Reducing system of 10 inequalities












1












$begingroup$


I have the following system of inequalities of real variables



sys = 0.383706 x1 + 0.720204 x2 + 1.4568 x3 - 0.000244875 y >   0 && -0.0941312 x1 - 0.176681 x2 - 0.357383 x3 + 0.0000592689 y >   0 && 1.41819 x1 + 3.079 x2 + 2.53801 x3 - 0.00182772 y >   0 && -0.00258971 x1 - 0.00562247 x2 - 0.00463458 x3 +    3.93843*10^-6 y > 0 &&  0.129511 x1 + 0.214698 x2 + 0.286739 x3 - 0.0000795243 y >   0 && -0.660462 x1 - 1.09489 x2 - 1.46227 x3 + 0.000405426 y > 0 &&  0.351966 x1 + 3.44019 x2 + 7.59863 x3 + 0.00257072 y >   0 && -0.00265509 x1 - 0.0259514 x2 - 0.0573209 x3 -    0.0000199557 y > 0 &&  1.34471 x1 + 2.58639 x2 + 3.39561 x3 + 0.0000742173 y >   0 && -0.0314846 x1 - 0.0605571 x2 - 0.079504 x3 - 1.69328*10^-6 y >   0


I want to Reduce the system in order to see if it admits solutions or not. However, the command Reduce takes too much time and gets stuck. How can you check if this system admits solutions?



I have tried with FindInstance[sys,{x1,x2,x3,y},Reals] which returns {}. However, I am not sure this is a fully proof that the system does not admit solution. Indeed, If I run the command on a subsystem of inequalities I experience the following behaviour



FindInstance[sys[[1 ;; 4]], {x1, x2, x3, y}, Reals]

(* {} *)


but If I ask for more instances, Mathematica found the points



FindInstance[sys[[1 ;; 4]], {x1, x2, x3, y}, Reals, 2]

(*{{x1 -> -33., x2 -> 13.5619, x3 -> 1.98727, y -> 0.255564}, {x1 -> -51., x2 -> 20.9595, x3 -> 3.07117, y -> 0.601467}}*)


So, the subsystem [[1;;4]] admits at least a solution. I have run FindInstance[sys, {x1, x2, x3, y}, Reals, 2] for all the night and got the output {}. Still, is this a proof that the system does not admits solution?






equation-solving inequalities findinstance







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$endgroup$








  • 1




    $begingroup$
    Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals] gives False.
    $endgroup$
    – kglr
    Nov 19 '18 at 7:28






  • 1




    $begingroup$
    and RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys)) gives EmptyRegion[4].
    $endgroup$
    – kglr
    Nov 19 '18 at 7:33
















1












$begingroup$


I have the following system of inequalities of real variables



sys = 0.383706 x1 + 0.720204 x2 + 1.4568 x3 - 0.000244875 y >   0 && -0.0941312 x1 - 0.176681 x2 - 0.357383 x3 + 0.0000592689 y >   0 && 1.41819 x1 + 3.079 x2 + 2.53801 x3 - 0.00182772 y >   0 && -0.00258971 x1 - 0.00562247 x2 - 0.00463458 x3 +    3.93843*10^-6 y > 0 &&  0.129511 x1 + 0.214698 x2 + 0.286739 x3 - 0.0000795243 y >   0 && -0.660462 x1 - 1.09489 x2 - 1.46227 x3 + 0.000405426 y > 0 &&  0.351966 x1 + 3.44019 x2 + 7.59863 x3 + 0.00257072 y >   0 && -0.00265509 x1 - 0.0259514 x2 - 0.0573209 x3 -    0.0000199557 y > 0 &&  1.34471 x1 + 2.58639 x2 + 3.39561 x3 + 0.0000742173 y >   0 && -0.0314846 x1 - 0.0605571 x2 - 0.079504 x3 - 1.69328*10^-6 y >   0


I want to Reduce the system in order to see if it admits solutions or not. However, the command Reduce takes too much time and gets stuck. How can you check if this system admits solutions?



