Merge pull request #1745 from kamalsaleh/master

Resolves a Bug in `Lift/Colift` methods of `ModulePresenationsForCAP`

Author: mohamed-barakat

ModulePresentationsForCAP/PackageInfo.g

@@ -10,7 +10,7 @@ SetPackageInfo( rec(
 
 PackageName := "ModulePresentationsForCAP",
 Subtitle := "Category R-pres for CAP",
-Version := "2024.09-02",
+Version := "2025.06-01",
 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)( ),
 License := "GPL-2.0-or-later",
 

ModulePresentationsForCAP/gap/ModulePresentationsForCAP.gi

@@ -1057,7 +1057,7 @@ InstallGlobalFunction( ADD_COEVALUATION_MORPHISM_RIGHT,
 
 end );
 
-InstallGlobalFunction( ADD_LIFT_AND_COLIFT_LEFT, 
+InstallGlobalFunction( ADD_LIFT_AND_COLIFT_LEFT,
 
   function( category )
   local homalg_ring, lift_via_compiled_linear_system_func, colift_via_compiled_linear_system_func;
@@ -1088,20 +1088,11 @@ InstallGlobalFunction( ADD_LIFT_AND_COLIFT_LEFT,
     M := UnderlyingMatrix( Source( morphism_2 ) );
 
     v := NrColumns( M );
-       
+    
     s := NrColumns( P );
 
     N := UnderlyingMatrix( Range(  morphism_1 ) );
 
-    # NrColumns( N ) = 0 implies coker(N)=0 and  s = 0 implies coker(P)=0, hence morphism_1 is zero, and the zero morphism can always be lifted. 
-    if NrColumns( N ) = 0 or s = 0 then
-        return ZeroMorphism( Source( morphism_1 ), Source( morphism_2 ) ); 
-    fi;
-    
-    # if NrColumns(M)=0 then M is zero, hence lift exists iff morphism_1 is zero.
-    if NrColumns( M ) = 0 and IsZeroForMorphisms( morphism_1 ) then
-        return ZeroMorphism( Source( morphism_1 ), Source( morphism_2 ) );
-    fi;
     A := UnderlyingMatrix( morphism_1 );
 
     B := UnderlyingMatrix( morphism_2 );
@@ -1110,31 +1101,23 @@ InstallGlobalFunction( ADD_LIFT_AND_COLIFT_LEFT,
 
     N_tr_I := KroneckerMat( TransposedMatrix( N ), HomalgIdentityMatrix( NrColumns( P ) ,homalg_ring ) );
 
-    zero_1  := HomalgZeroMatrix( NrRows( A )*NrColumns( A ), NrRows( P )*NrRows( M ), homalg_ring );
+    zero_1  := HomalgZeroMatrix( NrRows( A ) * NrColumns( A ), NrRows( P ) * NrRows( M ), homalg_ring );
 
     mat1 := UnionOfColumns( B_tr_I, N_tr_I, zero_1 );
 
     I_P := KroneckerMat( HomalgIdentityMatrix( NrColumns( M ) ,homalg_ring ), P );
 
-    zero_2 := HomalgZeroMatrix( NrRows( P )*NrColumns( M ), NrRows( A )*NrRows( N ), homalg_ring );
+    zero_2 := HomalgZeroMatrix( NrRows( P ) * NrColumns( M ), NrRows( A ) * NrRows( N ), homalg_ring );
 
-    M_tr_I := KroneckerMat( TransposedMatrix( M ), HomalgIdentityMatrix( NrRows( P ) ,homalg_ring ) );
+    M_tr_I := KroneckerMat( TransposedMatrix( M ), HomalgIdentityMatrix( NrRows( P ), homalg_ring ) );
 
     mat2 := UnionOfColumns( I_P, zero_2, M_tr_I );
 
     mat := UnionOfRows( mat1, mat2 );
 
