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b/Infrageometry/Kernel/Infrageometry.wl @@ -44,6 +44,7 @@ PackageExport[BarycentricRefinement] PackageExport[GraphTopology] +PackageExport[FaceMatrix] PackageExport[IndexMatrix] PackageExport[SignMatrix] PackageExport[ComplexIncidenceMatrix] @@ -207,6 +208,12 @@ BarycentricRefinement[x_, n_Integer, opts : OptionsPattern[]] := Nest[Barycentri GraphTopology[g_ ? GraphQ] := With[{c = GraphComplex[g]}, SimplexStar[c, #] & /@ c] +FaceQ /: FaceQ[i_Integer][x_List, y_List] := Length[x] === Length[y] - 1 && 0 <= i < Length[y] && Delete[y, i + 1] === x; + +FaceMatrix /: FaceMatrix[i_Integer][args___] := FaceMatrix[args][i] + +FaceMatrix[_, x : {___List}, y : {___List}] := Outer[Boole @* FaceQ[#], x, y, 1] & + IndexMatrix[_, x : {___List}, y : {___List}] := Outer[SimplexIndex &, x, y, 1] SignMatrix[_, x : {___List}, y : {___List}] := Outer[SimplexSign, x, y, 1] @@ -236,7 +243,7 @@ Scan[f |-> ( f[g : {___List}, args___] := f[g, g, args]; ) , - {IndexMatrix, SignMatrix, ConnectionMatrix, GreenFunctionMatrix} + {FaceMatrix, IndexMatrix, SignMatrix, ConnectionMatrix, GreenFunctionMatrix} ] DiracHodgeMatrix[args___] := Enclose @ With[{d = ConfirmBy[SignMatrix[args], SquareMatrixQ]},