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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346#############################################################################
##
## 4ti2Interface package
##
## Copyright 2013-2017, Sebastian Gutsche, Siegen University
##
## Reading the declaration part of the 4ti2Interface package.
##
#############################################################################
##
InstallGlobalFunction( 4ti2Interface_Cut_Vector,
function ( vec, l )
local d, new, i;
if Length( vec ) = 0 then
return [ ];
fi;
d := Length( vec ) / l;
new := [ ];
for i in [ 1 .. l ] do
Add( new, vec{[ d * (i - 1) + 1 .. d * i ]} );
od;
return new;
end );
##
InstallGlobalFunction( 4ti2Interface_Read_Matrix_From_File,
function( filename )
local filestream, matrix, string, nr_rows, nr_cols;
if not IsExistingFile( filename ) then
return [ ];
fi;
filestream := IO_File( filename, "r" );
matrix := [ ];
string := IO_ReadLine( filestream );
while string <> "" do
NormalizeWhitespace( string );
string := SplitString( string, " ", " \n" );
string := List( string, Int );
matrix := Concatenation( matrix, string );
string := IO_ReadLine( filestream );
od;
IO_Close( filestream );
nr_rows := Remove( matrix, 1 );
nr_cols := Remove( matrix, 1 );
if not Length( matrix ) = nr_cols * nr_rows then
Error( "wrong input matrix dimension" );
return [ fail, [ nr_rows, nr_cols ], matrix ];
fi;
matrix := 4ti2Interface_Cut_Vector( matrix, nr_rows );
return matrix;
end );
##
InstallGlobalFunction( 4ti2Interface_Write_Matrix_To_File,
function( matrix, string )
local filestream, i, j;
filestream := IO_File( string, "w" );
i := Length( matrix );
if i = 0 then
return matrix;
fi;
j := Length( matrix[ 1 ] );
if j = 0 then
return matrix;
fi;
if not ForAll( matrix, k -> Length( k ) = j ) then
Error( "Input is not a matrix" );
return fail;
fi;
IO_Write( filestream, Concatenation( String( i ), " ", String( j ), "\n" ) );
for i in matrix do
for j in i do
IO_Write( filestream, Concatenation( String( j ), " " ) );
od;
IO_Write( filestream, "\n" );
od;
IO_Flush( filestream );
IO_Close( filestream );
end );
##
InstallGlobalFunction( 4ti2Interface_groebner_matrix,
function( arg )
local matrix, dir, filename, exec, filestream;
if Length( arg ) < 1 then
Error( "too few arguments" );
fi;
matrix := arg[ 1 ];
dir := DirectoryTemporary();
filename := Filename( dir, "gap_4ti2_temp_matrix" );
## 4ti2 works with right kernel.
4ti2Interface_Write_Matrix_To_File( TransposedMat( matrix ), Concatenation( filename, ".mat" ) );
if Length( arg ) > 1 then
if not IsMatrix( arg[ 2 ] ) then
arg[ 2 ] := [ arg[ 2 ] ];
fi;
4ti2Interface_Write_Matrix_To_File( arg[ 2 ], Concatenation( filename, ".cost" ) );
fi;
exec := IO_FindExecutable( "groebner" );
filestream := IO_Popen2( exec, [ filename ]);
while IO_ReadLine( filestream.stdout ) <> "" do od;
IO_Close( filestream.stdin );
IO_Close( filestream.stdout );
matrix := 4ti2Interface_Read_Matrix_From_File( Concatenation( filename, ".gro" ) );
return matrix;
end );
##
InstallGlobalFunction( 4ti2Interface_groebner_basis,
function( arg )
local matrix, dir, filename, exec, filestream;
dir := DirectoryTemporary();
if Length( arg ) < 1 then
Error( "too few arguments" );