-    if NrColumns( A ) <= 1 then
-       
-       vec_A := A;
-       
-    else
-       
-       vec_A := UnionOfRows( List( [ 1 .. NrColumns( A ) ], i-> CertainColumns( A, [ i ] ) ) );
-       
-    fi;
+    vec_A := ConvertMatrixToColumn( A );
 
-    vec_zero := HomalgZeroMatrix( NrRows( P )*NrColumns( M ), 1, homalg_ring );
+    vec_zero := HomalgZeroMatrix( NrRows( P ) * NrColumns( M ), NrColumns( vec_A ), homalg_ring );
 
     vec := UnionOfRows( vec_A, vec_zero );
 
@@ -1155,11 +1138,7 @@ InstallGlobalFunction( ADD_LIFT_AND_COLIFT_LEFT,
 
     sol := CallFuncList( LeftDivide, lift_via_compiled_linear_system_func( morphism_1, morphism_2 ) );
 
-    if v <= 1 then
-        XX := CertainRows( sol, [ 1.. s ] );
-    else
-        XX := UnionOfColumns( List( [ 1 .. v ], i-> CertainRows( sol, [ (i-1)*s+1.. i*s ] ) ) );
-    fi;
+    XX := ConvertColumnToMatrix( CertainRows( sol, [ 1 .. s * v ] ), s, v );
 
     return PresentationMorphism( cat, Source( morphism_1 ), XX, Source( morphism_2 ) );
 
@@ -1195,21 +1174,11 @@ InstallGlobalFunction( ADD_LIFT_AND_COLIFT_LEFT,
     M := UnderlyingMatrix( Range( morphism_1 ) );
 
     v := NrColumns( M );
-       
+    
     s := NrColumns( I );
 
     N := UnderlyingMatrix( Source( morphism_1 ) );
 
-    # NrColumns( N ) = 0 implies coker(N)=0 and  s = 0 implies coker(I)=0, hence morphism_2 is zero, and the zero morphism can always be colifted.
-    if NrColumns( N ) = 0 or s = 0 then
-        return ZeroMorphism( Range( morphism_1 ), Range( morphism_2 ) );
-    fi;
-
-    # if NrColumns(M)=0 then M is zero, hence colift exists iff morphism_2 is zero.
-    if NrColumns( M ) = 0 and IsZeroForMorphisms( morphism_2 ) then
-        return ZeroMorphism( Range( morphism_1 ), Range( morphism_2 ) );
-    fi;
-
     B := UnderlyingMatrix( morphism_1 );
 
     A := UnderlyingMatrix( morphism_2 );
@@ -1226,12 +1195,8 @@ InstallGlobalFunction( ADD_LIFT_AND_COLIFT_LEFT,
 
     A_over_zero := UnionOfRows( A, zero_mat );
 
-    if NrColumns( A ) <= 1 then
-        vec := A_over_zero;
-    else
-        vec := UnionOfRows( List( [ 1 .. NrColumns( A ) ], i-> CertainColumns( A_over_zero, [ i ] ) ) );
-    fi;
-
+    vec := ConvertMatrixToColumn( A_over_zero );
+    
     return [ mat, vec ];
 
   end;
@@ -1249,15 +1214,7 @@ InstallGlobalFunction( ADD_LIFT_AND_COLIFT_LEFT,
 
     sol := CallFuncList( LeftDivide, colift_via_compiled_linear_system_func( morphism_1, morphism_2 ) );
 
-    v := NrColumns( M );
-    
-    s := NrColumns( I );
-    
-    if s <= 1 then
-        XX := CertainRows( sol, [ 1.. v ] );
-    else
-        XX := UnionOfColumns( List( [ 1 .. s ], i-> CertainRows( sol, [ (i-1)*v+1.. i*v ] ) ) );
-    fi;
+    XX := ConvertColumnToMatrix( CertainRows( sol, [ 1 .. v * s ] ), v, s );
 
     return PresentationMorphism( cat, Range( morphism_1 ), XX, Range( morphism_2 ) );
 
