|
InstallGlobalFunction( QPAStringQuiverRho,
function(Q,rho)
local rho_q, i,j,k,arr,arr1;
rho_q := [];
for i in [1..Length(rho)] do
arr := [];
for j in [1..Length(rho[i])] do
for k in [1..NumberOfArrows(Q)] do
if rho[i][j] = String(ArrowsOfQuiver(Q)[k])[1] then
Add(arr,ArrowsOfQuiver(Q)[k]);
fi;
od;
od;
arr1 := arr[1];
for k in [2..Length(arr)] do
arr1 := arr1*arr[k];
od;
Add(rho_q, arr1);
od;
return rho_q;
end
);
InstallGlobalFunction( QPAStringSigmaEps,
function( A )
local Q, rho1, rho, i, onerel, tworel, str, Composable_Matrix, IsComposable, temp_in, temp_out,
j, k, sigma, eps, x, y;
Q := QuiverOfPathAlgebra(A);
rho := RelationsOfAlgebra(A);
rho1 := [];
for i in [1..Length(rho)] do
onerel := CoefficientsAndMagmaElements(rho[i]);
tworel := WalkOfPath(onerel[1]);
str := Concatenation(List(tworel, a -> String(a)));
Append(rho1, [str]);
od;
Composable_Matrix := function(Q,rho)
local mat, x, str, i, j;
mat := [];
for i in [1..NumberOfArrows(Q)] do
str := [];
for j in [1..NumberOfArrows(Q)] do
if SourceOfPath(ArrowsOfQuiver(Q)[i]) =
TargetOfPath(ArrowsOfQuiver(Q)[j]) and not
\in(ArrowsOfQuiver(Q)[j]*ArrowsOfQuiver(Q)[i],rho) then
Append(str, [1]);
else
Append(str, [0]);
fi;
od;
Append(mat, [str]);
od;
return mat;
end;
IsComposable := function(Q,rho,arrow1,arrow2)
local i, Mat, pos1, pos2, j;
Mat := Composable_Matrix(Q,rho);
for i in [1..NumberOfArrows(Q)] do
if arrow1 = ArrowsOfQuiver(Q)[i] then
break;
fi;
od;
for j in [1..NumberOfArrows(Q)] do
if arrow2 = ArrowsOfQuiver(Q)[j] then
break;
fi;
od;
return Mat[i][j];
end;
temp_in := function(Q,i,j)
return SIntChar(String(IncomingArrowsOfVertex(VerticesOfQuiver(Q)[i])[j])[1])
- SIntChar('a') + 1;
end;
temp_out := function(Q,i,j)
return SIntChar(String(OutgoingArrowsOfVertex(VerticesOfQuiver(Q)[i])[j])[1])
- SIntChar('a') + 1;
end;
sigma := [];
eps := [];
for i in [1..NumberOfArrows(Q)] do
Append(sigma, [0]);
Append(eps, [0]);
od;
rho := QPAStringQuiverRho(Q,rho1);
for i in [1..NumberOfVertices(Q)] do
x := IncomingArrowsOfVertex(VerticesOfQuiver(Q)[i]);
y := OutgoingArrowsOfVertex(VerticesOfQuiver(Q)[i]);
if Length(x) = 2 then
eps[temp_in(Q, i, 1)] := 1;
eps[temp_in(Q, i, 2)] := -1;
if Length(y) = 1 then
if IsComposable(Q, rho, y[1], x[1]) = 1 then
sigma[temp_out(Q, i, 1)] := -1;
elif IsComposable(Q, rho, y[1], x[2]) = 1 then
sigma[temp_out(Q, i, 1)] := 1;
fi;
elif Length(y) = 2 then
if IsComposable(Q, rho, y[1], x[1]) = 1 or
IsComposable(Q, rho, y[2], x[2]) = 1 then
sigma[temp_out(Q, i, 1)] := -1;
sigma[temp_out(Q, i, 2)] := 1;
else
sigma[temp_out(Q, i, 1)] := 1;
sigma[temp_out(Q, i, 2)] := -1;
fi;
fi;
elif Length(x) = 1 then
if Length(y) = 1 then
eps[temp_in(Q, i, 1)] := 1;
sigma[temp_out(Q, i, 1)] := -1;
elif Length(y) = 2 then
sigma[temp_out(Q, i, 1)] := 1;
sigma[temp_out(Q, i, 2)] := -1;
if IsComposable(Q, rho, y[1], x[1]) = 1 then
eps[temp_in(Q, i, 1)] := -1;
else
eps[temp_in(Q, i, 1)] := 1;
fi;
fi;
elif Length(x) = 0 then
sigma[temp_out(Q, i, 1)] := 1;
sigma[temp_out(Q, i, 2)] := -1;
fi;
od;
return [sigma, eps];
end
);
InstallMethod( IsValidString,
"for stringalgebras and strings",
true,
[ IsAlgebra, IsString ], 0,
function( A, input_str )
