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##
#W perlist.gi GAP4 Package `RCWA' Stefan Kohl
##
## This file contains code which deals with periodic lists.
## Periodic lists are implemented in the FR package.
##
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#############################################################################
##
#M Permuted( <perlist>, <g> ) . for a periodic list and an rcwa permut. of Z
##
## Returns the periodic list which is obtained from <perlist> by permuting
## the entries by the rcwa permutation <g>.
## Periodic lists are implemented in the FR package, which therefore needs
## to be loaded in order to use this method.
##
InstallOtherMethod( Permuted,
"for a periodic list and an rcwa permutation of Z (RCWA)",
ReturnTrue, [ IsPeriodicList, IsRcwaMappingOfZ ], 0,
function ( perlist, g )
local preperiod, period,
preperiod_bound, preperiod_img, period_bound, period_img,
perlist_img, inv;
preperiod := PrePeriod(perlist);
period := Period(perlist);
if not IsBijective(g) then TryNextMethod(); fi;
if not IsSignPreserving(g) then
Error("`Permuted' for a periodic list <l> and a <g> in RCWA(Z): \n",
"<g> must fix the nonnegative integers setwise, as <l> \n",
"does not have entries at negative positions.");
TryNextMethod();
fi;
inv := Inverse(g);
period_bound := Mod(g) * Mult(g) * Div(g) * Length(period);
if not IsEmpty(preperiod) then
preperiod_bound := Maximum([0..Length(preperiod)-1]^g)+1;
preperiod_bound := period_bound
* (Int((preperiod_bound-1)/period_bound)+1);
else preperiod_bound := 0; fi;
preperiod_img := List([0..preperiod_bound-1],n->perlist[n^inv+1]);
period_img := List([preperiod_bound..preperiod_bound+period_bound-1],
n->perlist[n^inv+1]);
perlist_img := PeriodicList(preperiod_img,period_img);
CompressPeriodicList(perlist_img);
return perlist_img;
end );
#############################################################################
##
#M Permuted( <perlist>, <f> ) . for periodic list and non-bij. rcwa mapping
##
## Returns the periodic list whose n-th entry is the sum of the n^(f^-1)-th
## entries of <perlist>, where n^(f^-1) denotes the preimage of n under <f>.
## Periodic lists are implemented in the FR package, which therefore needs
## to be loaded in order to use this method.
##
InstallOtherMethod( Permuted,
"for a periodic list and an rcwa mapping of Z (RCWA)",
ReturnTrue, [ IsPeriodicList, IsRcwaMappingOfZ ], 0,
function ( perlist, f )
local preperiod, period,
preperiod_bound, preperiod_img, period_bound, period_img,
perlist_img, m, r, i;
preperiod := PrePeriod(perlist);
period := Period(perlist);
if IsBijective(f) or Multiplier(f) = 0 then TryNextMethod(); fi;
if not IsSignPreserving(f) then
Error("`Permuted' for a periodic list <l> and an rcwa mapping <f>: \n",
"<f> must fix the nonnegative integers setwise, as <l> \n",
"does not have entries at negative positions.");
TryNextMethod();
fi;
period_bound := Mod(f) * Mult(f) * Div(f) * Length(period);
if not IsEmpty(preperiod) then
preperiod_bound := Maximum([0..Length(preperiod)-1]^f)+1;
preperiod_bound := period_bound
* (Int((preperiod_bound-1)/period_bound)+1);
else preperiod_bound := 0; fi;
preperiod_img := List([0..preperiod_bound-1],
n->Sum(perlist{PreImagesElmNC(f,n)+1}));
period_img := List([preperiod_bound..preperiod_bound+period_bound-1],
n->Sum(perlist{PreImagesElmNC(f,n)+1}));
perlist_img := PeriodicList(preperiod_img,period_img);
CompressPeriodicList(perlist_img);
return perlist_img;
end );
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##
#M IsSubset( <C>, <perlist> ) . . . . . for a collection and a periodic list
##
InstallMethod( IsSubset,
"for a collection and a periodic list (RCWA)", ReturnTrue,
[ IsListOrCollection, IsPeriodicList ], 0,
function ( C, perlist )
return IsSubset(C,PrePeriod(perlist)) and IsSubset(C,Period(perlist));
end );
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##
#M SumOp( <perlist> ) . . . . . . . . . . . . . . . . . . for periodic lists
##
InstallMethod( SumOp,
"for periodic lists (RCWA)", true, [ IsPeriodicList ], 0,
function ( perlist )
if not IsSubset(Rationals,perlist) then TryNextMethod(); fi;
if ForAll(Period(perlist),IsZero) then return Sum(PrePeriod(perlist));
elif Sum(Period(perlist)) > 0 then return infinity;
elif Sum(Period(perlist)) < 0 then TryNextMethod(); # -infinity
else return fail; fi; # Alternating case, like 1, -1, 1, -1, 1, -1, ...
