Unexpected behavior of the procedure `Area` on the object 'Polygon'












9












$begingroup$


Sometimes get a results, sometimes left unevaluated.



For instance



 Area@Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}] 



12




Transpose@(a.b.Transpose[#]) & /@ Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}] 


(a,b - some 2x2 matrices)




Polygon[{{0, 0}, {8, -64}, {18, -24}, {36, -48}, {28, 16}}]




Area@(Transpose@(a.b.Transpose[#]) & /@ Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}] )



Area[Polygon[{{0, 0}, {8, -64}, {18, -24}, {36, -48}, {28, 16}}]]




Area@Polygon[{{0, 0}, {8, -64}, {18, -24}, {36, -48}, {28, 16}}]


(copy and paste)




1440




How to guess when a calculation will give a result and when it will not be evaluated? And why does it not evaluate?










share|improve this question











$endgroup$








  • 3




    $begingroup$
    What are the definitions of a and b?
    $endgroup$
    – MarcoB
    Mar 22 at 14:36










  • $begingroup$
    If you want to experiment with this and I haven't made a mistake then it looks like his a.b == {{2,7},{-16,4}} This seems to reproduce his results.
    $endgroup$
    – Bill
    Mar 22 at 16:15


















9












$begingroup$


Sometimes get a results, sometimes left unevaluated.



For instance



 Area@Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}] 



12




Transpose@(a.b.Transpose[#]) & /@ Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}] 


(a,b - some 2x2 matrices)




Polygon[{{0, 0}, {8, -64}, {18, -24}, {36, -48}, {28, 16}}]




Area@(Transpose@(a.b.Transpose[#]) & /@ Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}] )



Area[Polygon[{{0, 0}, {8, -64}, {18, -24}, {36, -48}, {28, 16}}]]




Area@Polygon[{{0, 0}, {8, -64}, {18, -24}, {36, -48}, {28, 16}}]


(copy and paste)




1440




How to guess when a calculation will give a result and when it will not be evaluated? And why does it not evaluate?










share|improve this question











$endgroup$








  • 3




    $begingroup$
    What are the definitions of a and b?
    $endgroup$
    – MarcoB
    Mar 22 at 14:36










  • $begingroup$
    If you want to experiment with this and I haven't made a mistake then it looks like his a.b == {{2,7},{-16,4}} This seems to reproduce his results.
    $endgroup$
    – Bill
    Mar 22 at 16:15
















9












9








9





$begingroup$


Sometimes get a results, sometimes left unevaluated.



For instance



 Area@Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}] 



12




Transpose@(a.b.Transpose[#]) & /@ Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}] 


(a,b - some 2x2 matrices)




Polygon[{{0, 0}, {8, -64}, {18, -24}, {36, -48}, {28, 16}}]




Area@(Transpose@(a.b.Transpose[#]) & /@ Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}] )



Area[Polygon[{{0, 0}, {8, -64}, {18, -24}, {36, -48}, {28, 16}}]]




Area@Polygon[{{0, 0}, {8, -64}, {18, -24}, {36, -48}, {28, 16}}]


(copy and paste)




1440




How to guess when a calculation will give a result and when it will not be evaluated? And why does it not evaluate?










share|improve this question











$endgroup$




Sometimes get a results, sometimes left unevaluated.



For instance



 Area@Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}] 



12




Transpose@(a.b.Transpose[#]) & /@ Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}] 


(a,b - some 2x2 matrices)




Polygon[{{0, 0}, {8, -64}, {18, -24}, {36, -48}, {28, 16}}]




Area@(Transpose@(a.b.Transpose[#]) & /@ Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}] )



Area[Polygon[{{0, 0}, {8, -64}, {18, -24}, {36, -48}, {28, 16}}]]




Area@Polygon[{{0, 0}, {8, -64}, {18, -24}, {36, -48}, {28, 16}}]


(copy and paste)




1440




How to guess when a calculation will give a result and when it will not be evaluated? And why does it not evaluate?







bugs evaluation computational-geometry polygons packed-arrays






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 2 days ago









kirma

10.2k13058




10.2k13058










asked Mar 22 at 14:22









Slepecky MamutSlepecky Mamut

630110




630110








  • 3




    $begingroup$
    What are the definitions of a and b?
    $endgroup$
    – MarcoB
    Mar 22 at 14:36