local IsValidStringSA, IsReducedWalk, IsValidWalk, Q, rho1, rho, vertices, arrows, i, x, y, str;
if IsStringAlgebra(A) = false then
Error("The input algebra is not a string algebra");
return 0;
fi;
Q := QuiverOfPathAlgebra(A);
rho1 := RelationsOfAlgebra(A);
vertices := VerticesOfQuiver(Q);
arrows := ArrowsOfQuiver(Q);
for i in [1..Length(vertices)] do
if Length(String(vertices[i])) <> 2 or String(vertices[i])[1] <> 'v' or
String(vertices[i])[2] <> String(i)[1] then
Error("The Quiver of A is not acceptable");
return 0;
fi;
od;
for i in [1..Length(arrows)] do
if Length(String(arrows[i])) <> 1 or String(arrows[i])[1] <> CharInt(i+96) then
Error("The Quiver of A is not acceptable");
return 0;
fi;
od;
rho := [];
for i in [1..Length(rho1)] do
x := CoefficientsAndMagmaElements(rho1[i]);
y := WalkOfPath(x[1]);
str := Concatenation(List(y, a -> String(a)));
Append(rho, [str]);
od;
IsReducedWalk := function(Q, input_str)
local x,y,i,j;
x := 0;
y := ['-','1'];
for i in [1..Length(ArrowsOfQuiver(Q))] do
Append(y, String(ArrowsOfQuiver(Q)[i]));
od;
for i in [1..Length(ArrowsOfQuiver(Q))] do
Append(y, [CharInt(SIntChar(String(ArrowsOfQuiver(Q)[i])[1])-32)]);
od;
for i in [1..Length(input_str)] do
if not input_str[i] in y then
return 0;
fi;
od;
for i in [1..Length(input_str) - 1] do
if SIntChar(input_str[i]) - SIntChar(input_str[i+1]) = 32 or
SIntChar(input_str[i + 1]) - SIntChar(input_str[i]) = 32 then
x := 1;
else continue;
fi;
od;
if x = 0 then return 1;
else return 0;
fi;
end;
IsValidWalk := function (Q, input_str)
local i,j,k,x,s,t,array, y;
x := 0;
y := [];
for i in [1..Length(ArrowsOfQuiver(Q))] do
Append(y, String(ArrowsOfQuiver(Q)[i]));
od;
for i in [1..Length(ArrowsOfQuiver(Q))] do
Append(y, [CharInt(SIntChar(String(ArrowsOfQuiver(Q)[i])[1]) - 32)]);
od;
for i in [1..Length(input_str)] do
if not input_str[i] in y then
return false;
fi;
od;
for i in [1..Length(input_str) - 1] do
if SIntChar(input_str[i]) > 96 then
if SIntChar(input_str[i + 1]) > 96 then
if SourceOfPath(ArrowsOfQuiver(Q)[SIntChar(input_str[i])
- SIntChar('a') + 1]) <>
TargetOfPath(ArrowsOfQuiver(Q)[SIntChar(input_str[i + 1])
- SIntChar('a') + 1]) then
x := 1;
fi;
else
if SourceOfPath(ArrowsOfQuiver(Q)[SIntChar(input_str[i])
- SIntChar('a') + 1]) <>
SourceOfPath(ArrowsOfQuiver(Q)[SIntChar(input_str[i + 1])
- SIntChar('A') + 1]) then
x := 1;
fi;
fi;
else
if SIntChar(input_str[i + 1]) > 96 then
if TargetOfPath(ArrowsOfQuiver(Q)[SIntChar(input_str[i])
- SIntChar('A') + 1]) <>
TargetOfPath(ArrowsOfQuiver(Q)[SIntChar(input_str[i + 1])
- SIntChar('a') + 1]) then
x := 1;
fi;
else
if TargetOfPath(ArrowsOfQuiver(Q)[SIntChar(input_str[i])
- SIntChar('A') + 1]) <>
SourceOfPath(ArrowsOfQuiver(Q)[SIntChar(input_str[i + 1])
- SIntChar('A') + 1]) then
x := 1;
fi;
fi;
fi;
od;
if x = 0 then
if SIntChar(input_str[Length(input_str)]) > 96 then
s := SourceOfPath(ArrowsOfQuiver(Q)[SIntChar(input_str[Length(input_str)])
- SIntChar('a') + 1]);
else
s := TargetOfPath(ArrowsOfQuiver(Q)[SIntChar(input_str[Length(input_str)])
- SIntChar('A') + 1]);
fi;
if SIntChar(input_str[1]) > 96 then
t := TargetOfPath(ArrowsOfQuiver(Q)[SIntChar(input_str[1])
- SIntChar('a') + 1]);