@@ -1272,21 +1229,21 @@ InstallGlobalFunction( ADD_LIFT_AND_COLIFT_LEFT,
 end );
 
 ##
-InstallGlobalFunction( ADD_LIFT_AND_COLIFT_RIGHT, 
+InstallGlobalFunction( ADD_LIFT_AND_COLIFT_RIGHT,
 
   function( category )
   local homalg_ring, lift_via_compiled_linear_system_func, colift_via_compiled_linear_system_func;
 
   homalg_ring := category!.ring_for_representation_category;
 
   lift_via_compiled_linear_system_func := function( morphism_1, morphism_2 )
-    local Pt, Nt, Mt, At, Bt, B_tr_I, N_tr_I, zero_1, 
+    local Pt, Nt, Mt, At, Bt, B_tr_I, N_tr_I, zero_1,
           mat1, mat2, I_P, zero_2, M_tr_I, mat, vec_A, vec_zero, vec, v, s;
     #                 rxs
     #                P
     #                |
-    #         uxr    | mxr 
-    #        X      (A) 
+    #         uxr    | mxr
+    #        X      (A)
     #                |
     #                V
     #    uxv    mxu   mxn
@@ -1296,10 +1253,10 @@ InstallGlobalFunction( ADD_LIFT_AND_COLIFT_RIGHT,
     #   We need to solve the system
     #       B*X = A mod N
     #       X*P + M*Y = 0
-    #   I.e., looking for X, Y, Z such that 
+    #   I.e., looking for X, Y, Z such that
     #       B*X + N*Y = A
     #       X*P + M*Z = 0
-    #   which is equivalent to 
+    #   which is equivalent to
     #       XX*B^t + YY*N^t = A^t
     #       P^t*XX + ZZ*M^t = 0
     #   which can be solved exactly as Lift in left presentations case.
@@ -1314,47 +1271,31 @@ InstallGlobalFunction( ADD_LIFT_AND_COLIFT_RIGHT,
 
     Nt := TransposedMatrix( UnderlyingMatrix( Range(  morphism_1 ) ) );
 
-    if NrRows( Nt ) = 0 or s = 0 then
-        return ZeroMorphism( Source( morphism_1 ), Source( morphism_2 ) ); 
-    fi;
-
-    if NrRows( Mt ) = 0 and IsZeroForMorphisms( morphism_1 ) then
-        return ZeroMorphism( Source( morphism_1 ), Source( morphism_2 ) );
-    fi;
-
     At := TransposedMatrix( UnderlyingMatrix( morphism_1 ) );
 
     Bt := TransposedMatrix( UnderlyingMatrix( morphism_2 ) );
 
     B_tr_I := KroneckerMat( TransposedMatrix( Bt ), HomalgIdentityMatrix( NrColumns( Pt ), homalg_ring ) );
 
-    N_tr_I := KroneckerMat( TransposedMatrix( Nt ), HomalgIdentityMatrix( NrColumns( Pt ) ,homalg_ring ) );
+    N_tr_I := KroneckerMat( TransposedMatrix( Nt ), HomalgIdentityMatrix( NrColumns( Pt ), homalg_ring ) );
 
-    zero_1  := HomalgZeroMatrix( NrRows( At )*NrColumns( At ), NrRows( Pt )*NrRows( Mt ), homalg_ring );
+    zero_1  := HomalgZeroMatrix( NrRows( At ) * NrColumns( At ), NrRows( Pt ) * NrRows( Mt ), homalg_ring );
 
     mat1 := UnionOfColumns( B_tr_I, N_tr_I, zero_1 );
 
-    I_P := KroneckerMat( HomalgIdentityMatrix( NrColumns( Mt ) ,homalg_ring ), Pt );
+    I_P := KroneckerMat( HomalgIdentityMatrix( NrColumns( Mt ), homalg_ring ), Pt );
 
