Simplify and Sign working only in small expressions












3












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I'm trying to find the sign of some very long expressions, but I don't seem to make it work using Simplify[Sign[...], Assumptions ...]. Here is an example of my problem. I can easily find the sign of these two expressions:



exp1 = θA1^2 θAU (16 θB1^3 (1 - λ)^4 + 

 64 θB1^2 θBU (1 - λ)^3 (1 + λ) + 

 5 θBU^3 (1 - λ) (1 + λ)^3 + 

 54 θB1 θBU^2 (1 - λ^2)^2);

 Simplify[Sign[8 (exp1)] , 

   Assumptions -> {(1 - λ) > 0, θA1 > 0, θAU > 0, θB1 > 0, θBU > 0, λ > 0}]


This expression correctly calculates as 1. A second expression:



exp2 = θA1 θAU^2 (16 θB1^3 (1 - λ)^3 (1 + λ) +  44 θB1 θBU^2 (1 - λ) (1 + λ)^3 + 

 5 θBU^3 (1 + λ)^4 +  54 θB1^2 θBU (1 - λ^2)^2);

Simplify[Sign[8 (exp2)] ,  

  Assumptions -> {(1 - λ) > 0, θA1 > 0, θAU >     0, θB1 > 0, θBU > 0, λ > 0}]


Correctly calculates as 1 too. BUT when I try:



Simplify[Sign[8 (exp1 + exp2)] ,  

  Assumptions -> {(1 - λ) > 0, θA1 > 0, θAU >    0, θB1 > 0, θBU > 0, λ > 0}]


Then Mathematica cannot compute... Any ideas on what may be going on here?






simplifying-expressions







share|improve this question











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    3












    $begingroup$


    I'm trying to find the sign of some very long expressions, but I don't seem to make it work using Simplify[Sign[...], Assumptions ...]. Here is an example of my problem. I can easily find the sign of these two expressions:



    exp1 = θA1^2 θAU (16 θB1^3 (1 - λ)^4 + 
    
 64 θB1^2 θBU (1 - λ)^3 (1 + λ) + 
    
 5 θBU^3 (1 - λ) (1 + λ)^3 + 
    
 54 θB1 θBU^2 (1 - λ^2)^2);
    
 Simplify[Sign[8 (exp1)] , 
    
   Assumptions -> {(1 - λ) > 0, θA1 > 0, θAU > 0, θB1 > 0, θBU > 0, λ > 0}]


    This expression correctly calculates as 1. A second expression:



    exp2 = θA1 θAU^2 (16 θB1^3 (1 - λ)^3 (1 + λ) +  44 θB1 θBU^2 (1 - λ) (1 + λ)^3 + 
    
 5 θBU^3 (1 + λ)^4 +  54 θB1^2 θBU (1 - λ^2)^2);
    
Simplify[Sign[8 (exp2)] ,  
    
  Assumptions -> {(1 - λ) > 0, θA1 > 0, θAU >     0, θB1 > 0, θBU > 0, λ > 0}]


    Correctly calculates as 1 too. BUT when I try:



    Simplify[Sign[8 (exp1 + exp2)] ,  
    
  Assumptions -> {(1 - λ) > 0, θA1 > 0, θAU >    0, θB1 > 0, θBU > 0, λ > 0}]


    Then Mathematica cannot compute... Any ideas on what may be going on here?






    simplifying-expressions







    share|improve this question











    $endgroup$















      3












      3








      3





      $begingroup$


      I'm trying to find the sign of some very long expressions, but I don't seem to make it work using Simplify[Sign[...], Assumptions ...]. Here is an example of my problem. I can easily find the sign of these two expressions:



      exp1 = θA1^2 θAU (16 θB1^3 (1 - λ)^4 + 
      
 64 θB1^2 θBU (1 - λ)^3 (1 + λ) + 
      
 5 θBU^3 (1 - λ) (1 + λ)^3 + 
      
 54 θB1 θBU^2 (1 - λ^2)^2);
      
 Simplify[Sign[8 (exp1)] , 
      
   Assumptions -> {(1 - λ) > 0, θA1 > 0, θAU > 0, θB1 > 0, θBU > 0, λ > 0}]


      This expression correctly calculates as 1. A second expression:



      exp2 = θA1 θAU^2 (16 θB1^3 (1 - λ)^3 (1 + λ) +  44 θB1 θBU^2 (1 - λ) (1 + λ)^3 + 
      
 5 θBU^3 (1 + λ)^4 +  54 θB1^2 θBU (1 - λ^2)^2);
      
Simplify[Sign[8 (exp2)] ,  
      
  Assumptions -> {(1 - λ) > 0, θA1 > 0, θAU >     0, θB1 > 0, θBU > 0, λ > 0}]


      Correctly calculates as 1 too. BUT when I try:



      Simplify[Sign[8 (exp1 + exp2)] ,  
      
  Assumptions -> {(1 - λ) > 0, θA1 > 0, θAU >    0, θB1 > 0, θBU > 0, λ > 0}]


      Then Mathematica cannot compute... Any ideas on what may be going on here?






      simplifying-expressions







      share|improve this question











      $endgroup$




      I'm trying to find the sign of some very long expressions, but I don't seem to make it work using Simplify[Sign[...], Assumptions ...]. Here is an example of my problem. I can easily find the sign of these two expressions:



      exp1 = θA1^2 θAU (16 θB1^3 (1 - λ)^4 + 
      
 64 θB1^2 θBU (1 - λ)^3 (1 + λ) + 
      
 5 θBU^3 (1 - λ) (1 + λ)^3 + 
      
 54 θB1 θBU^2 (1 - λ^2)^2);
      
 Simplify[Sign[8 (exp1)] , 
      
   Assumptions -> {(1 - λ) > 0, θA1 > 0, θAU > 0, θB1 > 0, θBU > 0, λ > 0}]


      This expression correctly calculates as 1. A second expression:



      exp2 = θA1 θAU^2 (16 θB1^3 (1 - λ)^3 (1 + λ) +  44 θB1 θBU^2 (1 - λ) (1 + λ)^3 + 
      
 5 θBU^3 (1 + λ)^4 +  54 θB1^2 θBU (1 - λ^2)^2);
      
Simplify[Sign[8 (exp2)] ,  
      
  Assumptions -> {(1 - λ) > 0, θA1 > 0, θAU >     0, θB1 > 0, θBU > 0, λ > 0}]


      Correctly calculates as 1 too. BUT when I try:



      Simplify[Sign[8 (exp1 + exp2)] ,  
      
  Assumptions -> {(1 - λ) > 0, θA1 > 0, θAU >    0, θB1 > 0, θBU > 0, λ > 0}]


      Then Mathematica cannot compute... Any ideas on what may be going on here?






      simplifying-expressions




      simplifying-expressions






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited Nov 18 '18 at 18:51









      kglr

      181k9200413




      181k9200413










      asked Nov 18 '18 at 18:40









      NinjaCowAndForksNinjaCowAndForks

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          1 Answer
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          5












          $begingroup$

          You need to increase the value of the suboption "AssumptionsMaxNonlinearVariables" to a value higher than its default value (4):



          SystemOptions["SimplificationOptions"]



          {"SimplificationOptions" -> {"AssumptionsMaxExponent" -> 25,
          "AssumptionsMaxNonlinearVariables" -> 4,
          "AssumptionsMaxVariables" -> 21, "AutosimplifyTrigs" -> True,
          "AutosimplifyTwoArgumentLog" -> True,
          "ConvertTrigsToRadicals" -> False, "FiniteSumMaxTerms" -> 30,
          "FunctionExpandMaxSteps" -> 15, "ListableFirst" -> True,
          "RestartELProver" -> False, "SimplifyMaxExponents" -> 100,
          "SimplifyToPiecewise" -> True}}




          Set the value of the suboption "AssumptionsMaxNonlinearVariables" to a higher value (say, 10):



          SetSystemOptions["SimplificationOptions" -> {"AssumptionsMaxNonlinearVariables" -> 10}];
          
Simplify[Sign[8 (exp1 + exp2)], 
          
   Assumptions -> {(1 - λ) > 0, θA1 > 0, θAU > 0, θB1 > 0, θBU > 0, λ > 0}]



          1




          Reset the suboption value to its default:



          SetSystemOptions["SimplificationOptions" -> {"AssumptionsMaxNonlinearVariables" ->  4}];





          share|improve this answer











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            1 Answer
            1






            active

            oldest

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            active

            oldest

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            active

            oldest

            votes









            5












            $begingroup$

            You need to increase the value of the suboption "AssumptionsMaxNonlinearVariables" to a value higher than its default value (4):



            SystemOptions["SimplificationOptions"]



            {"SimplificationOptions" -> {"AssumptionsMaxExponent" -> 25,
            "AssumptionsMaxNonlinearVariables" -> 4,
            "AssumptionsMaxVariables" -> 21, "AutosimplifyTrigs" -> True,
            "AutosimplifyTwoArgumentLog" -> True,
            "ConvertTrigsToRadicals" -> False, "FiniteSumMaxTerms" -> 30,
            "FunctionExpandMaxSteps" -> 15, "ListableFirst" -> True,
            "RestartELProver" -> False, "SimplifyMaxExponents" -> 100,
            "SimplifyToPiecewise" -> True}}




            Set the value of the suboption "AssumptionsMaxNonlinearVariables" to a higher value (say, 10):



            SetSystemOptions["SimplificationOptions" -> {"AssumptionsMaxNonlinearVariables" -> 10}];
            