else
t := SourceOfPath(ArrowsOfQuiver(Q)[SIntChar(input_str[1])
- SIntChar('A') + 1]);
fi;
array := [s, t];
fi;
if x = 1 then return false;
else return true;
fi;
end;
IsValidStringSA := function(A, Q, rho1, input_str)
local i, j, k, rel, temp, temp_caps, temp1, y, x, l, length, count, num,
num_digits, lit, sigma, eps, array, rho;
rho := QPAStringQuiverRho(Q,rho1);
array := QPAStringSigmaEps(A);
sigma := array[1];
eps := array[2];
num := NumberOfVertices(Q);
num_digits := 0;
while num <> 0 do
num := num - num mod 10;
num := num/10;
num_digits := num_digits + 1;
od;
y := "0123456789(-,)";
for i in [1..Length(ArrowsOfQuiver(Q))] do
y := Concatenation(String(ArrowsOfQuiver(Q)[i]), y);
od;
for i in [1..Length(ArrowsOfQuiver(Q))] do
y := Concatenation([CharInt(SIntChar(String(
ArrowsOfQuiver(Q)[i])[1]) - 32)], y);
od;
for i in [1..Length(input_str)] do
if not input_str[i] in y then
return false;
fi;
od;
if input_str[1] = '(' then
num := 0;
for j in [2..num_digits + 1] do
num := num + (SIntChar(input_str[j])
- SIntChar('0')) * 10^(num_digits - j + 1);
od;
if \in(num,[1..NumberOfVertices(Q)]) and input_str[num_digits + 2] =
',' and input_str[num_digits + 3] = '1' and
input_str[num_digits+4] = ')' then
return true;
elif \in(num,[1..NumberOfVertices(Q)]) and input_str[num_digits + 2]
= ',' and input_str[num_digits + 3] = '-' and
input_str[num_digits + 4] = '1' and
input_str[num_digits + 5] = ')' then
return true;
fi;
fi;
for i in [1..14] do
Unbind(y[Length(y)]);
od;
count := 0;
if Length(input_str) > 2 then
for i in [1..Length(input_str) - 2] do
if input_str[i] = '-' and input_str[i + 1] = '1' and
\in(input_str[i+2],y) then
if SIntChar(input_str[i + 2]) > 96 and
eps[SIntChar(input_str[i + 2]) - SIntChar('a') + 1] = 1 then
return false;
elif SIntChar(input_str[i + 2]) < 96 and
sigma[SIntChar(input_str[i + 2]) - SIntChar('A') + 1] = 1 then
return false;
else
for j in [i..Length(input_str) - 2] do
input_str[j] := input_str[j + 2];
od;
count := count + 2;
fi;
if input_str[i + 1] = '1' then input_str[i + 1] := '2';
fi;
fi;
od;
fi;
if Length(input_str) > 1 then
for i in [1..Length(input_str) - 1] do
if input_str[i] = '1' and \in(input_str[i + 1], y) then
if SIntChar(input_str[i + 1]) > 96 and
eps[SIntChar(input_str[i + 1]) - SIntChar('a') + 1] = -1 then
return false;
elif SIntChar(input_str[i + 1]) < 96 and
sigma[SIntChar(input_str[i + 1]) - SIntChar('A') + 1]= -1 then
return false;
else
for j in [i..Length(input_str) - 1] do
input_str[j] := input_str[j + 1];
od;
count := count + 1;
fi;
fi;
od;
fi;
if Length(input_str) > 1 then
if input_str[Length(input_str) - 1] = '-'
and input_str[Length(input_str)] = '1' and
\in(input_str[Length(input_str) - 2], y) then
if SIntChar(input_str[Length(input_str) - 2]) > 96 and
sigma[SIntChar(input_str[Length(input_str) - 2]) -
SIntChar('a') + 1] = -1 then
return false;
elif SIntChar(input_str[Length(input_str)-2]) < 96 and
eps[SIntChar(input_str[Length(input_str) - 2]) -
SIntChar('A') + 1] = -1 then
return false;
else count := count + 2;
fi;
elif input_str[Length(input_str)] = '1' and
\in(input_str[Length(input_str) - 1], y) then
if SIntChar(input_str[Length(input_str) - 1]) > 96 and
