Impressum pkghomalg.gi Sprache: Shell

####java.lang.StringIndexOutOfBoundsException: Index 80 out of bounds for length 80
##
## simpcomp java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
#java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2
## Loaded when(posfail)
#
# $$
##
######## (jmod 2)then

# helper AddToMatElmmatrices[-],os,,one);
# to the following java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 14
java.lang.StringIndexOutOfBoundsException: Range [10, 9) out of bounds for length 23
# 0 - rationals
#1-integers
# n - integers modreturn ;
java.lang.StringIndexOutOfBoundsException: Range [11, 7) out of bounds for length 11
 if(od;
 return matrices
 elifend)
 return
 elif
 return########################################java.lang.StringIndexOutOfBoundsException: Index 80 out of bounds for length 80
 else
 return HomalgRingOfIntegers(modulus);
 fi;
end;

SCIntFunc.bdOperator:=function(simplex)
 local b,cur,i,j,pos;
 b:=[];

 #all positions, i=kill entry
 for i in [1..Length(simplex)] do
 cur:=[];
 pos:=1;

 #extract one boundary face
 for j in [1..Length(simplex)] do
 if(i=j) then continue; fi;

 cur[pos]:=simplex[##<eth Name"A=complex,modulus">
 =pos1java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
 od;

 #add to list of boundary faces
 Add(b,ShallowCopy(cur));
 od;

 return bof <C0<C> the
#<M\{}/M>-homology, a valueof <>1<Ccomputesthe

################################################################################
##<#GAPDoc prime power <\athbb{F_</M>- ./>
## <ManSection>
## <Meth Name="SCHomalgBoundaryMatrices" Arg="complex,modulus"/>
## <Returns>a list of <Package>homalg</Package> objects# Notethatif you are interested not int ranksof homology
## <K>#<ef=" /.
###<<[DATA[
## #gap SCLibSearchByName"";
## #gap> :SCLibLoad(ast11);
## <Arg>modulus</Arg>: a value of <C>0</C> yields##gap>SCHomalgHomology,);
## a value of<C>1</> yields M\Z<M>matrices nd avalue
## <C>q</C>,## ]]></Example>
then
## <Example><![CDATA[
## gap> SCLib.SearchByName("CP^2 (VT)");
## gap> ( 2=)then
# >SCHomalgBoundaryMatrices(c,0);
## ]]></Example>
## </Description>
## </ManSection>
##<#/GAPDoc>
################################################################################
InstallMethod(SCHomalgBoundaryMatricesOp,
"for SCSimplicialComplex and Integer",
[SCIsSimplicialComplex, IsInt],
function(complex, modulus)
 local tmp,skel,x,matrices,one,minusone,k,p,i,j,b,ind,pos,res,d,ring;

 ring:=SCIntFunc.ModulusToHomalgRing(modulus);
 if(ring=fail) then
 return fail;
 fi;

 # for matrices
 matrices := [];

 # 1 and -1 in ring
 one:=One(ring);
 minusone:=MinusOne(ring);

 skel:=SCFaceLatticeEx(complex);
 d:=SCDim(complex);

 matrices[d+1]:=HomalgInitialMatrix(0,Length(skel[d+1]),ring);
 ResetFilterObj(matrices[d+1], IsInitialMatrix);
 for k in [2..d+1] do
 matrices[k-1] := HomalgInitialMatrix(Length(skel[k]),
 Length(skel[k-1]),ring);

 for i in [1..Length(skel[k])] do
 #get boundary of current simplex
 b:=SCIntFunc.bdOperator(skel[k][i]);

 for j in [1..Length(b)] do
 pos:=Position(skel[k-1],b[j]);
 if(pos<>fail) then
 if((j mod 2)=0) then
 AddToMatElm( matrices[k-1], i, pos, one );
 else
 AddToMatElm( matrices[k-1], i, pos, minusone );
 fi;
 else
 Info(InfoSimpcomp,1,"SCHomalgBoundaryOperatorMatrices: list of ",
 "boundary skel[k-1] is not complete k=",k,", b[j]=",b[j],"!");
 return fail;
 fi;
 od;
 od;
 ResetFilterObj(matrices[k-1],IsInitialMatrix);
 od;

 return matrices;
end);