  • $begingroup$
    If you want to experiment with this and I haven't made a mistake then it looks like his a.b == {{2,7},{-16,4}} This seems to reproduce his results.
    $endgroup$
    – Bill
    Mar 22 at 16:15
















  • 3




    $begingroup$
    What are the definitions of a and b?
    $endgroup$
    – MarcoB
    Mar 22 at 14:36










  • $begingroup$
    If you want to experiment with this and I haven't made a mistake then it looks like his a.b == {{2,7},{-16,4}} This seems to reproduce his results.
    $endgroup$
    – Bill
    Mar 22 at 16:15










3




3




$begingroup$
What are the definitions of a and b?
$endgroup$
– MarcoB
Mar 22 at 14:36




$begingroup$
What are the definitions of a and b?
$endgroup$
– MarcoB
Mar 22 at 14:36












$begingroup$
If you want to experiment with this and I haven't made a mistake then it looks like his a.b == {{2,7},{-16,4}} This seems to reproduce his results.
$endgroup$
– Bill
Mar 22 at 16:15






$begingroup$
If you want to experiment with this and I haven't made a mistake then it looks like his a.b == {{2,7},{-16,4}} This seems to reproduce his results.
$endgroup$
– Bill
Mar 22 at 16:15












2 Answers
2






active

oldest

votes


















8












$begingroup$

EDIT: Reported to WRI as CASE:4237867 - and apparently should work on V12. :)



Seems like a bug in my opinion. Consider the following:



With[{poly0 = Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]}, 
With[{poly = Transpose[IdentityMatrix[2].Transpose@#] & /@ poly0},
{poly0 === poly, Area /@ {poly0, poly}}]]



{True, {12, Area[Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]]}}




Although the Mma considers poly0 and its transformed but identical copy (coordinates transformed using IdentityMatrix) identical, they produce different results.



Probably the internal representation of poly is not the same as poly0. At the same time its output form is identical, which actually transforms it to other form if you copy and paste it.



This can be further simplified to show that from the perspective of Polygon two semantically identical coordinate lists can differ:



With[{coord0 = {{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}}, 
With[{coord = Transpose[IdentityMatrix[2].Transpose@coord0]},
{coord0 === coord, Area@*Polygon /@ {coord0, coord}}]]



{True, {12, Area[Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]]}}




I suspect there's something wrong with the way Polygon reads the internal representation of a list!



EDIT: I think there's a good chance this problem is caused by the fact coord is a packed array, while coord0 is not:



With[{coord0 = {{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}}, 
With[{coord = Transpose[IdentityMatrix[2].Transpose@coord0]},
{coord0 === coord, Developer`PackedArrayQ /@ {coord0, coord},
Area@*Polygon /@ {coord0, Developer`FromPackedArray@coord}}]]



{True, {False, True}, {12, 12}}




So, you can use FromPackedArray on the transformed coordinate list as a workaround.






share|improve this answer











$endgroup$





















    6












    $begingroup$

    This is a packed array issue:



    Area @ Polygon[Developer`ToPackedArray @ {{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]



    Area[Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]]




    This will be fixed in M12.






    share|improve this answer









    $endgroup$













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      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      8












      $begingroup$

      EDIT: Reported to WRI as CASE:4237867 - and apparently should work on V12. :)



      Seems like a bug in my opinion. Consider the following:



      With[{poly0 = Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]}, 
      With[{poly = Transpose[IdentityMatrix[2].Transpose@#] & /@ poly0},
      {poly0 === poly, Area /@ {poly0, poly}}]]



      {True, {12, Area[Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]]}}




      Although the Mma considers poly0 and its transformed but identical copy (coordinates transformed using IdentityMatrix) identical, they produce different results.



      Probably the internal representation of poly is not the same as poly0. At the same time its output form is identical, which actually transforms it to other form if you copy and paste it.