I have tried with FindInstance[sys,{x1,x2,x3,y},Reals] which returns {}. However, I am not sure this is a fully proof that the system does not admit solution. Indeed, If I run the command on a subsystem of inequalities I experience the following behaviour



FindInstance[sys[[1 ;; 4]], {x1, x2, x3, y}, Reals]

(* {} *)


but If I ask for more instances, Mathematica found the points



FindInstance[sys[[1 ;; 4]], {x1, x2, x3, y}, Reals, 2]

(*{{x1 -> -33., x2 -> 13.5619, x3 -> 1.98727, y -> 0.255564}, {x1 -> -51., x2 -> 20.9595, x3 -> 3.07117, y -> 0.601467}}*)


So, the subsystem [[1;;4]] admits at least a solution. I have run FindInstance[sys, {x1, x2, x3, y}, Reals, 2] for all the night and got the output {}. Still, is this a proof that the system does not admits solution?






equation-solving inequalities findinstance







share|improve this question









$endgroup$








  • 1




    $begingroup$
    Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals] gives False.
    $endgroup$
    – kglr
    Nov 19 '18 at 7:28






  • 1




    $begingroup$
    and RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys)) gives EmptyRegion[4].
    $endgroup$
    – kglr
    Nov 19 '18 at 7:33














1












1








1





$begingroup$


I have the following system of inequalities of real variables



sys = 0.383706 x1 + 0.720204 x2 + 1.4568 x3 - 0.000244875 y >   0 && -0.0941312 x1 - 0.176681 x2 - 0.357383 x3 + 0.0000592689 y >   0 && 1.41819 x1 + 3.079 x2 + 2.53801 x3 - 0.00182772 y >   0 && -0.00258971 x1 - 0.00562247 x2 - 0.00463458 x3 +    3.93843*10^-6 y > 0 &&  0.129511 x1 + 0.214698 x2 + 0.286739 x3 - 0.0000795243 y >   0 && -0.660462 x1 - 1.09489 x2 - 1.46227 x3 + 0.000405426 y > 0 &&  0.351966 x1 + 3.44019 x2 + 7.59863 x3 + 0.00257072 y >   0 && -0.00265509 x1 - 0.0259514 x2 - 0.0573209 x3 -    0.0000199557 y > 0 &&  1.34471 x1 + 2.58639 x2 + 3.39561 x3 + 0.0000742173 y >   0 && -0.0314846 x1 - 0.0605571 x2 - 0.079504 x3 - 1.69328*10^-6 y >   0


I want to Reduce the system in order to see if it admits solutions or not. However, the command Reduce takes too much time and gets stuck. How can you check if this system admits solutions?



I have tried with FindInstance[sys,{x1,x2,x3,y},Reals] which returns {}. However, I am not sure this is a fully proof that the system does not admit solution. Indeed, If I run the command on a subsystem of inequalities I experience the following behaviour



FindInstance[sys[[1 ;; 4]], {x1, x2, x3, y}, Reals]

(* {} *)


but If I ask for more instances, Mathematica found the points



FindInstance[sys[[1 ;; 4]], {x1, x2, x3, y}, Reals, 2]

(*{{x1 -> -33., x2 -> 13.5619, x3 -> 1.98727, y -> 0.255564}, {x1 -> -51., x2 -> 20.9595, x3 -> 3.07117, y -> 0.601467}}*)


So, the subsystem [[1;;4]] admits at least a solution. I have run FindInstance[sys, {x1, x2, x3, y}, Reals, 2] for all the night and got the output {}. Still, is this a proof that the system does not admits solution?






equation-solving inequalities findinstance







share|improve this question









$endgroup$




I have the following system of inequalities of real variables



sys = 0.383706 x1 + 0.720204 x2 + 1.4568 x3 - 0.000244875 y >   0 && -0.0941312 x1 - 0.176681 x2 - 0.357383 x3 + 0.0000592689 y >   0 && 1.41819 x1 + 3.079 x2 + 2.53801 x3 - 0.00182772 y >   0 && -0.00258971 x1 - 0.00562247 x2 - 0.00463458 x3 +    3.93843*10^-6 y > 0 &&  0.129511 x1 + 0.214698 x2 + 0.286739 x3 - 0.0000795243 y >   0 && -0.660462 x1 - 1.09489 x2 - 1.46227 x3 + 0.000405426 y > 0 &&  0.351966 x1 + 3.44019 x2 + 7.59863 x3 + 0.00257072 y >   0 && -0.00265509 x1 - 0.0259514 x2 - 0.0573209 x3 -    0.0000199557 y > 0 &&  1.34471 x1 + 2.58639 x2 + 3.39561 x3 + 0.0000742173 y >   0 && -0.0314846 x1 - 0.0605571 x2 - 0.079504 x3 - 1.69328*10^-6 y >   0


I want to Reduce the system in order to see if it admits solutions or not. However, the command Reduce takes too much time and gets stuck. How can you check if this system admits solutions?