sigma[SIntChar(input_str[Length(input_str) - 1]) -
SIntChar('a') + 1] = 1 then
return false;
elif SIntChar(input_str[Length(input_str) - 1]) < 96 and
eps[SIntChar(input_str[Length(input_str) - 1]) -
SIntChar('A') + 1] = 1 then
return false;
else
count := count + 1;
fi;
fi;
fi;
for i in [1..count] do
Unbind(input_str[Length(input_str)]);
od;
for i in [1..Length(input_str)] do
if not input_str[i] in y then
return false;
fi;
od;
if IsReducedWalk(Q, input_str) = 0 then return false;
fi;
if IsValidWalk(Q, input_str) = false then
return false;
fi;
x := 0;
for i in [1..Length(rho)] do
temp := "";
temp_caps := "";
rel := WalkOfPath(rho[i]);
for j in [1..Length(rel)] do
temp := Concatenation(String(rel[j]), temp);
od;
for j in [1..Length(rel)] do
temp1 := CharSInt(SIntChar(String(rel[j])[1]) - 32);
temp_caps[j] := temp1;
od;
l := Length(input_str)-Length(temp);
for j in [0..l] do
for k in [1..Length(temp)] do
if input_str[j + k] <> temp[k] then
break;
fi;
od;
if k = Length(temp) and input_str[j + k] = temp[k] then
x := 3;
break;
fi;
od;
for j in [0..l] do
for k in [1..Length(temp_caps)] do
if input_str[j + k] <> temp_caps[k] then
break;
fi;
od;
if k = Length(temp_caps) and input_str[j +k] = temp_caps[k] then
x := 3;
break;
fi;
od;
od;
if x=0 then return true;
else return false;
fi;
end;
return IsValidStringSA(A, Q, rho, input_str);
end
);
InstallGlobalFunction( QPAStringDirectLeft,
function(A, input_str, sigma, eps)
local Q, x, y, z, temp, output, num, num_digits, j, temp3;
output := IsValidString(A, input_str);
#if output <> "Valid Positive Length String" then
# return output;
#fi;
Q := QuiverOfPathAlgebra(A);
if output = true and input_str[1] = '(' then
num := NumberOfVertices(Q);
num_digits := 0;
while num <> 0 do
num := num - num mod 10;
num := num/10;
num_digits := num_digits + 1;
od;
num := 0;
for j in [2..num_digits + 1] do
num := num +
(SIntChar(input_str[j]) - SIntChar('0')) * 10^(num_digits - j + 1);
od;
temp := OutgoingArrowsOfVertex(VerticesOfQuiver(Q)[num]);
if input_str[num_digits + 3] = '1' then
if Length(temp) = 1 and
sigma[SIntChar(String(temp[1])[1]) - SIntChar('a') + 1] = -1 then
z := String(temp[1]);
elif Length(temp) = 2 then
if sigma[SIntChar(String(temp[1])[1]) - SIntChar('a') + 1] = -1 then
z := String(temp[1]);
else
z := String(temp[2]);
fi;
else z := "Cannot Perform The Operation";
fi;
return z;
elif input_str[num_digits + 3] = '-' then
if Length(temp) = 1 and
sigma[SIntChar(String(temp[1])[1]) - SIntChar('a') + 1] = 1 then
z := String(temp[1]);
elif Length(temp) = 2 then
if sigma[SIntChar(String(temp[1])[1]) - SIntChar('a') + 1] = 1 then
z := String(temp[1]);
else
z := String(temp[2]);
fi;
else z := "Cannot Perform The Operation";
fi;
return z;
fi;
fi;
if SIntChar(input_str[1]) > 96 then
x := SIntChar(String(TargetOfPath(ArrowsOfQuiver(Q)[
SIntChar(input_str[1]) - SIntChar('a') + 1]))[2]) - SIntChar('0');
temp3 := OutgoingArrowsOfVertex(VerticesOfQuiver(Q)[x]);
if Length(temp3) = 2 then
z := [String(temp3[1])[1]];
Append(z, input_str);
if IsValidString(A, z) = false then
z := [String(temp3[2])[1]];
Append(z, input_str);
if IsValidString(A, z) = false then
