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added support for options (reduced_)basis_of_relative_syzygies #31

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Merged
mohamed-barakat merged 3 commits into from
Nov 8, 2023
Merged

added support for options (reduced_)basis_of_relative_syzygies #31

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5260f34
relocated code
mohamed-barakat Nov 8, 2023
73e4f0c
improved code documentation
mohamed-barakat Nov 8, 2023
a467f65
added support for options (reduced_)basis_of_relative_syzygies
mohamed-barakat Nov 8, 2023
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2 changes: 1 addition & 1 deletion PackageInfo.g
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Expand Up @@ -10,7 +10,7 @@ SetPackageInfo( rec(

PackageName := "LoopIntegrals",
Subtitle := "Compute master integrals using commutative and noncommutative methods from computational algebraic geometry",
Version := "2023.11-03",
Version := "2023.11-04",

Date := (function ( ) if IsBound( GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE ) then return GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE; else return Concatenation( ~.Version{[ 1 .. 4 ]}, "-", ~.Version{[ 6, 7 ]}, "-01" ); fi; end)( ),

Expand Down
3 changes: 3 additions & 0 deletions examples/1LoopBox.g
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Expand Up @@ -120,4 +120,7 @@ gen2 := GeneratorsOfScalelessSectors( LD, [ 2, 2, 2, 2 ] );
#! <An unevaluated 1 x 4 matrix over an external ring>
Display( gen2 );
#! D1*D2*D3^2*D4^2,D1^2*D2*D3*D4^2,D1*D2^2*D3^2*D4,D1^2*D2^2*D3*D4
prel2 := ColumnReversedMatrixOfCoefficientsOfParametricIBPs( LD, 2 );
#! [ <A non-zero 7 x 11 matrix over an external ring>,
#! [ D1_*D3_, D1_*D4_, D2_*D4_, D3_*D4_, D1_, D2_, D3_, D4_, 1, D1, D2 ] ]
#! @EndExample
8 changes: 4 additions & 4 deletions gap/LoopIntegrals.gd
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Expand Up @@ -206,12 +206,12 @@ DeclareAttribute( "BasisOfIBPRelations",
IsLoopDiagram );

#! @Arguments LD
DeclareAttribute( "MatrixOfSpecialIBPRelations",
IsLoopDiagram );
DeclareOperation( "MatrixOfSpecialIBPRelations",
[ IsLoopDiagram ] );

#! @Arguments LD
DeclareAttribute( "BasisOfSpecialIBPRelations",
IsLoopDiagram );
DeclareOperation( "BasisOfSpecialIBPRelations",
[ IsLoopDiagram ] );

#! @Arguments LD
DeclareAttribute( "MatrixOfIBPRelationsInWeylAlgebra",
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81 changes: 62 additions & 19 deletions gap/LoopIntegrals.gi
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Expand Up @@ -1310,10 +1310,19 @@ InstallMethod( MatrixOfSpecialIBPRelations,

## Q[m,s,D][D1,...,Ds]
syz := SyzygiesOfColumns( PairOfMatricesOfLoopDiagramInPropagators( LD ) );
#syz := ReducedBasisOfColumnModule( syz );

## this line speeds up the linear algebra in the rational double shift algebra
syz := BasisOfColumnModule( syz );
if ValueOption( "basis_of_relative_syzygies" ) = true then

## this line might sometimes speed up the linear algebra in the rational double shift algebra
syz := BasisOfColumnModule( syz );

fi;

if ValueOption( "reduced_basis_of_relative_syzygies" ) = true then

syz := ReducedBasisOfColumnModule( syz );

fi;

return MatrixOfIBPRelations( syz, LD );

Expand All @@ -1328,8 +1337,18 @@ InstallMethod( MatrixOfSpecialIBPRelations,

syz := SyzygiesOfColumns( PairOfMatricesOfLoopDiagramInPropagators( LD ) );

## this line speeds up the linear algebra in the rational double shift algebra
syz := BasisOfColumnModule( syz );
if ValueOption( "basis_of_relative_syzygies" ) = true then

## this line might sometimes speed up the linear algebra in the rational double shift algebra
syz := BasisOfColumnModule( syz );

fi;

if ValueOption( "reduced_basis_of_relative_syzygies" ) = true then

syz := ReducedBasisOfColumnModule( syz );

fi;

return MatrixOfIBPRelations( syz, LD, exponents );

Expand Down Expand Up @@ -1411,8 +1430,18 @@ InstallMethod( MatrixOfSpecialIBPRelationsInWeylAlgebra,

syz := SyzygiesOfColumns( PairOfMatricesOfLoopDiagramInPropagators( LD ) );

## this line speeds up the linear algebra in the rational double shift algebra
syz := BasisOfColumnModule( syz );
if ValueOption( "basis_of_relative_syzygies" ) = true then