################################################################################
##<#GAPDoc Label="SCHomalgCoboundaryMatrices">
## <ManSection>
## <Meth Name="SCHomalgCoboundaryMatrices" Arg="complex,modulus"/>
## <Returns>a list of <Package>homalg</Package> objects upon success,
## <K>fail</K> otherwise.</Returns>
## <Description>
## This function computes the coboundary operator matrices for the simplicial
## complex <Arg>complex</Arg> with a ring of coefficients as specified by
## <Arg>modulus</Arg>: a value of <C>0</C> yields <M>\mathbb{Q}</M>-matrices,
## a value of <C>1</C> yields <M>\mathbb{Z}</M>-matrices and a value of
## <C>q</C>, q a prime or a prime power, computes the
## <M>\mathbb{F}_q</M>-matrices.
## <Example><![CDATA[
## gap> SCLib.SearchByName("CP^2 (VT)");
## gap> c:=SCLib.Load(last[1][1]);;
## gap> SCHomalgCoboundaryMatrices(c,0);
## ]]></Example>
## </Description>
## </ManSection>
##<#/GAPDoc>
################################################################################
InstallMethod(SCHomalgCoboundaryMatricesOp,
"for SCSimplicialComplex and Integer",
[SCIsSimplicialComplex, IsInt],
 function( complex, modulus )
 local tmp,skel,x,matrices,one,minusone,k,p,i,j,b,ind,pos,res,d,ring;

 ring:=SCIntFunc.ModulusToHomalgRing(modulus);
 if(ring=fail) then
 return fail;
 fi;

 # for matrices
 matrices := [];

 # 1 and -1 in ring
 one:=One(ring);
 minusone:=MinusOne(ring);

 skel:=SCFaceLatticeEx(complex);
 d:=SCDim(complex);

 matrices[d+1]:=HomalgInitialMatrix(Length(skel[d+1]),0,ring);
 ResetFilterObj(matrices[d+1],IsInitialMatrix);
 for k in [2..d+1] do
 matrices[k-1]:=HomalgInitialMatrix(Length(skel[k-1]),Length(skel[k]),ring);

 for i in [1..Length(skel[k])] do
 #get boundary of current simplex
 b:=SCIntFunc.bdOperator(skel[k][i]);

 for j in [1..Length(b)] do
 pos:=Position(skel[k-1],b[j]);
 if(pos<>fail) then
 if((j mod 2)=0) then
 AddToMatElm(matrices[k-1],pos,i,one);
 else
 AddToMatElm(matrices[k-1],pos,i,minusone);
 fi;
 else
 Info(InfoSimpcomp,1,"SCHomalgCoboundaryOperatorMatrices: list of ",
 "boundary skel[k] is not complete!");
 return fail;
 fi;
 od;
 od;
 ResetFilterObj(matrices[k-1],IsInitialMatrix);
 od;
 return matrices;
end);

################################################################################
##<#GAPDoc Label="SCHomalgHomology">
## <ManSection>
## <Meth Name="SCHomalgHomology" Arg="complex,modulus"/>
## <Returns>a list of integers upon success, <K>fail</K> otherwise.</Returns>
## <Description>
## This function computes the ranks of the homology groups of
## <Arg>complex</Arg> with a ring of coefficients as specified by
## <Arg>modulus</Arg>: a value of <C>0</C> computes the
## <M>\mathbb{Q}</M>-homology, a value of <C>1</C> computes the
## <M>\mathbb{Z}</M>-homology and a value of <C>q</C>, q a prime or a
## prime power, computes the <M>\mathbb{F}_q</M>-homology ranks.
## Note that if you are interested not only in the ranks of the homology
## groups, but rather their full structure, have a look at the function
## <Ref Meth="SCHomalgHomologyBasis" />.
## <Example><![CDATA[
## gap> SCLib.SearchByName("K3");
## gap> c:=SCLib.Load(last[1][1]);;
## gap> SCHomalgHomology(c,0);
## ]]></Example>
## </Description>
## </ManSection>
##<#/GAPDoc>
################################################################################
InstallMethod(SCHomalgHomologyOp,
"for SCSimplicialComplex and Integer",
[SCIsSimplicialComplex, IsInt],
function(complex,modulus)
 #homology: ker(M[i])/im(M[i+1])
 local M,C,m,morphisms,L,i,H,ring,rnam;

 ring:=SCIntFunc.ModulusToHomalgRing(modulus);
 if ring=fail then
 return fail;
 fi;

 rnam:=RingName(ring);

 M:=SCHomalgBoundaryMatrices(complex,modulus);