return "Cannot Perform The Operation";
fi;
fi;
elif Length(temp3) = 1 then
z := [String(temp3[1])[1]];
Append(z, input_str);
if IsValidString(A, z) = false then
return "Cannot Perform The Operation";
fi;
else return "Cannot Perform The Operation";
fi;
else
x := SIntChar(String(SourceOfPath(ArrowsOfQuiver(Q)[
SIntChar(input_str[1]) - SIntChar('A') + 1]))[2]) - SIntChar('0');
temp3 := OutgoingArrowsOfVertex(VerticesOfQuiver(Q)[x]);
if Length(temp3) = 2 then
if SIntChar(String(temp3[1])[1])
- SIntChar(input_str[1]) = 32 then
y := String(temp3[2])[1];
else
y := String(temp3[1])[1];
fi;
z := [y];
Append(z, input_str);
if IsValidString(A, z) = false then
return "Cannot Perform The Operation";
fi;
else
return "Cannot Perform The Operation";
fi;
fi;
return z;
end
);
InstallGlobalFunction( QPAStringInverseLeft,
function(A, input_str, sigma, eps)
local Q, x, y, z, temp, output, num, num_digits, j, temp2;
output := IsValidString(A, input_str);
#if output = "Valid Positive Length String" then
# return output;
#fi;
Q := QuiverOfPathAlgebra(A);
if output = true and input_str[1] = '(' then
num := NumberOfVertices(Q);
num_digits := 0;
while num <> 0 do
num := num - num mod 10;
num := num/10;
num_digits := num_digits + 1;
od;
num := 0;
for j in [2..num_digits + 1] do
num := num +
(SIntChar(input_str[j]) - SIntChar('0')) * 10^(num_digits - j + 1);
od;
temp := IncomingArrowsOfVertex(VerticesOfQuiver(Q)[num]);
if input_str[num_digits + 3] = '1' then
if Length(temp) = 1 and eps[SIntChar(String(temp[1])[1])
- SIntChar('a') + 1] = -1 then
z := [CharInt(SIntChar(String(temp[1])[1]) - 32)];
elif Length(temp) = 2 then
if eps[SIntChar(String(temp[1])[1]) - SIntChar('a') + 1] = -1 then
z := [CharInt(SIntChar(String(temp[1])[1]) - 32)];
else
z := [CharInt(SIntChar(String(temp[2])[1]) - 32)];
fi;
else z := "Cannot Perform The Operation";
fi;
return z;
elif input_str[num_digits + 3] = '-' then
if Length(temp) = 1 and
eps[SIntChar(String(temp[1])[1]) - SIntChar('a') + 1] = 1 then
z := [CharInt(SIntChar(String(temp[1])[1]) - 32)];
elif Length(temp) = 2 then
if eps[SIntChar(String(temp[1])[1]) - SIntChar('a') + 1] = 1 then
z := [CharInt(SIntChar(String(temp[1])[1]) - 32)];
else
z := [CharInt(SIntChar(String(temp[2])[1]) - 32)];
fi;
else z := "Cannot Perform The Operation";
fi;
return z;
fi;
fi;
if SIntChar(input_str[1]) > 96 then
x := SIntChar(String(TargetOfPath(ArrowsOfQuiver(Q)[
SIntChar(input_str[1]) - SIntChar('a') + 1]))[2]) - SIntChar('0');
temp2 := IncomingArrowsOfVertex(VerticesOfQuiver(Q)[x]);
if Length(temp2) = 2 then
if String(temp2[1])[1] = input_str[1] then
y := String(temp2[2])[1];
else
y := String(temp2[1])[1];
fi;
z := [CharInt(SIntChar(y) - 32)];
Append(z, input_str);
if IsValidString(A, z) = false then
return "Cannot Perform The Operation";
fi;
else
return "Cannot Perform The Operation";
fi;
else
x := SIntChar(String(SourceOfPath(ArrowsOfQuiver(Q)[
SIntChar(input_str[1]) - SIntChar('A') + 1]))[2]) - SIntChar('0');
temp2 := IncomingArrowsOfVertex(VerticesOfQuiver(Q)[x]);
if Length(temp2) = 2 then
z := [CharInt(SIntChar(String(temp2[1])[1]) - 32)];
Append(z, input_str);
if IsValidString(A, z) = false then