## this line might sometimes speed up the linear algebra in the rational double shift algebra
syz := BasisOfColumnModule( syz );

fi;

if ValueOption( "reduced_basis_of_relative_syzygies" ) = true then

syz := ReducedBasisOfColumnModule( syz );

fi;

ibps := List( [ 1 .. NrColumns( syz ) ], j -> IBPRelationInWeylAlgebra( CertainColumns( syz, [ j ] ), LD ) );

Expand Down Expand Up @@ -1480,6 +1509,9 @@ InstallMethod( MatrixOfCoefficientsOfIBPs,
function( IBPS )
local Y, weights_a, weights_D, weights, powers, coeffs, orig, monoms, deg, A;

## example: 1LoopBubble.g
## called by MatrixOfCoefficientsOfParametricIBPs( LD, 2 : basis_of_relative_syzygies := false );

## example: Q[d,s][a1,a2]<D1,D1_,D2,D2_>/( D2*D2_-1, D1*D1_-1 )
Y := HomalgRing( IBPS );

Expand Down Expand Up @@ -1601,6 +1633,9 @@ InstallMethod( MatrixOfCoefficientsOfIBPs,
function( IBPS, degree )
local Y, weights_a, weights_D, weights, powers, subset;

## example: 1LoopBubble.g
## called by MatrixOfCoefficientsOfParametricIBPs( LD, 2 : basis_of_relative_syzygies := false );

## example: Q[d,s][a1,a2]<D1,D1_,D2,D2_>/( D2*D2_-1, D1*D1_-1 )
Y := HomalgRing( IBPS );

Expand Down Expand Up @@ -1651,7 +1686,10 @@ InstallMethod( MatrixOfCoefficientsOfParametricIBPs,
[ IsLoopDiagram and HasPropagators, IsInt, IsHomalgRing ],

function( LD, degree, Qa )
local sibps, coeffs_monoms, coeffs, monoms, homalg_io_mode, m, trafo, pure_monoms, mixed_monoms, range;
local sibps, coeffs_monoms, coeffs, monoms, homalg_io_mode, m, pure_monoms, mixed_monoms, trafo, range;

## example: 1LoopBubble.g
## MatrixOfCoefficientsOfParametricIBPs( LD, 2 : basis_of_relative_syzygies := false );

sibps := MatrixOfSpecialIBPRelations( LD );

Expand Down Expand Up @@ -1685,6 +1723,15 @@ InstallMethod( MatrixOfCoefficientsOfParametricIBPs,

m := Qa * coeffs;

## example: monoms[1] = [ D1*D2_^2, D1_^2*D2, D1*D2_, D1_*D2 ]
mixed_monoms := Length( monoms[1] );

## example:
## monoms[2] = [ D2, D1, 1 ], ## pure monomials in D: only Di
## monoms[3] = [ D2_, D1_, D2_^2, D1_*D2_, D1_^2 ] ## pure monomials in D_: only Dj_
## pure_monom = [ D2, D1, 1; D2_, D1_, D2_^2, D1_*D2_, D1_^2 ]
pure_monoms := Concatenation( monoms[2], monoms[3] );

trafo := ValueOption( "trafo" );

if not trafo = true then
Expand All @@ -1696,18 +1743,13 @@ InstallMethod( MatrixOfCoefficientsOfParametricIBPs,
m := CertainColumns( m, [ 1 .. NrColumns( m ) - NrRows( m ) ] );
fi;

## example: [ D2, D1, 1; D2_, D1_, D2_^2, D1_*D2_, D1_^2 ], where
## monoms[2] = [ D2, D1, 1 ], ## pure monomials in D: only Di
## monoms[3] = [ D2_, D1_, D2_^2, D1_*D2_, D1_^2 ] ## pure monomials in D_: only Dj_
pure_monoms := Concatenation( monoms[2], monoms[3] );

## extract the lower right corner which gives relations among the pure_monoms,
## and trim the trafo matrix accordingly:
## ( * | * | * )
## ( 0 | x | 0 ) -> ( x | 0 )
## ( 0 | y | z ) -> ( y | z )
mixed_monoms := Length( monoms[1] );
## ( 0 | u | v ) -> ( u | v )
## ( 0 | x | 0 ) -> ( x | 0 )
## ( 0 | y | z ) -> ( y | z )

range := ZeroRows( CertainColumns( m, [ 1 .. mixed_monoms ] ) );

m := CertainRows( CertainColumns( m, [ mixed_monoms + 1 .. NrColumns( m ) ] ), range );
Expand All @@ -1718,8 +1760,9 @@ InstallMethod( MatrixOfCoefficientsOfParametricIBPs,

## exclude the rows which give relations (here x) exclusively among the D's,
## and trim the trafo matrix accordingly:
## ( x | 0 )
## ( y | z ) -> ( y | z )
## ( 0 | u | v )
## ( 0 | x | 0 ) -> ( u | v )
## ( 0 | y | z ) -> ( y | z )
range := NonZeroRows( CertainColumns( m, [ Length( monoms[2] ) + 1 .. NrColumns( m ) ] ) );

m := CertainRows( m, range );
Expand Down