      This can be further simplified to show that from the perspective of Polygon two semantically identical coordinate lists can differ:



      With[{coord0 = {{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}}, 
      With[{coord = Transpose[IdentityMatrix[2].Transpose@coord0]},
      {coord0 === coord, Area@*Polygon /@ {coord0, coord}}]]



      {True, {12, Area[Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]]}}




      I suspect there's something wrong with the way Polygon reads the internal representation of a list!



      EDIT: I think there's a good chance this problem is caused by the fact coord is a packed array, while coord0 is not:



      With[{coord0 = {{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}}, 
      With[{coord = Transpose[IdentityMatrix[2].Transpose@coord0]},
      {coord0 === coord, Developer`PackedArrayQ /@ {coord0, coord},
      Area@*Polygon /@ {coord0, Developer`FromPackedArray@coord}}]]



      {True, {False, True}, {12, 12}}




      So, you can use FromPackedArray on the transformed coordinate list as a workaround.






      share|improve this answer











      $endgroup$


















        8












        $begingroup$

        EDIT: Reported to WRI as CASE:4237867 - and apparently should work on V12. :)



        Seems like a bug in my opinion. Consider the following:



        With[{poly0 = Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]}, 
        With[{poly = Transpose[IdentityMatrix[2].Transpose@#] & /@ poly0},
        {poly0 === poly, Area /@ {poly0, poly}}]]



        {True, {12, Area[Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]]}}




        Although the Mma considers poly0 and its transformed but identical copy (coordinates transformed using IdentityMatrix) identical, they produce different results.



        Probably the internal representation of poly is not the same as poly0. At the same time its output form is identical, which actually transforms it to other form if you copy and paste it.



        This can be further simplified to show that from the perspective of Polygon two semantically identical coordinate lists can differ:



        With[{coord0 = {{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}}, 
        With[{coord = Transpose[IdentityMatrix[2].Transpose@coord0]},
        {coord0 === coord, Area@*Polygon /@ {coord0, coord}}]]



        {True, {12, Area[Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]]}}




        I suspect there's something wrong with the way Polygon reads the internal representation of a list!



        EDIT: I think there's a good chance this problem is caused by the fact coord is a packed array, while coord0 is not:



        With[{coord0 = {{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}}, 
        With[{coord = Transpose[IdentityMatrix[2].Transpose@coord0]},
        {coord0 === coord, Developer`PackedArrayQ /@ {coord0, coord},
        Area@*Polygon /@ {coord0, Developer`FromPackedArray@coord}}]]



        {True, {False, True}, {12, 12}}




        So, you can use FromPackedArray on the transformed coordinate list as a workaround.






        share|improve this answer











        $endgroup$
















          8












          8








          8





          $begingroup$

          EDIT: Reported to WRI as CASE:4237867 - and apparently should work on V12. :)



          Seems like a bug in my opinion. Consider the following:



          With[{poly0 = Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]}, 
          With[{poly = Transpose[IdentityMatrix[2].Transpose@#] & /@ poly0},
          {poly0 === poly, Area /@ {poly0, poly}}]]



          {True, {12, Area[Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]]}}




          Although the Mma considers poly0 and its transformed but identical copy (coordinates transformed using IdentityMatrix) identical, they produce different results.



          Probably the internal representation of poly is not the same as poly0. At the same time its output form is identical, which actually transforms it to other form if you copy and paste it.



          This can be further simplified to show that from the perspective of Polygon two semantically identical coordinate lists can differ:



          With[{coord0 = {{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}}, 
          With[{coord = Transpose[IdentityMatrix[2].Transpose@coord0]},
          {coord0 === coord, Area@*Polygon /@ {coord0, coord}}]]



          {True, {12, Area[Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]]}}




          I suspect there's something wrong with the way Polygon reads the internal representation of a list!



          EDIT: I think there's a good chance this problem is caused by the fact coord is a packed array, while coord0 is not:



          With[{coord0 = {{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}}, 
          With[{coord = Transpose[IdentityMatrix[2].Transpose@coord0]},
          {coord0 === coord, Developer`PackedArrayQ /@ {coord0, coord},
          Area@*Polygon /@ {coord0, Developer`FromPackedArray@coord}}]]



          {True, {False, True}, {12, 12}}




          So, you can use FromPackedArray on the transformed coordinate list as a workaround.






          share|improve this answer











          $endgroup$



          EDIT: Reported to WRI as CASE:4237867 - and apparently should work on V12. :)



          Seems like a bug in my opinion. Consider the following:



          With[{poly0 = Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]}, 
          With[{poly = Transpose[IdentityMatrix[2].Transpose@#] & /@ poly0},
          {poly0 === poly, Area /@ {poly0, poly}}]]



          {True, {12, Area[Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]]}}




          Although the Mma considers poly0 and its transformed but identical copy (coordinates transformed using IdentityMatrix) identical, they produce different results.