fi;
matrix := arg[ 1 ];
filename := Filename( dir, "gap_4ti2_temp_lattice" );
4ti2Interface_Write_Matrix_To_File( matrix, Concatenation( filename, ".lat" ) );
if Length( arg ) > 1 then
if not IsMatrix( arg[ 2 ] ) then
arg[ 2 ] := [ arg[ 2 ] ];
fi;
4ti2Interface_Write_Matrix_To_File( [ arg[ 2 ] ], Concatenation( filename, ".cost" ) );
fi;
exec := IO_FindExecutable( "groebner" );
filestream := IO_Popen2( exec, [ filename ]);
while IO_ReadLine( filestream.stdout ) <> "" do od;
IO_Close( filestream.stdin );
IO_Close( filestream.stdout );
matrix := 4ti2Interface_Read_Matrix_From_File( Concatenation( filename, ".gro" ) );
return matrix;
end );
##
InstallGlobalFunction( 4ti2Interface_hilbert_inequalities,
function( matrix )
local dir, filename, rel_list, sign_list, exec, filestream;
if matrix = [ ] then
return [ ];
fi;
dir := DirectoryTemporary();
filename := Filename( dir, "gap_4ti2_temp_ineqs" );
4ti2Interface_Write_Matrix_To_File( matrix, Concatenation( filename, ".mat" ) );
rel_list := [ List( matrix, i -> ">" ) ];
4ti2Interface_Write_Matrix_To_File( rel_list, Concatenation( filename, ".rel" ) );
sign_list := [ List( matrix[ 1 ], i -> 0 ) ];
4ti2Interface_Write_Matrix_To_File( sign_list, Concatenation( filename, ".sign" ) );
exec := IO_FindExecutable( "hilbert" );
filestream := IO_Popen2( exec, [ filename ]);
while IO_ReadLine( filestream.stdout ) <> "" do od;
IO_Close( filestream.stdin );
IO_Close( filestream.stdout );
matrix := 4ti2Interface_Read_Matrix_From_File( Concatenation( filename, ".hil" ) );
return matrix;
end );
##
InstallGlobalFunction( 4ti2Interface_hilbert_inequalities_in_positive_orthant,
function( matrix )
local dir, filename, rel_list, sign_list, exec, filestream;
if matrix = [ ] then
return [ ];
fi;
dir := DirectoryTemporary();
filename := Filename( dir, "gap_4ti2_temp_ineqs" );
4ti2Interface_Write_Matrix_To_File( matrix, Concatenation( filename, ".mat" ) );
rel_list := [ List( matrix, i -> ">" ) ];
4ti2Interface_Write_Matrix_To_File( rel_list, Concatenation( filename, ".rel" ) );
exec := IO_FindExecutable( "hilbert" );
filestream := IO_Popen2( exec, [ filename ]);
while IO_ReadLine( filestream.stdout ) <> "" do od;
IO_Close( filestream.stdin );
IO_Close( filestream.stdout );
matrix := 4ti2Interface_Read_Matrix_From_File( Concatenation( filename, ".hil" ) );
return matrix;
end );
##
InstallGlobalFunction( 4ti2Interface_hilbert_equalities_in_positive_orthant,
function( matrix )
local dir, filename, rel_list, sign_list, exec, filestream;
if matrix = [ ] then
return [ ];
fi;
dir := DirectoryTemporary();
filename := Filename( dir, "gap_4ti2_temp_ineqs" );
4ti2Interface_Write_Matrix_To_File( matrix, Concatenation( filename, ".mat" ) );
rel_list := [ List( matrix, i -> "=" ) ];
4ti2Interface_Write_Matrix_To_File( rel_list, Concatenation( filename, ".rel" ) );
exec := IO_FindExecutable( "hilbert" );
filestream := IO_Popen2( exec, [ filename ]);
while IO_ReadLine( filestream.stdout ) <> "" do od;
IO_Close( filestream.stdin );
IO_Close( filestream.stdout );
matrix := 4ti2Interface_Read_Matrix_From_File( Concatenation( filename, ".hil" ) );
return matrix;
end );
##
InstallGlobalFunction( 4ti2Interface_hilbert_equalities_and_inequalities,