end );
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##
#M ProductOp( <perlist> ) . . . . . . . . . . . . . . . . for periodic lists
##
InstallMethod( ProductOp,
"for periodic lists (RCWA)", true, [ IsPeriodicList ], 0,
function ( perlist )
if not IsSubset(Rationals,perlist) then TryNextMethod(); fi;
if Product(PrePeriod(perlist)) = 0 or Product(Period(perlist)) = 0
then return 0;
elif Product(List(Period(perlist),AbsoluteValue)) < 1 then return 0;
elif Minimum(Period(perlist)) > 0 and Product(Period(perlist)) > 1
then return infinity;
elif Set(Period(perlist)) = [1] # Constant period 1, 1, 1, ... case.
then return Product(PrePeriod(perlist));
else return fail; fi; # Negative factors, non-convergent case.
end );
#############################################################################
##
#M AdditiveInverseOp( <perlist> ) . . . . . . . . . . . . for periodic lists
##
InstallOtherMethod( AdditiveInverseOp,
"for periodic lists (RCWA)", true, [ IsPeriodicList ], 0,
l -> PeriodicList(-PrePeriod(l),-Period(l)));
#############################################################################
##
#M \+( <l1>, <l2> ) . . . . . . . . . . . . . . . . . . . for periodic lists
##
InstallOtherMethod( \+,
"for periodic lists (RCWA)", ReturnTrue,
[ IsPeriodicList, IsPeriodicList ], 0,
function ( l1, l2 )
local prelng, perlng, sum;
prelng := Maximum(Length(PrePeriod(l1)),Length(PrePeriod(l2)));
perlng := Lcm(Length(Period(l1)),Length(Period(l2)));
sum := PeriodicList(l1{[1..prelng]} + l2{[1..prelng]},
l1{[prelng+1..prelng+perlng]}
+ l2{[prelng+1..prelng+perlng]});
CompressPeriodicList(sum);
return sum;
end );
#############################################################################
##
#M \-( <l1>, <l2> ) . . . . . . . . . . . . . . . . . . . for periodic lists
##
InstallOtherMethod( \-,
"for periodic lists (RCWA)", ReturnTrue,
[ IsPeriodicList, IsPeriodicList ], 0,
function ( l1, l2 ) return l1 + (-l2); end );
#############################################################################
##
#M \+( <l>, <n> ) . . . . . . . . . . . . . . for periodic list and constant
#M \+( <n>, <l> ) . . . . . . . . . . . . . . for constant and periodic list
##
InstallOtherMethod( \+,"for periodic list and constant (RCWA)", ReturnTrue,
[ IsPeriodicList, IsAdditiveElement ], 0,
function ( l, n ) return PeriodicList(PrePeriod(l)+n,Period(l)+n); end );
InstallOtherMethod( \+,"for constant and periodic list (RCWA)", ReturnTrue,
[ IsAdditiveElement, IsPeriodicList ], 0,
function ( n, l ) return PeriodicList(n+PrePeriod(l),n+Period(l)); end );
#############################################################################
##
#M \-( <l>, <n> ) . . . . . . . . . . . . . . for periodic list and constant
#M \-( <n>, <l> ) . . . . . . . . . . . . . . for constant and periodic list
##
InstallOtherMethod( \-,"for periodic list and constant (RCWA)", ReturnTrue,
[ IsPeriodicList, IsAdditiveElement ], 0,
function ( l, n ) return PeriodicList(PrePeriod(l)-n,Period(l)-n); end );
InstallOtherMethod( \-,"for constant and periodic list (RCWA)", ReturnTrue,
[ IsAdditiveElement, IsPeriodicList ], 0,
function ( n, l ) return PeriodicList(n-PrePeriod(l),n-Period(l)); end );
#############################################################################
##
#M \*( <l>, <n> ) . . . . . . . . . . . . . . for periodic list and constant
#M \*( <n>, <l> ) . . . . . . . . . . . . . . for constant and periodic list
##
InstallOtherMethod( \*,"for periodic list and constant (RCWA)", ReturnTrue,
[ IsPeriodicList, IsMultiplicativeElement ], 0,
function ( l, n ) return PeriodicList(PrePeriod(l)*n,Period(l)*n); end );
InstallOtherMethod( \*,"for constant and periodic list (RCWA)", ReturnTrue,
[ IsMultiplicativeElement, IsPeriodicList ], 0,
function ( n, l ) return PeriodicList(n*PrePeriod(l),n*Period(l)); end );
#############################################################################
##
#M \/( <l>, <n> ) . . . . . . . . . . . . . . for periodic list and constant
##
InstallOtherMethod( \/,"for periodic list and constant (RCWA)", ReturnTrue,
[ IsPeriodicList, IsMultiplicativeElement ], 0,
function ( l, n ) return PeriodicList(PrePeriod(l)/n,Period(l)/n); end );
#############################################################################
##
#E perlist.gi . . . . . . . . . . . . . . . . . . . . . . . . . . ends here