          Probably the internal representation of poly is not the same as poly0. At the same time its output form is identical, which actually transforms it to other form if you copy and paste it.



          This can be further simplified to show that from the perspective of Polygon two semantically identical coordinate lists can differ:



          With[{coord0 = {{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}}, 
          With[{coord = Transpose[IdentityMatrix[2].Transpose@coord0]},
          {coord0 === coord, Area@*Polygon /@ {coord0, coord}}]]



          {True, {12, Area[Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]]}}




          I suspect there's something wrong with the way Polygon reads the internal representation of a list!



          EDIT: I think there's a good chance this problem is caused by the fact coord is a packed array, while coord0 is not:



          With[{coord0 = {{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}}, 
          With[{coord = Transpose[IdentityMatrix[2].Transpose@coord0]},
          {coord0 === coord, Developer`PackedArrayQ /@ {coord0, coord},
          Area@*Polygon /@ {coord0, Developer`FromPackedArray@coord}}]]



          {True, {False, True}, {12, 12}}




          So, you can use FromPackedArray on the transformed coordinate list as a workaround.







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited 2 days ago

























          answered 2 days ago









          kirmakirma

          10.2k13058




          10.2k13058























              6












              $begingroup$

              This is a packed array issue:



              Area @ Polygon[Developer`ToPackedArray @ {{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]



              Area[Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]]




              This will be fixed in M12.






              share|improve this answer









              $endgroup$


















                6












                $begingroup$

                This is a packed array issue:



                Area @ Polygon[Developer`ToPackedArray @ {{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]



                Area[Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]]




                This will be fixed in M12.






                share|improve this answer









                $endgroup$
















                  6












                  6








                  6





                  $begingroup$

                  This is a packed array issue:



                  Area @ Polygon[Developer`ToPackedArray @ {{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]



                  Area[Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]]




                  This will be fixed in M12.






                  share|improve this answer









                  $endgroup$



                  This is a packed array issue:



                  Area @ Polygon[Developer`ToPackedArray @ {{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]



                  Area[Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}]]




                  This will be fixed in M12.







