Sort with assumptions












6












$begingroup$


I have a list which looks like this



list = {0, Subscript[x,7], -Subscript[x,3]-Subscript[x,9], -Subscript[x,9]};



and all the $x_i$'s are positive semidefinite (i.e. nonnegative) real numbers. I would like to be able to sort this into



sortedlist = {-Subscript[x,3]-Subscript[x,9], -Subscript[x,9], 0, Subscript[x,7]}



How do I achieve this? I tried



Assuming[Subscript[x,3] > 0 && Subscript[x,7] > 0 && Subscript[x,9] > 0, Sort[list]]



But this obviously does not work. In general, I'd like to be able to impose more constraints on the $x_i's$ when they're being sorted.






list-manipulation symbolic array sorting







share|improve this question









$endgroup$








  • 1




    $begingroup$
    An interesting idea, but a symbolic list where you have an ordering for all the elements is rare
    $endgroup$
    – mikado
    yesterday
















6












$begingroup$


I have a list which looks like this



list = {0, Subscript[x,7], -Subscript[x,3]-Subscript[x,9], -Subscript[x,9]};



and all the $x_i$'s are positive semidefinite (i.e. nonnegative) real numbers. I would like to be able to sort this into



sortedlist = {-Subscript[x,3]-Subscript[x,9], -Subscript[x,9], 0, Subscript[x,7]}



How do I achieve this? I tried



Assuming[Subscript[x,3] > 0 && Subscript[x,7] > 0 && Subscript[x,9] > 0, Sort[list]]



But this obviously does not work. In general, I'd like to be able to impose more constraints on the $x_i's$ when they're being sorted.






list-manipulation symbolic array sorting







share|improve this question









$endgroup$








  • 1




    $begingroup$
    An interesting idea, but a symbolic list where you have an ordering for all the elements is rare
    $endgroup$
    – mikado
    yesterday














6












6








6


3



$begingroup$


I have a list which looks like this



list = {0, Subscript[x,7], -Subscript[x,3]-Subscript[x,9], -Subscript[x,9]};



and all the $x_i$'s are positive semidefinite (i.e. nonnegative) real numbers. I would like to be able to sort this into



sortedlist = {-Subscript[x,3]-Subscript[x,9], -Subscript[x,9], 0, Subscript[x,7]}



How do I achieve this? I tried



Assuming[Subscript[x,3] > 0 && Subscript[x,7] > 0 && Subscript[x,9] > 0, Sort[list]]



But this obviously does not work. In general, I'd like to be able to impose more constraints on the $x_i's$ when they're being sorted.






list-manipulation symbolic array sorting







share|improve this question









$endgroup$




I have a list which looks like this



list = {0, Subscript[x,7], -Subscript[x,3]-Subscript[x,9], -Subscript[x,9]};



and all the $x_i$'s are positive semidefinite (i.e. nonnegative) real numbers. I would like to be able to sort this into



sortedlist = {-Subscript[x,3]-Subscript[x,9], -Subscript[x,9], 0, Subscript[x,7]}



How do I achieve this? I tried



Assuming[Subscript[x,3] > 0 && Subscript[x,7] > 0 && Subscript[x,9] > 0, Sort[list]]



But this obviously does not work. In general, I'd like to be able to impose more constraints on the $x_i's$ when they're being sorted.






list-manipulation symbolic array sorting




list-manipulation symbolic array sorting






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked yesterday









leastactionleastaction

244210




244210








  • 1




    $begingroup$
    An interesting idea, but a symbolic list where you have an ordering for all the elements is rare
    $endgroup$
    – mikado
    yesterday














  • 1




    $begingroup$
    An interesting idea, but a symbolic list where you have an ordering for all the elements is rare
    $endgroup$
    – mikado
    yesterday








1




1




$begingroup$
An interesting idea, but a symbolic list where you have an ordering for all the elements is rare
$endgroup$
– mikado
yesterday




$begingroup$
An interesting idea, but a symbolic list where you have an ordering for all the elements is rare
$endgroup$
– mikado
yesterday