z := [CharInt(SIntChar(String(temp2[2])[1]) - 32)];
Append(z, input_str);
if IsValidString(A, z) = false then
return "Cannot Perform The Operation";
fi;
fi;
elif Length(temp2) = 1 then
z := [CharInt(SIntChar(String(temp2[1])[1]) - 32)];
Append(z, input_str);
if IsValidString(A, z) = false then
return "Cannot Perform The Operation";
fi;
else return "Cannot Perform The Operation";
fi;
fi;
return z;
end
);
InstallGlobalFunction( QPAStringDirectRight,
function(A, input_str, sigma, eps)
local Q, x, y, z, temp, output, i, num, num_digits, j, temp2;
#if IsValidString(Q,rho,input_str) = false then
#return false;
#fi;
output := IsValidString(A, input_str);
Q := QuiverOfPathAlgebra(A);
if output = true and input_str[1] = '(' then
num := NumberOfVertices(Q);
num_digits := 0;
while num <> 0 do
num := num - num mod 10;
num := num/10;
num_digits := num_digits + 1;
od;
num := 0;
for j in [2..num_digits+1] do
num := num +
(SIntChar(input_str[j])-SIntChar('0')) * 10^(num_digits -j + 1);
od;
temp := IncomingArrowsOfVertex(VerticesOfQuiver(Q)[num]);
if input_str[num_digits + 3] = '1' then
if Length(temp) = 1 and eps[SIntChar(String(temp[1])[1])
- SIntChar('a')+1] = 1 then
z := temp;
elif Length(temp) = 2 then
if eps[SIntChar(String(temp[1])[1]) - SIntChar('a') + 1] = 1
then z := String(temp[1]);
else
z := String(temp[2]);
fi;
else z := "Cannot Perform The Operation";
fi;
return z;
elif input_str[num_digits + 3] = '-' then
if Length(temp) = 1 and eps[SIntChar(String(temp[1])[1])
- SIntChar('a') + 1] = -1 then
z := String(temp[1]);
elif Length(temp) = 2 then
if eps[SIntChar(String(temp[1])[1]) - SIntChar('a') + 1] = -1
then z := String(temp[1]);
else
z := String(temp[2]);
fi;
else z := "Cannot Perform The Operation";
fi;
return z;
fi;
fi;
#temp := input_str;
temp := [];
for i in [1..Length(input_str)] do
Add(temp, input_str[i]);
od;
if SIntChar(temp[Length(temp)]) > 96 then
x := SIntChar(String(SourceOfPath(ArrowsOfQuiver(Q)[
SIntChar(temp[Length(temp)]) - SIntChar('a') + 1]))[2])
- SIntChar('0');
temp2 := IncomingArrowsOfVertex(VerticesOfQuiver(Q)[x]);
if Length(temp2) = 2 then
z := [String(temp2[1])[1]];
temp := Concatenation(temp, z);
if IsValidString(A, temp) = false then
z := [String(temp2[2])[1]];
temp := input_str;
temp := Concatenation(temp, z);
if IsValidString(A, temp) = false then
return "Cannot Perform The Operation";
fi;
fi;
elif Length(temp2) = 1 then
z := [String(temp2[1])[1]];
temp := Concatenation(temp, z);
if IsValidString(A, temp) = false then
return "Cannot Perform The Operation";
fi;
else return "Cannot Perform The Operation";
fi;
else
x := SIntChar(String(TargetOfPath(ArrowsOfQuiver(Q)[
SIntChar(temp[Length(temp)]) - SIntChar('A') + 1]))[2])
- SIntChar('0');
temp2 := IncomingArrowsOfVertex(VerticesOfQuiver(Q)[x]);
if Length(temp2) = 2 then
if SIntChar(String(temp2[1])[1])
- SIntChar(temp[Length(temp)]) = 32 then
y := String(temp2[2])[1];
else
y := String(temp2[1])[1];
fi;
z := [y];
temp := Concatenation(temp, z);
if IsValidString(A, temp) = false then
return "Cannot Perform The Operation";
fi;
else
return "Cannot Perform The Operation";
fi;
fi;
return temp;
end
);
InstallGlobalFunction( QPAStringInverseRight,