 Info(InfoSimpcomp,2,"SCHomalgHomologyOp: computing ",
 rnam,"-homology ranks...");

 L := [];
 for i in [ 1 .. Length( M ) ] do
 L[i] := SCIntFunc.DeepCopy(DimensionsMat( M[i] ));
 L[i][3] := RowRankOfMatrix( M[i] );
 L[i][4] := L[i][2] - L[i][3];
 od;

 H := [ L[1][4] ]; #first image dimension
 for i in [ 2 .. Length( L ) ] do
 H[i] := L[i][4] - L[i-1][3]; #dim ker - dim im
 od;

 Info(InfoSimpcomp,1,"SCHomalgHomologyOp: ",rnam,"-homology ranks: ",H);
 return complex,modulus)
end);

################################################################################
##<#GAPDoc Label="SCHomalgHomologyBasis">
## <ManSection>
## <Meth Name="SCHomalgHomologyBasis" Arg="complex,modulus"/>
## <Returns>a <Package>homalg</Package> object upon success, <K>fail</K>
## otherwise.</Returns>
## <Description>
## This function computes the homology groups (including explicit bases of
## the modules involved) of <Arg>complex</Arg> with a ring of coefficients
## as specified by <Arg>modulus</Arg>: a value of <C>0</C> computes the
## <M>\mathbb{Q}</M>-homology, a value of <C>1</C> computes the
## <M>\mathbb{Z}</M>-homology and a value of <C>q</C>, q a prime or a prime
## power, computes the <M>\mathbb{F}_q</M>-homology groups.
## The <M>k</M>-th homology group <C>hk</C> can be obtained by calling
## <C>hk:=CertainObject(homology,k);</C>, where <C>homology</C> is the
## <Package>homalg</Package> object returned by this function. The
## generators of <C>hk</C> can then be obtained via
## <C>GeneratorsOfModule(hk);</C>.
## Note that if you are only interested in the ranks of the homology groups,
## then it is better to use the funtion <Ref Meth="SCHomalgHomology" />
## which is way faster.
## <Example><![CDATA[
## gap> SCLib.SearchByName("K3");
## gap> c:=SCLib.Load(last[1][1]);;
## gap> SCHomalgHomologyBasis(c,0);
>/java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
## <java.lang.StringIndexOutOfBoundsException: Range [26, 27) out of bounds for length 17
#<ManSection
##<#/## gap>SCHomalgHomologyBasis,)
########################################
InstallMethod(SCHomalgHomologyBasisOp,
"for SCSimplicialComplex and Integer"#/Description>
[omplex IsInt,
function(complex,modulus)
 #homology: java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 12
local ,,,mmorphismsL,,H,ingrnamjava.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
 f Integer"
 S,IsInt]java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
ring
 java.lang.StringIndexOutOfBoundsException: Range [16, 17) out of bounds for length 16
 fi;

 rnam:=RingName(ring);

 failjava.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
C=HomalgComplex(HomalgMap(M1 ,1)java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 45
 for m { . Length(M )1 }djava.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
 ,m)java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
 odjava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5

 # C=(C;
 # C!.SkipHighestDegreeHomology := true;
 # C!.java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 2
 # C !SkipHighestDegreeHomology: ;
C!.StringBeforeDisplay :="";
java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2
(,,S:constructed,rnamjava.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 67
java.lang.StringIndexOutOfBoundsException: Range [4, 1) out of bounds for length 25
 ## <Mmathbb{}/>cohomology and ofCq/> prime or
end# power,computesthe M\{F_</Mcohomology ranks.P>

############################################## that ifyou nterested not inthe of cohomologyjava.lang.StringIndexOutOfBoundsException: Index 75 out of bounds for length 75
#<G">
## <ManSection>
#<"" ","java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
# <list of integers upon success, <K>fail</K> otherwise.</Returns>
## <Description>
## This function computes the ranks of the cohomology groups of
## <Arg>complex</Arg> with a java.lang.StringIndexOutOfBoundsException: Range [49, 31) out of bounds for length 49
>/> value of <C>0</C> computes the
## <M>\mathbb{Q}</M>-cohomology,
# <>mathbb{}/>canda C><C,q primeora
## f iin[1. M)]do
## Note that if you are interested not only in [i =S.DimensionsMat(M[ )java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
## L[]4]: []1 Li[]java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
#< " /.
## < for i in [ 2 .. Length( L ) ] do
#gap .""java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
#gap :Loadlast1][1]);;
## gap> SCHomalgCohomology(c,0);
## ]]></Example>
## </Description>
## </ManSection>
##<#/GAPDoc>
###########################################
InstallMethod(SCHomalgCohomologyOp,
"for SCSimplicialComplex and Integer",
[ returnH;
function(complex,modulus)
 #cohomology: ker;
 local###########################################

ring:=.(modulus)
 # < Name"" =c,modulus/
 eturn ;
# otherwise<Returns>

 rnam:=RingName(ring);