4 Answers
4






active

oldest

votes


















5












$begingroup$

Here is a possibility:



sortWithAssumptions[list_, assum_] := Module[{order},

    order[a_, b_] := Simplify[a < b, assum];

    Sort[list, order]

]


For your example:



sortWithAssumptions[

    {0,Subscript[x,7],-Subscript[x,3]-Subscript[x,9],-Subscript[x,9]},

    Subscript[x,3]>0&&Subscript[x,7]>0&&Subscript[x,9]>0

] //TeXForm



$left{-x_3-x_9,-x_9,0,x_7right}$




Another example:



sortWithAssumptions[

    {0,Subscript[x,7],-Subscript[x,3]-Subscript[x,9],-Subscript[x,9], Subscript[x,9]},

    Subscript[x,3]>0&&Subscript[x,7]>0&&Subscript[x,9]>0&&Subscript[x,7]<Subscript[x,9]

] //TeXForm



$left{-x_3-x_9,-x_9,0,x_7,x_9right}$







share|improve this answer









$endgroup$













  • $begingroup$
    Thank you, Carl!
    $endgroup$
    – leastaction
    yesterday



















5












$begingroup$

How about:



list[[Ordering[list /. _Subscript -> 1]]]



{-Subscript[x, 3] - Subscript[x, 9], -Subscript[x, 9], 0, Subscript[x, 7]}




So basically we sort it the way it would be sorted with all subscripts == 1.






share|improve this answer









$endgroup$













  • $begingroup$
    Thanks! Seems to work like a charm, but can you shed some light on why?
    $endgroup$
    – leastaction
    yesterday










  • $begingroup$
    @leastaction just take a look at list /. _Subscript -> 1 and at Ordering[list /. _Subscript -> 1].
    $endgroup$
    – Kuba♦
    yesterday










  • $begingroup$
    I see, so you basically assigned the value $x_i = 1$ to each $x_i$. It works in this case, but generically, $x_i$'s may be different.
    $endgroup$
    – leastaction
    yesterday






  • 1




    $begingroup$
    @leastaction sure, which means there isn't only one correct answer and every valid within constraints is correct.
    $endgroup$
    – Kuba♦
    yesterday





















4












$begingroup$

Sort[list, TrueQ@Simplify[#1 < #2, _Subscript > 0] &]



(* Out: {-Subscript[x, 3] - Subscript[x, 9], -Subscript[x, 9], 0, Subscript[x, 7]} *)





share|improve this answer









$endgroup$





















    4












    $begingroup$

    In this case, we can use RankedMin and FullSimplify to get the answer you seek



    Assuming[
    
 Subscript[x, 3] > 0 && Subscript[x, 7] > 0 && Subscript[x, 9] > 0, 
    
 FullSimplify[Table[RankedMin[list, i], {i, 1, Length[list]}]]]
    
(* {-Subscript[x, 3] - Subscript[x, 9], -Subscript[x, 9], 0, Subscript[x, 7]} *)


    This has the advantage of not returning a (potentially) wrong answer if the sort order is uncertain.






    share|improve this answer











    $endgroup$













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      4 Answers
      4






      active

      oldest

      votes








      4 Answers
      4






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      5












      $begingroup$

      Here is a possibility:



      sortWithAssumptions[list_, assum_] := Module[{order},
      
    order[a_, b_] := Simplify[a < b, assum];
      
    Sort[list, order]
      
]


      For your example:



      sortWithAssumptions[
      
    {0,Subscript[x,7],-Subscript[x,3]-Subscript[x,9],-Subscript[x,9]},
      
    Subscript[x,3]>0&&Subscript[x,7]>0&&Subscript[x,9]>0
      
] //TeXForm



      $left{-x_3-x_9,-x_9,0,x_7right}$




      Another example:



      sortWithAssumptions[
      
    {0,Subscript[x,7],-Subscript[x,3]-Subscript[x,9],-Subscript[x,9], Subscript[x,9]},
      