function(A, input_str, sigma, eps)
local Q, x, y, z, temp, output, i, num_digits, num, j, temp3;
#if IsValidString(Q,rho,input_str) = false then
# return false;
#fi;
output := IsValidString(A, input_str);
Q := QuiverOfPathAlgebra(A);
if output = true and input_str[1] = '(' then
num := NumberOfVertices(Q);
num_digits := 0;
while num <> 0 do
num := num - num mod 10;
num := num/10;
num_digits := num_digits + 1;
od;
num := 0;
for j in [2..num_digits + 1] do
num := num +
(SIntChar(input_str[j]) - SIntChar('0')) * 10^(num_digits - j + 1);
od;
temp := OutgoingArrowsOfVertex(VerticesOfQuiver(Q)[num]);
if input_str[num_digits + 3] = '1' then
if Length(temp) = 1 and sigma[SIntChar(String(temp[1])[1])
- SIntChar('a') + 1] = 1 then
z := [CharInt(SIntChar(String(temp[1])[1]) - 32)];
elif Length(temp) = 2 then
if sigma[SIntChar(String(temp[1])[1]) - SIntChar('a') + 1] = 1 then
z := [CharInt(SIntChar(String(temp[1])[1]) - 32)];
else
z := [CharInt(SIntChar(String(temp[2])[1]) - 32)];
fi;
else z := "Cannot Perform The Operation";
fi;
return z;
elif input_str[num_digits + 3] = '-' then
if Length(temp) = 1 and
sigma[SIntChar(String(temp[1])[1]) - SIntChar('a') + 1] = -1 then
z := [CharInt(SIntChar(String(temp[1])[1]) - 32)];
elif Length(temp) = 2 then
if sigma[SIntChar(String(temp[1])[1]) - SIntChar('a') + 1] = -1 then
z := [CharInt(SIntChar(String(temp[1])[1]) - 32)];
else
z := [CharInt(SIntChar(String(temp[2])[1]) - 32)];
fi;
else z := "Cannot Perform The Operation";
fi;
return z;
fi;
fi;
#temp1 := input_str;
temp := [];
for i in [1..Length(input_str)] do
Add(temp,input_str[i]);
od;
#temp := input_str;
#input_str := temp1;
if SIntChar(temp[Length(temp)]) > 96 then
x := SIntChar(String(SourceOfPath(ArrowsOfQuiver(Q)[
SIntChar(temp[Length(temp)]) - SIntChar('a') + 1]))[2]) - SIntChar('0');
temp3 := OutgoingArrowsOfVertex(VerticesOfQuiver(Q)[x]);
if Length(temp3) = 2 then
if String(temp3[1])[1] = temp[Length(temp)] then
y := String(temp3[2])[1];
else
y := String(temp3[1])[1];
fi;
z := [CharInt(SIntChar(y) - 32)];
Append(temp, z);
if IsValidString(A, temp) = false then
return "Cannot Perform The Operation";
fi;
else
return "Cannot Perform The Operation";
fi;
else
x := SIntChar(String(TargetOfPath(ArrowsOfQuiver(Q)[
SIntChar(temp[Length(temp)]) - SIntChar('A') + 1]))[2]) - SIntChar('0');
temp3 := OutgoingArrowsOfVertex(VerticesOfQuiver(Q)[x]);
if Length(temp3) = 2 then
z := [CharInt(SIntChar(String(temp3[1])[1]) - 32)];
temp := Concatenation(temp, z);
if IsValidString(A, temp) = false then
temp := input_str;
z := [CharInt(SIntChar(String(temp3[2])[1]) - 32)];
Append(temp, z);
if IsValidString(A, temp) = false then
return "Cannot Perform The Operation";
fi;
fi;
elif Length(temp3) = 1 then
z := [CharInt(SIntChar(String(temp3[1])[1]) - 32)];
Append(temp, z);
if IsValidString(A, temp) = false then
return "Cannot Perform The Operation";
fi;
else return "Cannot Perform The Operation";
fi;
fi;
return temp;
end
);
InstallMethod( LocalARQuiver,
"for stringalgebras and strings",
true,
[ IsAlgebra, IsString ], 0,
function( A, input_str )
local Q, rho1, rho, vertices, arrows, onerel, tworel, str, arr, temp, temp1,
temp2, temp3, La, Lb, Ra, Rb, array,