-    zero_2 := HomalgZeroMatrix( NrRows( Pt )*NrColumns( Mt ), NrRows( At )*NrRows( Nt ), homalg_ring );
+    zero_2 := HomalgZeroMatrix( NrRows( Pt ) * NrColumns( Mt ), NrRows( At ) * NrRows( Nt ), homalg_ring );
 
-    M_tr_I := KroneckerMat( TransposedMatrix( Mt ), HomalgIdentityMatrix( NrRows( Pt ) ,homalg_ring ) );
+    M_tr_I := KroneckerMat( TransposedMatrix( Mt ), HomalgIdentityMatrix( NrRows( Pt ), homalg_ring ) );
 
     mat2 := UnionOfColumns( I_P, zero_2, M_tr_I );
 
     mat := UnionOfRows( mat1, mat2 );
 
-    if NrColumns( At ) <= 1 then
-       
-       vec_A := At;
-       
-    else
-       
-       vec_A := UnionOfRows( List( [ 1 .. NrColumns( At ) ], i-> CertainColumns( At, [ i ] ) ) );
-       
-    fi;
+    vec_A := ConvertMatrixToColumn( At );
 
-    vec_zero := HomalgZeroMatrix( NrRows( Pt )*NrColumns( Mt ), 1, homalg_ring );
+    vec_zero := HomalgZeroMatrix( NrRows( Pt ) * NrColumns( Mt ), NrColumns( vec_A ), homalg_ring );
 
     vec := UnionOfRows( vec_A, vec_zero );
 
@@ -1363,7 +1304,7 @@ InstallGlobalFunction( ADD_LIFT_AND_COLIFT_RIGHT,
   end;
 
   AddLift( category, function( cat, morphism_1, morphism_2 )
-    local Pt, Mt, v, s, sol, XX;
+    local Pt, Mt, v, s, sol, XX_tr;
 
     Pt := TransposedMatrix( UnderlyingMatrix( Source( morphism_1 ) ) );
     Mt := TransposedMatrix( UnderlyingMatrix( Source( morphism_2 ) ) );
@@ -1374,13 +1315,9 @@ InstallGlobalFunction( ADD_LIFT_AND_COLIFT_RIGHT,
 
     sol := CallFuncList( LeftDivide, lift_via_compiled_linear_system_func( morphism_1, morphism_2 ) );
 
-    if v <= 1 then
-        XX := TransposedMatrix( CertainRows( sol, [ 1.. s ] ) );
-    else
-        XX := TransposedMatrix( UnionOfColumns( List( [ 1 .. v ], i-> CertainRows( sol, [ (i-1)*s+1.. i*s ] ) ) ) );
-    fi;
+    XX_tr := ConvertColumnToMatrix( CertainRows( sol, [ 1 .. s * v ] ), s, v );
 
-    return PresentationMorphism( cat, Source( morphism_1 ), XX, Source( morphism_2 ) );
+    return PresentationMorphism( cat, Source( morphism_1 ), TransposedMatrix( XX_tr ), Source( morphism_2 ) );
 
   end );
 
@@ -1398,19 +1335,11 @@ InstallGlobalFunction( ADD_LIFT_AND_COLIFT_RIGHT,
     Mt := TransposedMatrix( UnderlyingMatrix( Range( morphism_1 ) ) );
 
     v := NrColumns( Mt );
-       
+    
     s := NrColumns( It );
-        
-    Nt := TransposedMatrix( UnderlyingMatrix( Source( morphism_1 ) ) );
 
-    if NrRows( Nt ) = 0 or s = 0 then
-        return ZeroMorphism( Range( morphism_1 ), Range( morphism_2 ) );
-    fi;
+    Nt := TransposedMatrix( UnderlyingMatrix( Source( morphism_1 ) ) );
 
