcgsByPcSequenceNC(pcgs, pcgs{[i..Length(pcgs)]});
[all …]
/dports/math/gap/gap-4.11.0/src/
H A Dobjpcgel.cc108 static Obj DepthOfPcElement(Obj self, Obj pcgs, Obj w) in DepthOfPcElement() argument
114 return INTOBJ_INT( LEN_LIST(pcgs) + 1 ); in DepthOfPcElement()
200 static Obj ExponentsOfPcElement(Obj self, Obj pcgs, Obj w) in ExponentsOfPcElement() argument
214 len=LEN_LIST(pcgs); in ExponentsOfPcElement()
265 return DepthOfPcElement<UInt1>(self, pcgs, w); in Func8Bits_DepthOfPcElement()
275 return ExponentOfPcElement<UInt1>(self, pcgs, w, pos); in Func8Bits_ExponentOfPcElement()
294 return ExponentsOfPcElement<UInt1>(self, pcgs, w); in Func8Bits_ExponentsOfPcElement()
304 return DepthOfPcElement<UInt2>(self, pcgs, w); in Func16Bits_DepthOfPcElement()
333 return ExponentsOfPcElement<UInt2>(self, pcgs, w); in Func16Bits_ExponentsOfPcElement()
343 return DepthOfPcElement<UInt4>(self, pcgs, w); in Func32Bits_DepthOfPcElement()
[all …]
/dports/math/gap/gap-4.11.0/pkg/autpgrp-1.10.2/gap/
H A Dgeneral.gi23 #F RewriteDef( pcgs, defn, p )
25 RewriteDef := function( pcgs, defn, p )
33 w := pcgs[d]^p;
38 w := Comm( pcgs[d[1]], pcgs[d[2]] );
88 #F InducedPcgsByBasis( pcgs, basis )
90 InducedPcgsByBasis := function( pcgs, basis )
92 pcgsN := NumeratorOfModuloPcgs( pcgs );
129 local pcgs;
130 pcgs := Pcgs(H);
140 local pcgs, auts, alpha, fac, i, imgs;
[all …]
H A Dinitmat.gi17 pcgs := SpecialPcgs( G );
18 first := LGFirst( pcgs );
22 max := Length(pcgs);
29 pcgsN := InducedPcgsByPcSequenceNC( pcgs, pcgs{[f..max]} );
30 pcgsM := InducedPcgsByPcSequenceNC( pcgs, pcgs{[m..max]} );
31 pcgsH := InducedPcgsByPcSequenceNC( pcgs, pcgs{[n..max]} );
56 pcgs := SpecialPcgs( G );
60 first := LGFirst( pcgs );
63 max := Length(pcgs);
67 pcgsN := InducedPcgsByPcSequenceNC( pcgs, pcgs{[first[i]..max]} );
[all …]

1234567891011