d&i new method Algebroid for [ IsHomalgRing, IsFpCategory ]

Author: mohamed-barakat

PackageInfo.g

@@ -11,7 +11,7 @@ SetPackageInfo( rec(
 PackageName := "Algebroids",
 Subtitle := "Algebroids and bialgebroids as preadditive categories generated by enhanced quivers",
 Version := Maximum( [
-                   "2020.10-11", ## Mohamed's version
+                   "2020.10-12", ## Mohamed's version
                    ## this line prevents merge conflicts
                    "2020.09-08", ## Kamal's version
                    ## this line prevents merge conflicts

gap/Algebroids.gd

@@ -336,6 +336,16 @@ DeclareOperation( "Algebroid",
 DeclareOperation( "Algebroid",
         [ IsHomalgRing, IsQuiver ] );
 
+#! @Arguments R, C
+#! @Group Algebroid
+DeclareOperation( "Algebroid",
+        [ IsHomalgRing, IsFpCategory ] );
+
+#! @Arguments R, C
+#! @Group Algebroid
+DeclareOperation( "[]",
+        [ IsHomalgRing, IsFpCategory ] );
+
 #! @Description
 #! The argument is an algebroid $A$ with left acting domain given by the field of rationals $\mathbb{Q}$,
 #! either realized by <C>Rationals</C> or by <C>HomalgFieldOfRationals</C> (in no external CAS).

gap/Algebroids.gi

@@ -1012,6 +1012,45 @@ InstallMethod( Algebroid,
 
 end );
 
+##
+InstallMethodWithCache( Algebroid,
+        "for a homalg ring and a finitely presented category",
+        [ IsHomalgRing, IsFpCategory ],
+        
+  function( k, C )
+    local relations, kq, A;
+    
+    relations := C!.relations;
+    
+    if relations = [ ] and not IsPathAlgebra( UnderlyingQuiverAlgebra( C ) ) then
+        Error( "the underlying quiver algebra is not a path algebra, nevertheless the list of relations is empty\n" );
+    fi;
+    
+    kq := PathAlgebra( k, UnderlyingQuiver( C ) );
+    
+    relations := List( relations, a -> PathAsAlgebraElement( kq, a[1] ) - PathAsAlgebraElement( kq, a[2] ) );
+    
+    A := kq / Ideal( kq, relations );
+    
+    A := kq / GroebnerBasis( IdealOfQuotient( A ) );
+    
+    A := Algebroid( A, false ); ## do not call the single argument method Algebroid as it is an attribute
+    
+    SetUnderlyingCategory( A, C );
+    
+    SetIsLinearClosureOfACategory( A, true );
+    
+    return A;
+    
+end );
+
+##
+InstallMethod( \[\],
+        "for a homalg ring and a finitely presented category",
+        [ IsHomalgRing, IsFpCategory ],
+        
+  Algebroid );
+
 ##
 InstallMethod( DescentToZDefinedByBasisPaths,
         "for an algebroid",