-    if NrRows( Mt ) = 0 and IsZeroForMorphisms( morphism_2 ) then
-        return ZeroMorphism( Range( morphism_1 ), Range( morphism_2 ) );
-    fi;
-
     Bt := TransposedMatrix( UnderlyingMatrix( morphism_1 ) );
 
     At := TransposedMatrix( UnderlyingMatrix( morphism_2 ) );
@@ -1427,18 +1356,14 @@ InstallGlobalFunction( ADD_LIFT_AND_COLIFT_RIGHT,
 
     A_over_zero := UnionOfRows( At, zero_mat );
 
-    if NrColumns( At ) <= 1 then
-        vec := A_over_zero;
-    else
-        vec := UnionOfRows( List( [ 1 .. NrColumns( At ) ], i-> CertainColumns( A_over_zero, [ i ] ) ) );
-    fi;
-
+    vec := ConvertMatrixToColumn( A_over_zero );
+    
     return [ mat, vec ];
 
   end;
 
   AddColift( category, function( cat, morphism_1, morphism_2 )
-    local It, Mt, v, s, sol, XX;
+    local It, Mt, v, s, sol, XX_tr;
 
     It := TransposedMatrix( UnderlyingMatrix( Range( morphism_2 ) ) );
 
@@ -1450,17 +1375,9 @@ InstallGlobalFunction( ADD_LIFT_AND_COLIFT_RIGHT,
 
     sol := CallFuncList( LeftDivide, colift_via_compiled_linear_system_func( morphism_1, morphism_2 ) );
 
-    v := NrColumns( Mt );
-    
-    s := NrColumns( It );
-    
-    if s <= 1 then
-        XX := TransposedMatrix( CertainRows( sol, [ 1.. v ] ) );
-    else
-        XX := TransposedMatrix( UnionOfColumns( List( [ 1 .. s ], i-> CertainRows( sol, [ (i-1)*v+1.. i*v ] ) ) ) );
-    fi;
+    XX_tr := ConvertColumnToMatrix( CertainRows( sol, [ 1 .. v * s ] ), v, s );
 
-    return PresentationMorphism( cat, Range( morphism_1 ), XX, Range( morphism_2 ) );
+    return PresentationMorphism( cat, Range( morphism_1 ), TransposedMatrix( XX_tr ), Range( morphism_2 ) );
 
   end, 1000 );
 