:SCHomalgCoboundaryMatricescomplex,)java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49

 Info(InfoSimpcomp,2,"SCHomalgCohomologyOp: computing ",rnam,
 "-cohomology ranks...");

 L := [];
 for i in [ 1# Arg></Arg> avalue of <>0/> computes the
 []:=SCIntFunc.eepCopyDimensionsMat(Mi )
 L#<\{}/>- value Cq/> a or
#power,computes the M\{F_/>h </java.lang.StringIndexOutOfBoundsException: Range [63, 64) out of bounds for length 63
 od;
 H := [ L[1][4] ]; #first# Cck=c,)<C,where
 for i in [ 2 .. Length( L ) ] do
 H[i] := L[i][4] - L[i-1][3]; #dim ker - dim im
 od;

 Info(InfoSimpcomp,1,"SCHomalgCohomologyOp: ",rnam,"-cohomology ranks: ",H);
 return H;
end);

################################################################################
##<#GAPDoc Label="SCHomalgCohomologyBasis">
## <ManSection>
## <Meth Name="SCHomalgCohomologyBasis" Arg="complex,modulus"/>
## <Returns>a <Package>homalg</Package> object upon success, <K>fail</K>
## otherwise.</Returns>
## <Description>
## This function computes the cohomology groups (including explicit bases of
## the modules involved) of <Arg>complex</Arg> with a ring of coefficients as
## specified by <Arg>modulus</Arg>: a value of <C>0</C> computes the
## <M>\mathbb{Q}</M>-cohomology, a value of <C>1</C> computes the
## <M>\mathbb{Z}</M>-cohomology and a value of <C>q</C>, q a prime or a prime
## power, computes the <M>\mathbb{F}_q</M>-homology groups.
## The <M>k</M>-th cohomology group <C>ck</C> can be obtained by calling
## <C>ck:=CertainObject(cohomology,k);</C>, where <C>cohomology</C> is the
## <Package>homalg</Package> object returned by this function. The
## generators of <C>ck</C> can then be obtained via
## <C>GeneratorsOfModule(ck);</C>.
## Note that if you are only interested in the ranks of the cohomology groups,
## then it is better to use the funtion <Ref Meth="SCHomalgCohomology" />
## which is way faster.
## <Example><![CDATA[
## gap> SCLib.SearchByName("K3");
## gap> c:=SCLib.Load(last[1][1]);;
## gap> SCHomalgCohomologyBasis(c,0);
## ]]></Example>
## </Description>
## </ManSection>
##<#/GAPDoc>
################################################################################
InstallMethod(SCHomalgCohomologyBasisOp,
"for SCSimplicialComplex and Integer",
[SCIsSimplicialComplex, IsInt],
function(complex,modulus)
 #cohomology: ker( M[i+1] ) / im( M[i] )
 local M,R, C, m,morphisms,L,i,H,ring,rnam;

 ring:=SCIntFunc.ModulusToHomalgRing(modulus);
 if ring=fail then
 return fail;
 fi;

 rnam:=RingName(ring);

 M:=SCHomalgCoboundaryMatrices(complex,modulus);
 C := HomalgCocomplex( HomalgMap( M[1] ), 1 );
 for m in M{[ 2 .. Length( M )-1 ]} do
 Add( C, m );
 od;

 # C:=ByASmallerPresentation(C);
 # C!.SkipHighestDegreeHomology := true;
 # C!.HomologyOnLessGenerators := true;
 # C!.DisplayHomology := true;
 # C!.StringBeforeDisplay :="";

 Info(InfoSimpcomp,1,"SCHomalgCohomologyBasisOp: constructed ",rnam,
 "-cohomology groups.");
 return Cohomology(C);
end);

#homologybasis:=
#function(h,k)
# local hk;
# hk:=CertainObject(h,k);
# return GeneratorsOfModule(hk);
#end;

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