function( eqs, ineqs )
local concat_list, dir, filename, rel_list, sign_list,
return_matrix, exec, filestream;
if eqs = [ ] and ineqs = [ ] then
return [ ];
fi;
dir := DirectoryTemporary();
filename := Filename( dir, "gap_4ti2_temp_ineqs" );
concat_list := Concatenation( eqs, ineqs );
4ti2Interface_Write_Matrix_To_File( concat_list, Concatenation( filename, ".mat" ) );
rel_list := [ Concatenation( List( eqs, i -> "=" ), List( ineqs, i -> ">" ) ) ];
4ti2Interface_Write_Matrix_To_File( rel_list, Concatenation( filename, ".rel" ) );
sign_list := [ List( concat_list[ 1 ] , i -> 0 ) ];
4ti2Interface_Write_Matrix_To_File( sign_list, Concatenation( filename, ".sign" ) );
exec := IO_FindExecutable( "hilbert" );
filestream := IO_Popen2( exec, [ filename ]);
while IO_ReadLine( filestream.stdout ) <> "" do od;
IO_Close( filestream.stdin );
IO_Close( filestream.stdout );
return_matrix := 4ti2Interface_Read_Matrix_From_File( Concatenation( filename, ".hil" ) );
return return_matrix;
end );
##
InstallGlobalFunction( 4ti2Interface_hilbert_equalities_and_inequalities_in_positive_orthant,
function( eqs, ineqs )
local concat_list, dir, filename, rel_list, sign_list,
exec, filestream, return_matrix;
if eqs = [ ] and ineqs = [ ] then
return [ ];
fi;
dir := DirectoryTemporary();
filename := Filename( dir, "gap_4ti2_temp_ineqs" );
concat_list := Concatenation( eqs, ineqs );
4ti2Interface_Write_Matrix_To_File( concat_list, Concatenation( filename, ".mat" ) );
rel_list := [ Concatenation( List( eqs, i -> "=" ), List( ineqs, i -> ">" ) ) ];
4ti2Interface_Write_Matrix_To_File( rel_list, Concatenation( filename, ".rel" ) );
sign_list := [ List( concat_list[ 1 ] , i -> 0 ) ];
4ti2Interface_Write_Matrix_To_File( sign_list, Concatenation( filename, ".sign" ) );
exec := IO_FindExecutable( "hilbert" );
filestream := IO_Popen2( exec, [ filename ]);
while IO_ReadLine( filestream.stdout ) <> "" do od;
IO_Close( filestream.stdin );
IO_Close( filestream.stdout );
return_matrix := 4ti2Interface_Read_Matrix_From_File( Concatenation( filename, ".hil" ) );
return return_matrix;
end );
##
InstallGlobalFunction( 4ti2Interface_zsolve_equalities_and_inequalities,
function( arg )
local eqs, eqs_rhs, ineqs, ineqs_rhs, signs,
concat_list, dir, filename, rel_list, concat_rhs,
return_matrix, exec, filestream, precision, std_err_out;
if Length( arg ) < 4 then
Error( "too few arguments" );
return [ ];
fi;
eqs := arg[ 1 ];
eqs_rhs := arg[ 2 ];
ineqs := arg[ 3 ];
ineqs_rhs := arg[ 4 ];
if eqs = [ ] and ineqs = [ ] then
return [ ];
fi;
if Length( arg ) > 4 then
signs := [ arg[ 5 ] ];
else
if Length( eqs ) > 0 then
signs := [ ListWithIdenticalEntries( Length( eqs[ 1 ] ), 0 ) ];
else
signs := [ ListWithIdenticalEntries( Length( ineqs[ 1 ] ), 0 ) ];
fi;
fi;
precision := ValueOption( "precision" );
if IsInt( precision ) then
precision := String( precision );
elif precision = fail then
precision := "32";
fi;
dir := DirectoryTemporary();
filename := Filename( dir, "gap_4ti2_zsolve" );
concat_list := Concatenation( eqs, ineqs );
4ti2Interface_Write_Matrix_To_File( concat_list, Concatenation( filename, ".mat" ) );
rel_list := [ Concatenation( List( eqs, i -> "=" ), List( ineqs, i -> ">" ) ) ];
