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LoadPackage( "CddInterface" );
#! @Chunk Fourier
#! To illustrate this projection, Let $P= \mathrm{conv}( (1,2), (4,5) )$ in $\mathbb{Q}^2$.
#! $\newline$
#! To find its projection on the subspace $(O, x_1)$, we apply the Fourier elemination to get rid of $x_2$
#! @Example
P := Cdd_PolyhedronByGenerators( [ [ 1, 1, 2 ], [ 1, 4, 5 ] ] );
#! <Polyhedron given by its V-representation>
H := Cdd_H_Rep( P );
#! <Polyhedron given by its H-representation>
Display( H );
#! H-representation
#! linearity 1, [ 3 ]
#! begin
#! 3 X 3 rational
#!
#! 4 -1 0
#! -1 1 0
#! -1 -1 1
#! end
P_x1 := Cdd_FourierProjection( H, 2);
#! <Polyhedron given by its H-representation>
Display( P_x1 );
#! H-representation
#! linearity 1, [ 3 ]
#! begin
#! 3 X 3 rational
#!
#! 4 -1 0
#! -1 1 0
#! 0 0 1
#! end
Display( Cdd_V_Rep( P_x1 ) );
#! V-representation
#! begin
#! 2 X 3 rational
#!
#! 1 1 0
#! 1 4 0
#! end
#! @EndExample
#! Let again $Q= Conv( (2,3,4), (2,4,5) )+ nonneg( (1,1,1) )$, and let us compute its projection on $(O,x_2,x_3)$
#! @Example
Q := Cdd_PolyhedronByGenerators( [ [ 1, 2, 3, 4 ],[ 1, 2, 4, 5 ], [ 0, 1, 1, 1 ] ] );
#! <Polyhedron given by its V-representation>
R := Cdd_H_Rep( Q );
#! <Polyhedron given by its H-representation>
Display( R );
#! H-representation
#! linearity 1, [ 4 ]
#! begin
#! 4 X 4 rational
#!
#! 2 1 -1 0
#! -2 1 0 0
#! -1 -1 1 0
#! -1 0 -1 1
#! end
P_x2_x3 := Cdd_FourierProjection( R, 1);
#! <Polyhedron given by its H-representation>
Display( P_x2_x3 );
#! H-representation
#! linearity 2, [ 1, 3 ]
#! begin
#! 3 X 4 rational
#!
#! -1 0 -1 1
#! -3 0 1 0
#! 0 1 0 0
#! end
Display( Cdd_V_Rep( last ) ) ;
#! V-representation
#! begin
#! 2 X 4 rational
#!
#! 0 0 1 1
#! 1 0 3 4
#! end
#! @EndExample
#! @EndChunk
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