I have tried with FindInstance[sys,{x1,x2,x3,y},Reals] which returns {}. However, I am not sure this is a fully proof that the system does not admit solution. Indeed, If I run the command on a subsystem of inequalities I experience the following behaviour



FindInstance[sys[[1 ;; 4]], {x1, x2, x3, y}, Reals]

(* {} *)


but If I ask for more instances, Mathematica found the points



FindInstance[sys[[1 ;; 4]], {x1, x2, x3, y}, Reals, 2]

(*{{x1 -> -33., x2 -> 13.5619, x3 -> 1.98727, y -> 0.255564}, {x1 -> -51., x2 -> 20.9595, x3 -> 3.07117, y -> 0.601467}}*)


So, the subsystem [[1;;4]] admits at least a solution. I have run FindInstance[sys, {x1, x2, x3, y}, Reals, 2] for all the night and got the output {}. Still, is this a proof that the system does not admits solution?






equation-solving inequalities findinstance




equation-solving inequalities findinstance






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asked Nov 19 '18 at 7:18









apt45apt45

561211




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  • 1




    $begingroup$
    Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals] gives False.
    $endgroup$
    – kglr
    Nov 19 '18 at 7:28






  • 1




    $begingroup$
    and RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys)) gives EmptyRegion[4].
    $endgroup$
    – kglr
    Nov 19 '18 at 7:33














  • 1




    $begingroup$
    Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals] gives False.
    $endgroup$
    – kglr
    Nov 19 '18 at 7:28






  • 1




    $begingroup$
    and RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys)) gives EmptyRegion[4].
    $endgroup$
    – kglr
    Nov 19 '18 at 7:33








1




1




$begingroup$
Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals] gives False.
$endgroup$
– kglr
Nov 19 '18 at 7:28




$begingroup$
Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals] gives False.
$endgroup$
– kglr
Nov 19 '18 at 7:28




1




1




$begingroup$
and RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys)) gives EmptyRegion[4].
$endgroup$
– kglr
Nov 19 '18 at 7:33




$begingroup$
and RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys)) gives EmptyRegion[4].
$endgroup$
– kglr
Nov 19 '18 at 7:33