                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered 2 days ago









                  Carl WollCarl Woll

                  71.5k394186




                  71.5k394186






























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Hall Of Fame””Slayer Wins 'Best Metal' Grammy Award””Slayer Guitarist Jeff Hanneman Dies””Bullet-For My Valentine booed at Metal Hammer Golden Gods Awards””Unholy Aliance””The End Of Slayer?””Slayer: We Could Thrash Out Two More Albums If We're Fast Enough...””'The Unholy Alliance: Chapter III' UK Dates Added”originalet”Megadeth And Slayer To Co-Headline 'Canadian Carnage' Trek”originalet”World Painted Blood””Release “World Painted Blood” by Slayer””Metallica Heading To Cinemas””Slayer, Megadeth To Join Forces For 'European Carnage' Tour - Dec. 18, 2010”originalet”Slayer's Hanneman Contracts Acute Infection; Band To Bring In Guest Guitarist””Cannibal Corpse's Pat O'Brien Will Step In As Slayer's Guest Guitarist”originalet”Slayer’s Jeff Hanneman Dead at 49””Dave Lombardo Says He Made Only $67,000 In 2011 While Touring With Slayer””Slayer: We Do Not Agree With Dave Lombardo's Substance Or Timeline Of Events””Slayer Welcomes Drummer Paul Bostaph Back To The Fold””Slayer Hope to Unveil Never-Before-Heard Jeff Hanneman Material on Next Album””Slayer Debut New Song 'Implode' During Surprise Golden Gods Appearance””Release group Repentless by Slayer””Repentless - Slayer - Credits””Slayer””Metal Storm Awards 2015””Slayer - to release comic book "Repentless #1"””Slayer To Release 'Repentless' 6.66" Vinyl Box Set””BREAKING NEWS: Slayer Announce Farewell Tour””Slayer Recruit Lamb of God, Anthrax, Behemoth + Testament for Final Tour””Slayer lägger ner efter 37 år””Slayer Announces Second North American Leg Of 'Final' Tour””Final World Tour””Slayer Announces Final European Tour With Lamb of God, Anthrax And Obituary””Slayer To Tour Europe With Lamb of God, Anthrax And Obituary””Slayer To Play 'Last French Show Ever' At Next Year's Hellfst””Slayer's Final World Tour Will Extend Into 2019””Death Angel's Rob Cavestany On Slayer's 'Farewell' Tour: 'Some Of Us Could See This Coming'””Testament Has No Plans To Retire Anytime Soon, Says Chuck Billy””Anthrax's Scott Ian On Slayer's 'Farewell' Tour Plans: 'I Was Surprised And I Wasn't Surprised'””Slayer””Slayer's Morbid Schlock””Review/Rock; For Slayer, the Mania Is the Message””Slayer - Biography””Slayer - Reign In Blood”originalet”Dave Lombardo””An exclusive oral history of Slayer”originalet”Exclusive! Interview With Slayer Guitarist Jeff Hanneman”originalet”Thinking Out Loud: Slayer's Kerry King on hair metal, Satan and being polite””Slayer Lyrics””Slayer - Biography””Most influential artists for extreme metal music””Slayer - Reign in Blood””Slayer guitarist Jeff Hanneman dies aged 49””Slatanic Slaughter: A Tribute to Slayer””Gateway to Hell: A Tribute to Slayer””Covered In Blood””Slayer: The Origins of Thrash in San Francisco, CA.””Why They Rule - #6 Slayer”originalet”Guitar World's 100 Greatest Heavy Metal Guitarists Of All Time”originalet”The fans have spoken: Slayer comes out on top in readers' polls”originalet”Tribute to Jeff Hanneman (1964-2013)””Lamb Of God Frontman: We Sound Like A Slayer Rip-Off””BEHEMOTH Frontman Pays Tribute To SLAYER's JEFF HANNEMAN””Slayer, Hatebreed Doing Double Duty On This Year's Ozzfest””System of a Down””Lacuna Coil’s Andrea Ferro Talks Influences, Skateboarding, Band Origins + More””Slayer - Reign in Blood””Into The Lungs of Hell””Slayer rules - en utställning om fans””Slayer and Their Fans Slashed Through a No-Holds-Barred Night at Gas Monkey””Home””Slayer””Gold & Platinum - The Big 4 Live from Sofia, Bulgaria””Exclusive! Interview With Slayer Guitarist Kerry King””2008-02-23: Wiltern, Los Angeles, CA, USA””Slayer's Kerry King To Perform With Megadeth Tonight! - Oct. 21, 2010”originalet”Dave Lombardo - Biography”Slayer Case DismissedArkiveradUltimate Classic Rock: Slayer guitarist Jeff Hanneman dead at 49.”Slayer: "We could never do any thing like Some Kind Of Monster..."””Cannibal Corpse'S Pat O'Brien Will Step In As Slayer'S Guest Guitarist | The Official Slayer Site”originalet”Slayer Wins 'Best Metal' Grammy Award””Slayer Guitarist Jeff Hanneman Dies””Kerrang! Awards 2006 Blog: Kerrang! Hall Of Fame””Kerrang! Awards 2013: Kerrang! Legend”originalet”Metallica, Slayer, Iron Maien Among Winners At Metal Hammer Awards””Metal Hammer Golden Gods Awards””Bullet For My Valentine Booed At Metal Hammer Golden Gods Awards””Metal Storm Awards 2006””Metal Storm Awards 2015””Slayer's Concert History””Slayer - Relationships””Slayer - Releases”Slayers officiella webbplatsSlayer på MusicBrainzOfficiell webbplatsSlayerSlayerr1373445760000 0001 1540 47353068615-5086262726cb13906545x(data)6033143kn20030215029