Package: tilingsgui
A graphical interface forTilings.Install and runpipinstalltilingsguitilingsguitilingsgui-j'tilingsgui json object'Note for LinuxPyperclip requires clipboard tools that might not come pre-installed.sudoapt-getinstallxclipWithout them the app still works but pasting won’t.Known issuesReport a bugAlong with the description of the bug, please provide a json of the tiling which is exportable in the gui.User manualSummaryPoint insertionPermutation insertionExportFactorFactor with interleavingFusion with column setFusion with row setComponent fusion with column setComponent fusion with row setHighlight hovered cellMoveObstruction transitivityEast placementNorth placementSouth placementWest placementEast partial placementNorth partial placementSouth partial placementWest partial placementPretty pointsUndoRedoRow column separationSequeceShadingShow crossingShow localizedPrintVerificationTikzObstruction inferralTiling inputThe input box directly above the tiling canvas can be used to create an initial tiling. It accepts both strings and json, usingfrom_stringandfrom_jsonrespectively. A right click activates it. To confirm your input, press enter or click away from the text box. Escape cancels the input. Right clicking when activated will paste whatever is on the clipboard.Example:
The following two inputs are two ways of producing the same initial tiling.1432_12345

{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}The initial tiling in question would be the following.+-+|1|+-+1:Av(0321,01234)Cell insertionTo insert a permutation into a single cell, one can choose either to add a point,, or a custom permutation,. For the latter, the latest confirmed input in the text box above the button grid is used. The text box works just like the one for inputting tilings. It usesto_standardto convert the input to a permutation. After having selected the permutation to insert, then clicking a cell will insert it. Left click inserts it as a requirement while a right click inserts it as a obstruction, usingadd_single_cell_requirementandadd_single_cell_obstructionrespectively.FactorThere are two types of factorization, factorand factor with interleaving. In both cases they are applied to the cell that is clicked. Two active cells are in the same factor if they are in the same row or column, or they share an obstruction or a requirement. For factoring with interleaving, two non-empty cells are in the same factor if they share an obstruction or a requirement.Place pointsBy clicking a point of a requirement, we pass its gridded permutation along with its index within it toplace_point_of_gridded_permutationand the direction set by the button chosen, east, north, southor west.defplace_point_of_gridded_permutation(self,gp:GriddedPerm,idx:int,direction:int)->"Tiling":"""
        Return the tiling where the directionmost occurrence of the idx point
        in the gridded permutaion gp is placed.
        """Partially place pointsBy clicking a point of a requirement, we pass its gridded permutation along with its index within it topartial_place_point_of_gridded_permutationand the direction set by the button chosen, east, north, southor west.defpartial_place_point_of_gridded_permutation(self,gp:GriddedPerm,idx:int,direction:int)->"Tiling":"""
    Return the tiling where the directionmost occurrence of the idx point
    in the gridded permutaion gp is placed. The point is placed onto its
    own row or own column depending on the direction.
    """FusionLetc_randc_cbe the row and column respectively of the clicked cell. There are 4 types of fusions available. Fusion withrow=c_r,, fusion withcol=c_c,, component fusion withrow=c_r,, and component fusion withcol=c_c,. If the fusion are invalid, then exceptions are caught and nothing happens.Fusion:"""
Fuse the tilings.
If `row` is not `None` then `row` and `row+1` are fused together.
If `col` is not `None` then `col` and `col+1` are fused together.
"""Component fusion:"""
Fuse the tilings in such a way that it can be unfused by drawing a line between skew/sum-components.
If `row` is not `None` then `row` and `row+1` are fused together.
If `col` is not `None` then `col` and `col+1` are fused together.
"""Undo and redoGiven that there are previously drawn tilings, then undo,, will redraw the one before the last action. If you wish to revert the undo, you can use redo,. There is a limit on how many tilings are stored in memory.Row column separationsplits the row and columns of a tilings using the inequalities implied by the length two obstructions.Obstruction transitivityadds length 2 obstructions to the tiling using transitivity over positive cells.ExportExport,, will store the current tiling in memory and upon closing the app, will add all stored tilings in the session to./export/history.json. There is a session limit so the file become too large. If the session limit is reached, than adding more will remove the oldest. The format of the json can be seen below with time and tiling values empty. Any time export is used, a copy of the history is placed in the current working directory.[{"session_time":"","tilings":[{"tiling_time":"","tiling":{}},{"tiling_time":"","tiling":{}}]},{"session_time":"","tilings":[{"tiling_time":"","tiling":{}}]}]PrintWriting the current tiling tostdout,, will produce both the__str__and__repr__representation of the tiling. An example output is shown below.+-+-+-+||●||+-+-+-+|1||1|+-+-+-+1:Av(021)●:pointCrossingobstructions:01:(0,0),(2,0)Requirement0:0:(1,1)Tiling(obstructions=(GriddedPerm(Perm((0,)),((0,1),)),GriddedPerm(Perm((0,)),((1,0),)),GriddedPerm(Perm((0,)),((2,1),)),GriddedPerm(Perm((0,1)),((0,0),(2,0))),GriddedPerm(Perm((0,1)),((1,1),(1,1))),GriddedPerm(Perm((1,0)),((1,1),(1,1))),GriddedPerm(Perm((0,2,1)),((0,0),(0,0),(0,0))),GriddedPerm(Perm((0,2,1)),((2,0),(2,0),(2,0)))),requirements=((GriddedPerm(Perm((0,)),((1,1),)),),),assumptions=())SequenceThe first few terms of the sequence of gridded permutations griddable on the current tiling can be written tostdout,, where for example the following tiling+-+-+-+-+||●|||+-+-+-+-+|1||1||+-+-+-+-+||||●|+-+-+-+-+|||1||+-+-+-+-+1:Av(021)●:pointCrossingobstructions:01:(0,2),(2,2)01:(2,0),(2,2)Requirement0:0:(1,3)Requirement1:0:(3,1)would produce this output.[0,0,1,3,9,28,90,297]ShadingWith shading on,, then a 1 restriction is not drawn as a point but rather as a filled cell.Pretty pointsWith pretty points on,, then 12 and 21 restrictions along with a 1 requirement within the same cell are drawn as a single point.Show localizedWith localized shown,, requirements and obstructions that are contained in a single cell are shown. Without it they are not.Show crossingWith crossing shown,, requirements and obstructions that reach across different cells are shown. Without it they are not.Highlight hovered cellTurning on the hovered cell highlighting,, obstructions in the hovered cell are colored differently.Obstruction inferralAdd all obstructions up to a length that does not change the set of gridded permutations. Pressingwill use the upper right input box to determine the lenght. It is maxed at 7 and defaults to 3.TikzUseto produce the current tiling with the current positions as a tikz figure.VerificationGiven a tilingt, the verification button,, will produce the following result.[BasicVerificationStrategy().verified(t),DatabaseVerificationStrategy().verified(t),ElementaryVerificationStrategy().verified(t),InsertionEncodingVerificationStrategy().verified(t),LocallyFactorableVerificationStrategy().verified(t),LocalVerificationStrategy(no_factors=False).verified(t),MonotoneTreeVerificationStrategy().verified(t),OneByOneVerificationStrategy().verified(t)]An example output is shown below.BasicVerificationStrategy:TrueDatabaseVerificationStrategy:FalseElementaryVerificationStrategy:FalseInsertionEncodingVerificationStrategy:TrueLocallyFactorableVerificationStrategy:FalseLocalVerificationStrategy:TrueMonotoneTreeVerificationStrategy:FalseOneByOneVerificationStrategy:True