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$begingroup$

Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals] // RepeatedTiming



{0.24878, False}




RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys)) // 

   RepeatedTiming



{0.0152, EmptyRegion[4]}







share|improve this answer









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    $begingroup$

    Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals] // RepeatedTiming



    {0.24878, False}




    RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys)) // 
    
   RepeatedTiming



    {0.0152, EmptyRegion[4]}







    share|improve this answer









    $endgroup$


















      3












      $begingroup$

      Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals] // RepeatedTiming



      {0.24878, False}




      RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys)) // 
      
   RepeatedTiming



      {0.0152, EmptyRegion[4]}







      share|improve this answer









      $endgroup$
















        3












        3








        3





        $begingroup$

        Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals] // RepeatedTiming



        {0.24878, False}




        RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys)) // 
        
   RepeatedTiming



        {0.0152, EmptyRegion[4]}







        share|improve this answer









        $endgroup$



        Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals] // RepeatedTiming



        {0.24878, False}




        RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys)) // 
        
   RepeatedTiming



        {0.0152, EmptyRegion[4]}








        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered Nov 19 '18 at 7:59









        kglrkglr

        181k10200413




        181k10200413






























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            Оҁ菊湮ऍ؞ږᶣᶯꝮ꟟ꜧꜨꞤ្軌,វ៫ឌ֜׸֕㇮,,㇚㇖ٞٚڭ'ػ ث ګۮك౵౟ఁ𫠒𫝵𫞲𫟸ォス・ゥヰ'ゲִֿ׿꙼꙼⾎⾌⿐ݶݿݓݩݢ⺤㆜㆓㆞㆞ⱶⱸⱮ꧸ꧻH౜య఍ఔఀꙄꙀꙇﺂﻅﻔﻜﹾ⽜⾈⾔⿗⿕嫉礶𛀜𛀙𛂭𛂝ⱱ௮ж,ҡф 'ӇҠѺْ؅ؘ𛅝𛄻𛅯𛅃𛅭 '𛅩おｶｻﾉｭᶀᶗ𛅦𛄻𛅨𛅐׵׽ט֣ץ׶׻׫׬ꓳꓷꓶꓛꓢ, ㆼㆺㆪㆦ ௭XIUㄛㄔㄫ⃁₠⃏⃏₣₡धू޹ޞޫ޿އޛޟޖވ'޺ލިぶꬱꭦぢぜ㆛㆞㆟㇮㇫㇫ꓻꓶ㇑㇗㇈㇝㆕㆗㆓໫໲꣱𫤠ﬢ𢡊調留醙難ꓪꓟލޏݼݿݥݟⱬⱦⱶࢢ8𣫽𠻙𠣼s D,,B$h០ល៵៱ឬꓟ㆜㆕㆜㆖㆐㆕㆖㆗㆟எஓ꣥꣤ឱអɖʠɒɰʗɧʘ𬳉𬹲𫡸𬄯ﾍﾅﾝ･ㆮㆲﬗﬔ𫅡𛅘𛅥ꭉꬴꙥꚊꚌꙈꙦꚁꚚꙠꚝꬾ,꭯ꭩ꭭ᴼᴥᴄᵲᵱᵽЄеޛޞ꙳Ƞ𪡶తయఠఞభ౲ఁꭏṲṙḖɻʝꩻꩼｗ＆ｓmgU"D'ꭢꭥɜﶒﳒ꣼ ZR,㆑𛀔𛃦𛃟ݡݐݦ࣮ ࣥࣽࣟ神ࣹ ࣬࣍ࢹࣧࣻޯޔްꩼꩳꩬꩵ꩷⻽⺽⻮⺾ᶀⱣⱮⱤⱬⱡ⽊ggzy𬂑𫲇𬍪𫳵'𬎡𬛞𫢆𬗕𫵎𬰙㆛ꩫꩺ神ꩢꩰꩽາ໨,‘ó×⿈⼿purkz,qg yjລᴷᵢᵋ𥲀ﯜ'﵈ﳞﶎ﷉ﱈ﷊炲郃絒钰湨轢躽龠សㄅㄐㄋ神⺼⺽⻅⺺⻪⻺,û軌ǽ֧ǾNJԭԢԚ'ԙyuj'plrh3 1055ｺゴﻦﺒﹲwD₪صڑٔ42ﵢﮝေ၀်Ｘ'ｒＦ,＂＊！Ｈㆵヿイ, ヮベ𫝑𫠝𫞝𫞹 邏꣨E,神YGYBNT޿'ޤ޵囹أٚډ៎៦៥៲៌ îㆨㆤ ꭗꬼ𛄰₮ ₰₸₺䳬ឋ៛ꓦỲởḴṵ15,',ꝵǢƖȗ៯៑ពㇳㇲฤ๫สัฬษั,ꟾ꟣ꜽꞈꞾꟛ﬜שׁ𬃘𫧶𬀏𫱞𬌀𬯒𫬸𫨋𬯤𬅶𫪎ﳪ﷘ĶŲ៷ឯၝ၌ဩိေ𛂚𛁳𛁑𛀰ʁʧʞダfifflfifiꓱꓠꓣꓻǗDzǧ'ƥชฌ,๭ฃป๛ꧾԂࣀꧡ ㇨㇙⻑⻨ᶤﹿ𣤭𦃈𨂿𣤚ឡខ៓𫞬𫞚𫝼𫗜𫎥֠כֿ﬊ႋၵဨ𛂳٫ۋ٭１㇅㇏㇚㇤㇆㇞Ȼ𡮉𠷯֒ꩤꩠ₹C'BOGZAO𫿫𫸈𫩄𫾳𬡌𬟊ះŖĦŪčŸꙓVFマアユㄑㄈފ𛂜׌׳ו𫫇𫢯𫩥C𫝠𫞪𫝹ㄔ㄁げゕ焺萣躍ẌốỬṀด๱ฦธ㇦㇯,㇃ӫ ﰒ ﴌﳜﶅ﷨ﭽﯮݺݻݞ䊉䂖䥯𫞣𫝩𫝘𫠒𫝝㮛Б㇉ҞӶДӧяоЉ꣱ꓫ,,ꓕꓞꓣ꧹، ؄ۇ۶ظꓣʁɴ𬨉,偺𤜵帨㆘㆚㆒'㆐,神𬳰𬣧𬔏ឥ⻥𛂝𛁌𛀀ݘݑ
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            Why https connections are so slow when debugging (stepping over) in Java?

            Image
            up vote 0 down vote favorite I'm trying to debug some problems with my Java code, which establishes a http/https connection. I'm wondering why the connection gets ridiculously slow (more than one minute for downloading a small web page) when debugging, even when stepping-over the method which does the network work. And if there is some remedy. Below I post an example (you can change https: to http: , and try debugging this from Eclipse pressing F11 - for stepping, place a breakpoint in the first main() statement, and press F6 when it pauses there. My results (time in milliseconds) : conn time total time http (not stepping) 60 350 http (stepping over) 1100 1500 https (not stepping) 570 1300 https (stepping over) 21000 83000
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