4ti2Interface_Write_Matrix_To_File( rel_list, Concatenation( filename, ".rel" ) );
4ti2Interface_Write_Matrix_To_File( signs, Concatenation( filename, ".sign" ) );
concat_rhs := [ Concatenation( eqs_rhs, ineqs_rhs ) ];
4ti2Interface_Write_Matrix_To_File( concat_rhs, Concatenation( filename, ".rhs" ) );
exec := IO_FindExecutable( "zsolve" );
filestream := IO_Popen3( exec, [ Concatenation( "-p=", precision ), filename ] );
while IO_ReadLine( filestream.stdout ) <> "" do od;
std_err_out := Concatenation( IO_ReadLines( filestream.stderr ) );
IO_Close( filestream.stdin );
IO_Close( filestream.stdout );
IO_Close( filestream.stderr );
if std_err_out <> "" then
Error( Concatenation( "4ti2 Error:\n", std_err_out, "If you continue, your results might be wrong" ) );
fi;
return_matrix := [ 1, 2, 3 ];
return_matrix[ 1 ] := 4ti2Interface_Read_Matrix_From_File( Concatenation( filename, ".zinhom" ) );
return_matrix[ 2 ] := 4ti2Interface_Read_Matrix_From_File( Concatenation( filename, ".zhom" ) );
return_matrix[ 3 ] := 4ti2Interface_Read_Matrix_From_File( Concatenation( filename, ".zfree" ) );
return return_matrix;
end );
##
InstallGlobalFunction( 4ti2Interface_zsolve_equalities_and_inequalities_in_positive_orthant,
function( eqs, eqs_rhs, ineqs, ineqs_rhs )
local signs, call_list;
call_list := [ eqs, eqs_rhs, ineqs, ineqs_rhs ];
if Length( eqs ) = 0 and Length( ineqs ) = 0 then
return [ ];
fi;
if Length( eqs ) > 0 then
signs := ListWithIdenticalEntries( Length( eqs[ 1 ] ), 1 );
else
signs := ListWithIdenticalEntries( Length( ineqs[ 1 ] ), 1 );
fi;
Add( call_list, signs );
return CallFuncList( 4ti2Interface_zsolve_equalities_and_inequalities, call_list );
end );
##
InstallGlobalFunction( 4ti2Interface_graver_equalities,
function( arg )
local eqs, signs,
dir, filename,
return_matrix, exec, filestream;
if Length( arg ) < 1 then
Error( "too few arguments" );
return [ ];
fi;
eqs := arg[ 1 ];
if eqs = [ ] then
return [ ];
fi;
if Length( arg ) > 1 then
signs := [ arg[ 2 ] ];
else
signs := [ ListWithIdenticalEntries( Length( eqs[ 1 ] ), 0 ) ];
fi;
dir := DirectoryTemporary();
filename := Filename( dir, "gap_4ti2_graver" );
4ti2Interface_Write_Matrix_To_File( eqs, Concatenation( filename, ".mat" ) );
4ti2Interface_Write_Matrix_To_File( signs, Concatenation( filename, ".sign" ) );
exec := IO_FindExecutable( "graver" );
filestream := IO_Popen2( exec, [ filename ]);
while IO_ReadLine( filestream.stdout ) <> "" do od;
IO_Close( filestream.stdin );
IO_Close( filestream.stdout );
return_matrix := 4ti2Interface_Read_Matrix_From_File( Concatenation( filename, ".gra" ) );
return return_matrix;
end );
##
InstallGlobalFunction( 4ti2Interface_graver_equalities_in_positive_orthant,
function( eqs )
local dir, filename,
return_matrix, exec, filestream;
dir := DirectoryTemporary();
filename := Filename( dir, "gap_4ti2_graver" );
4ti2Interface_Write_Matrix_To_File( eqs, Concatenation( filename, ".mat" ) );
exec := IO_FindExecutable( "graver" );
filestream := IO_Popen2( exec, [ filename ]);
while IO_ReadLine( filestream.stdout ) <> "" do od;
IO_Close( filestream.stdin );
IO_Close( filestream.stdout );
return_matrix := 4ti2Interface_Read_Matrix_From_File( Concatenation( filename, ".gra" ) );
return return_matrix;
end );