Simplify[Sign[8 (exp1 + exp2)], 
            
   Assumptions -> {(1 - λ) > 0, θA1 > 0, θAU > 0, θB1 > 0, θBU > 0, λ > 0}]



            1




            Reset the suboption value to its default:



            SetSystemOptions["SimplificationOptions" -> {"AssumptionsMaxNonlinearVariables" ->  4}];





            share|improve this answer











            $endgroup$


















              5












              $begingroup$

              You need to increase the value of the suboption "AssumptionsMaxNonlinearVariables" to a value higher than its default value (4):



              SystemOptions["SimplificationOptions"]



              {"SimplificationOptions" -> {"AssumptionsMaxExponent" -> 25,
              "AssumptionsMaxNonlinearVariables" -> 4,
              "AssumptionsMaxVariables" -> 21, "AutosimplifyTrigs" -> True,
              "AutosimplifyTwoArgumentLog" -> True,
              "ConvertTrigsToRadicals" -> False, "FiniteSumMaxTerms" -> 30,
              "FunctionExpandMaxSteps" -> 15, "ListableFirst" -> True,
              "RestartELProver" -> False, "SimplifyMaxExponents" -> 100,
              "SimplifyToPiecewise" -> True}}




              Set the value of the suboption "AssumptionsMaxNonlinearVariables" to a higher value (say, 10):



              SetSystemOptions["SimplificationOptions" -> {"AssumptionsMaxNonlinearVariables" -> 10}];
              
Simplify[Sign[8 (exp1 + exp2)], 
              
   Assumptions -> {(1 - λ) > 0, θA1 > 0, θAU > 0, θB1 > 0, θBU > 0, λ > 0}]



              1




              Reset the suboption value to its default:



              SetSystemOptions["SimplificationOptions" -> {"AssumptionsMaxNonlinearVariables" ->  4}];





              share|improve this answer











              $endgroup$
















                5












                5








                5





                $begingroup$

                You need to increase the value of the suboption "AssumptionsMaxNonlinearVariables" to a value higher than its default value (4):



                SystemOptions["SimplificationOptions"]



                {"SimplificationOptions" -> {"AssumptionsMaxExponent" -> 25,
                "AssumptionsMaxNonlinearVariables" -> 4,
                "AssumptionsMaxVariables" -> 21, "AutosimplifyTrigs" -> True,
                "AutosimplifyTwoArgumentLog" -> True,
                "ConvertTrigsToRadicals" -> False, "FiniteSumMaxTerms" -> 30,
                "FunctionExpandMaxSteps" -> 15, "ListableFirst" -> True,
                "RestartELProver" -> False, "SimplifyMaxExponents" -> 100,
                "SimplifyToPiecewise" -> True}}




                Set the value of the suboption "AssumptionsMaxNonlinearVariables" to a higher value (say, 10):



                SetSystemOptions["SimplificationOptions" -> {"AssumptionsMaxNonlinearVariables" -> 10}];
                
Simplify[Sign[8 (exp1 + exp2)], 
                
   Assumptions -> {(1 - λ) > 0, θA1 > 0, θAU > 0, θB1 > 0, θBU > 0, λ > 0}]



                1




                Reset the suboption value to its default:



                SetSystemOptions["SimplificationOptions" -> {"AssumptionsMaxNonlinearVariables" ->  4}];





                share|improve this answer











                $endgroup$



                You need to increase the value of the suboption "AssumptionsMaxNonlinearVariables" to a value higher than its default value (4):



                SystemOptions["SimplificationOptions"]



                {"SimplificationOptions" -> {"AssumptionsMaxExponent" -> 25,
                "AssumptionsMaxNonlinearVariables" -> 4,
                "AssumptionsMaxVariables" -> 21, "AutosimplifyTrigs" -> True,
                "AutosimplifyTwoArgumentLog" -> True,
                "ConvertTrigsToRadicals" -> False, "FiniteSumMaxTerms" -> 30,
                "FunctionExpandMaxSteps" -> 15, "ListableFirst" -> True,
                "RestartELProver" -> False, "SimplifyMaxExponents" -> 100,
                "SimplifyToPiecewise" -> True}}




                Set the value of the suboption "AssumptionsMaxNonlinearVariables" to a higher value (say, 10):



                SetSystemOptions["SimplificationOptions" -> {"AssumptionsMaxNonlinearVariables" -> 10}];
                
Simplify[Sign[8 (exp1 + exp2)], 
                
   Assumptions -> {(1 - λ) > 0, θA1 > 0, θAU > 0, θB1 > 0, θBU > 0, λ > 0}]



                1




                Reset the suboption value to its default:



                SetSystemOptions["SimplificationOptions" -> {"AssumptionsMaxNonlinearVariables" ->  4}];






                share|improve this answer














                share|improve this answer



                share|improve this answer








                edited Nov 18 '18 at 19:00

























                answered Nov 18 '18 at 18:50









                kglrkglr

                181k9200413




                181k9200413






























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