ModulePresentationsForCAP/tst/Lift_Colift.tst

@@ -0,0 +1,32 @@
+gap> START_TEST( "Lift/Colift" );
+
+gap> LoadPackage( "ModulePresentationsForCAP", false );
+true
+
+gap> LoadPackage( "RingsForHomalg", false );
+true
+
+gap> Qx := HomalgFieldOfRationalsInSingular() * "x";;
+gap> Qx_lpres := LeftPresentations( Qx );;
+gap> M_mat := HomalgMatrix( "[ [ 31*x^2, 34*x^2+11*x+32, 0, 0, 42*x ], [ 0, 0, 0, 0, 0 ] ]", 2, 5, Qx );;
+gap> M := AsLeftPresentation( M_mat );;
+gap> N_mat := HomalgMatrix( "[ [ 0, 0, 0, 0, 128954616*x^3+941617341*x^2+907117596*x+56921403, 39256140*x^3+41218947*x^2, 72623859*x^2+69844593*x+907117596, 70661052, 37293333*x^3+25516491*x, 98140350*x^3+69688290*x^2+561548988*x ], [ 0, 39*x, 38*x^3, 18*x^3+38*x^2, 0, 0, 48*x^3+37*x, 0, 0, 8*x^2 ], [ 0, 0, 0, 0, -580852608*x^3-1254907101*x^2-827402436*x-141045009, -97272420*x^3-102136041*x^2, -179953977*x^2-447450297*x-827402436, -175090356, -92408799*x^3-63227073*x, -243181050*x^3-342536124*x^2-512201508*x ] ]", 3, 10, Qx );;
+gap> N := AsLeftPresentation( N_mat );;
+gap> P_mat := HomalgMatrix( "[ [ 0, 0, 714*x-3696, 0 ] ]", 1, 4, Qx );;
+gap> P := AsLeftPresentation( P_mat );;
+gap> f_mat := HomalgMatrix( "[ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 166751424*x^5+94916052*x^4-127178772*x^3-42880992*x^2+13268892*x, 69479760*x^5+82104708*x^4+9608508*x^3, 128537556*x^4+75987072*x^3+7778316*x^2-143626644*x, 125063568*x^2+16471728*x, 66005772*x^5+8693412*x^4+45161844*x^3+5948124*x^2, 173699400*x^5+106253112*x^4+10981152*x^3-88911732*x^2 ], [ 1450*x^4+1161*x^3+162*x^2, 1400*x^3+252*x^2, 0, 0, 450*x+81, 0, 0, 500*x^4+90*x^3+800*x^2+144*x, 2350*x^3+2523*x^2+1028*x+117, 0 ], [ 0, 0, 0, 0, 71464896*x^5+40678308*x^4-54505188*x^3-18377568*x^2+5686668*x, 29777040*x^5+35187732*x^4+4117932*x^3+420*x^2+555*x+240, 55087524*x^4+32566428*x^3+3333564*x^2-61554276*x, 53598672*x^2+7059312*x, 28288188*x^5+3725748*x^4+19355076*x^3+2549196*x^2, 74442600*x^5+45537048*x^4+4706358*x^3-38105028*x^2+720*x+480 ], [ 0, 0, 0, 0, -3970272000*x^4-2259906000*x^3+3028066000*x^2+1020976000*x-315926000, -1654280000*x^4-1954874000*x^3-228774000*x^2, -3060418000*x^3-1809216000*x^2-185198000*x+3419682000, -2977704000*x-392184000, -1571566000*x^4-206986000*x^3-1075282000*x^2-141622000*x, -4135700000*x^4-2529836000*x^3-261456000*x^2+2116946000*x ] ]", 5, 10, Qx );;
+gap> f := PresentationMorphism( M, f_mat, N );;
+gap> g_mat := HomalgMatrix( "[ [ 29*x^3+18*x^2, 28*x^2, 0, 0, 9, 0, 0, 10*x^3+16*x, 47*x^2+42*x+13, 0 ], [ 0, 0, 0, 0, 0, 28*x^2+37*x+16, 36*x^3, 0, 0, 10*x^3+48*x+32 ], [ 0, 0, 0, 0, 1985136*x^4+1129953*x^3-1514033*x^2-510488*x+157963, 827140*x^4+977437*x^3+114387*x^2, 1530209*x^3+904608*x^2+92599*x-1709841, 1488852*x+196092, 785783*x^4+103493*x^3+537641*x^2+70811*x, 2067850*x^4+1264918*x^3+130728*x^2-1058473*x ], [ 43*x, 0, 0, 0, 5*x, 0, 0, 0, 14*x^3, 34 ] ]", 4, 10, Qx );;
+gap> g := PresentationMorphism( P, g_mat, N );;
+gap> l := Lift( f, g );;
+gap> Assert( 0, PreCompose( l, Colift( l, f ) ) = f and PreCompose( l, g ) = f );
+gap> Qx_rpres := RightPresentations( Qx );;
+gap> M := AsRightPresentation( TransposedMatrix( M_mat ) );;
+gap> N := AsRightPresentation( TransposedMatrix( N_mat ) );;
+gap> P := AsRightPresentation( TransposedMatrix( P_mat ) );;
+gap> f := PresentationMorphism( M, TransposedMatrix( f_mat ), N );;
+gap> g := PresentationMorphism( P, TransposedMatrix( g_mat ), N );;
+gap> l := Lift( f, g );;
+gap> Assert( 0, PreCompose( l, Colift( l, f ) ) = f and PreCompose( l, g ) = f );;
+
+gap> STOP_TEST( "Lift/Colift" );