sigma, eps, k, kQ, rel, arr1, gens, i, j;
if IsStringAlgebra(A) = false then
Error("The input algebra is not a string algebra");
return 0;
fi;
Q := QuiverOfPathAlgebra(A);
rho1 := RelationsOfAlgebra(A);
vertices := VerticesOfQuiver(Q);
arrows := ArrowsOfQuiver(Q);
for i in [1..Length(vertices)] do
if Length(String(vertices[i])) <> 2 or String(vertices[i])[1] <> 'v' or
String(vertices[i])[2] <> String(i)[1] then
Error("The Quiver of A is not acceptable");
return 0;
fi;
od;
for i in [1..Length(arrows)] do
if Length(String(arrows[i])) <> 1 or String(arrows[i])[1] <> CharInt(i+96) then
Error("The Quiver of A is not acceptable");
return 0;
fi;
od;
rho := [];
for i in [1..Length(rho1)] do
onerel := CoefficientsAndMagmaElements(rho1[i]);
tworel := WalkOfPath(onerel[1]);
str := Concatenation(List(tworel, a -> String(a)));
Append(rho, [str]);
od;
temp := IsValidString(A, input_str);
if temp = false then
Error("The input string is invalid");
fi;
array := QPAStringSigmaEps(A);
sigma := array[1];
eps := array[2];
La := function(A, input_str)
local x,y;
#output := IsValidString(Q,rho,input_str);
#if output <> "Valid Positive Length String" and output <> "Valid Zero Length String" then return output;
#fi;
x := QPAStringInverseLeft(A, input_str, sigma, eps);
if x = "Cannot Perform The Operation" then return 0;
fi;
while true do
y := QPAStringDirectLeft(A, x, sigma, eps);
if y = "Cannot Perform The Operation" then return x;
else x := y;
fi;
od;
end;
Lb := function(A, input_str)
local x, y;
x := QPAStringDirectLeft(A, input_str, sigma, eps);
if x = "Cannot Perform The Operation" then return 0;
fi;
while true do
y := QPAStringInverseLeft(A, x, sigma, eps);
if y = "Cannot Perform The Operation" then return x;
else x := y;
fi;
od;
end;
Ra := function(A, input_str)
local x, y;
x := QPAStringInverseRight(A, input_str, sigma, eps);
if x = "Cannot Perform The Operation" then return 0;
fi;
while true do
y := QPAStringDirectRight(A, x, sigma, eps);
if y = "Cannot Perform The Operation" then return x;
else x := y;
fi;
od;
end;
Rb := function(A, input_str)
local x, y;
x := QPAStringDirectRight(A, input_str, sigma, eps);
if x = "Cannot Perform The Operation" then return 0;
fi;
while true do
y := QPAStringInverseRight(A, x, sigma, eps);
if y = "Cannot Perform The Operation" then return x;
else x := y;
fi;
od;
end;
arr := [];
temp1 := La(A, input_str);
if temp1 <> 0 then
Append(arr, [Concatenation
("The canonical embedding StringModule(", input_str, ") to StringModule(", temp1, ")")]);
fi;
temp1 := Lb(A, input_str);
if temp1 <> 0 then
Append(arr, [Concatenation
("The canonical projection StringModule(", temp1, ") to StringModule(", input_str, ")")]);
fi;
temp1 := Ra(A, input_str);
if temp1 <> 0 then
Append(arr, [Concatenation
("The canonical projection StringModule(", temp1, ") to StringModule(", input_str, ")")]);
fi;
temp1 := Rb(A, input_str);
if temp1 <> 0 then
Append(arr, [Concatenation
("The canonical embedding StringModule(", input_str, ") to StringModule(", temp1, ")")]);
fi;
return arr;
end
);
[ Dauer der Verarbeitung: 0.51 Sekunden
(vorverarbeitet)
]
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