-
Notifications
You must be signed in to change notification settings - Fork 9
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
- Loading branch information
1 parent
3bb9360
commit 6ae2939
Showing
28 changed files
with
527 additions
and
49 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1 +1 @@ | ||
| 24 May 2023 | ||
| 25 July 2023 |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,146 @@ | ||
|
|
||
|
|
||
| ###################################################### | ||
| ###################################################### | ||
| InstallGlobalFunction(HAP_ChainComplexToEquivariantChainComplex, | ||
| function(C) | ||
| local R, G, Elts, Boundary, i, x, m; | ||
|
|
||
| G:=Group( () ); | ||
| Elts:=Elements(G); | ||
|
|
||
| Boundary:=function(n,k) | ||
| local v, bnd; | ||
| v:=C!.boundary(n,k); | ||
| bnd:=[]; | ||
|
|
||
| for i in [1..Length(v)] do | ||
| if v[i]<>0 then x:=[SignInt(v[i])*i,1]; | ||
| for m in [1..AbsInt(v[i])] do | ||
| Add(bnd,x); | ||
| od; | ||
| fi; | ||
| od; | ||
| return bnd; | ||
| end; | ||
|
|
||
| R:=Objectify(HapResolution, | ||
| rec( | ||
| dimension:=C!.dimension, | ||
| boundary:=Boundary, | ||
| homotopy:=fail, | ||
| elts:=Elts, | ||
| group:=G, | ||
| vectorField:=fail, | ||
| properties:= | ||
| [["length",EvaluateProperty(C,"length")], | ||
| ["reduced",true], | ||
| ["type","resolution"], | ||
| ["characteristic",0] ])); | ||
|
|
||
|
|
||
| return R; | ||
| end); | ||
| ###################################################### | ||
| ###################################################### | ||
|
|
||
|
|
||
| ################################################################### | ||
| ################################################################### | ||
| InstallGlobalFunction(HAP_bockstein, | ||
| function(A) | ||
| local G,i,prime,x,a,b,c,h,s,bhomc,B,C,psi,R,dim,cons,homs,bas,bok,gens; | ||
|
|
||
| G:=Group(()); | ||
| prime:=Characteristic(A); | ||
| x:=[2..prime^2]; | ||
| Add(x,1); | ||
| x:=PermList(x); | ||
|
|
||
| a:=Group(x^prime);; | ||
| b:=Group(x);; | ||
| c:=Group(x^prime);; | ||
|
|
||
| #bhomc:=NaturalHomomorphismByNormalSubgroup(b,a); | ||
| B:=TrivialGModuleAsGOuterGroup(G,b); | ||
| #C:=TrivialGModuleAsGOuterGroup(G,Image(bhomc)); | ||
| C:=TrivialGModuleAsGOuterGroup(G,c); | ||
| bhomc:=GroupHomomorphismByImages(b,c,[x],[x^prime]); | ||
| psi:=GOuterGroupHomomorphism(); | ||
| psi!.Source:=B; | ||
| psi!.Target:=C; | ||
| psi!.Mapping:=bhomc; | ||
|
|
||
| C:=A!.chainComplex; | ||
| dim:=Length(C); | ||
| R:=HAP_ChainComplexToEquivariantChainComplex(C); | ||
| R!.properties[1]:=["length",dim+1]; | ||
|
|
||
| cons:=[]; | ||
| for i in [1..dim-1] do | ||
| Add(cons, ConnectingCohomologyHomomorphism(psi,i,R)); | ||
| od; | ||
| homs:=[]; | ||
| for h in cons do | ||
| s:=Source(h); | ||
| Add(homs,s!.nat); | ||
| od; | ||
| s:=Target(h); | ||
| Add(homs,s!.nat); | ||
|
|
||
| bas:=Basis(A); | ||
| gens:=List(homs,h->Target(h!.Mapping)); | ||
| gens:=List(gens,g->GeneratorsOfGroup(g)); | ||
|
|
||
| ######################################## | ||
| bok:=function(x) | ||
| local w,ww,h,z,cnt; | ||
|
|
||
| w:=Coefficients(bas,x); | ||
| ww:=[]; | ||
| for i in [2..Length(w)] do | ||
| Add(ww,[IntFFE(w[i]),A!.int2pair[i]]- [0,[1,0]]); | ||
| od; | ||
|
|
||
|
|
||
| ww:=Filtered(ww,x->x[2][1]<dim); | ||
|
|
||
| h:=[]; | ||
| for i in [1..Length(ww)] do | ||
| Add(h,[ww[i][2][1]+1 , | ||
|
|
||
| Image(cons[ww[i][2][1]]!.Mapping, gens[ww[i][2][1]][ww[i][2][2]])^ww[i][1] | ||
|
|
||
| ] ); | ||
| od; | ||
|
|
||
| h:=List(h,x->[x[1], ExtRepOfObj( | ||
| Factorization(Source(homs[x[1]]!.Mapping), | ||
| PreImagesRepresentative(homs[x[1]]!.Mapping, x[2])) | ||
| ) | ||
| ]); | ||
|
|
||
| h:=Filtered(h,z->Length(z[2])>0); | ||
| w:=0*A.1; | ||
| for z in h do | ||
| cnt:=A!.pair2int[z[1]+1][1]-1; | ||
|
|
||
| w:=w+ | ||
| Sum(List([1..Length(z[2])/2],k-> bas[ cnt+ z[2][2*k-1] ]*z[2][2*k])); | ||
| ; | ||
| od; | ||
|
|
||
| return w; | ||
|
|
||
| end; | ||
| ######################################## | ||
|
|
||
| return bok; | ||
| end); | ||
| ################################################################### | ||
| ################################################################### | ||
|
|
||
|
|
||
|
|
||
|
|
||
|
|
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Oops, something went wrong.