    Subscript[x,3]>0&&Subscript[x,7]>0&&Subscript[x,9]>0&&Subscript[x,7]<Subscript[x,9]
      
] //TeXForm



      $left{-x_3-x_9,-x_9,0,x_7,x_9right}$







      share|improve this answer









      $endgroup$













      • $begingroup$
        Thank you, Carl!
        $endgroup$
        – leastaction
        yesterday
















      5












      $begingroup$

      Here is a possibility:



      sortWithAssumptions[list_, assum_] := Module[{order},
      
    order[a_, b_] := Simplify[a < b, assum];
      
    Sort[list, order]
      
]


      For your example:



      sortWithAssumptions[
      
    {0,Subscript[x,7],-Subscript[x,3]-Subscript[x,9],-Subscript[x,9]},
      
    Subscript[x,3]>0&&Subscript[x,7]>0&&Subscript[x,9]>0
      
] //TeXForm



      $left{-x_3-x_9,-x_9,0,x_7right}$




      Another example:



      sortWithAssumptions[
      
    {0,Subscript[x,7],-Subscript[x,3]-Subscript[x,9],-Subscript[x,9], Subscript[x,9]},
      
    Subscript[x,3]>0&&Subscript[x,7]>0&&Subscript[x,9]>0&&Subscript[x,7]<Subscript[x,9]
      
] //TeXForm



      $left{-x_3-x_9,-x_9,0,x_7,x_9right}$







      share|improve this answer









      $endgroup$













      • $begingroup$
        Thank you, Carl!
        $endgroup$
        – leastaction
        yesterday














      5












      5








      5





      $begingroup$

      Here is a possibility:



      sortWithAssumptions[list_, assum_] := Module[{order},
      
    order[a_, b_] := Simplify[a < b, assum];
      
    Sort[list, order]
      
]


      For your example:



      sortWithAssumptions[
      
    {0,Subscript[x,7],-Subscript[x,3]-Subscript[x,9],-Subscript[x,9]},
      
    Subscript[x,3]>0&&Subscript[x,7]>0&&Subscript[x,9]>0
      
] //TeXForm



      $left{-x_3-x_9,-x_9,0,x_7right}$




      Another example:



      sortWithAssumptions[
      
    {0,Subscript[x,7],-Subscript[x,3]-Subscript[x,9],-Subscript[x,9], Subscript[x,9]},
      
    Subscript[x,3]>0&&Subscript[x,7]>0&&Subscript[x,9]>0&&Subscript[x,7]<Subscript[x,9]
      
] //TeXForm



      $left{-x_3-x_9,-x_9,0,x_7,x_9right}$







      share|improve this answer









      $endgroup$



      Here is a possibility:



      sortWithAssumptions[list_, assum_] := Module[{order},
      
    order[a_, b_] := Simplify[a < b, assum];
      
    Sort[list, order]
      
]


      For your example:



      sortWithAssumptions[
      
    {0,Subscript[x,7],-Subscript[x,3]-Subscript[x,9],-Subscript[x,9]},
      
    Subscript[x,3]>0&&Subscript[x,7]>0&&Subscript[x,9]>0
      
] //TeXForm



      $left{-x_3-x_9,-x_9,0,x_7right}$




      Another example:



      sortWithAssumptions[
      
    {0,Subscript[x,7],-Subscript[x,3]-Subscript[x,9],-Subscript[x,9], Subscript[x,9]},
      
    Subscript[x,3]>0&&Subscript[x,7]>0&&Subscript[x,9]>0&&Subscript[x,7]<Subscript[x,9]
      
] //TeXForm



      $left{-x_3-x_9,-x_9,0,x_7,x_9right}$








      share|improve this answer












      share|improve this answer



      share|improve this answer










      answered yesterday









      Carl WollCarl Woll

      70.9k394185




      70.9k394185












      • $begingroup$
        Thank you, Carl!
        $endgroup$
        – leastaction
        yesterday


















      • $begingroup$
        Thank you, Carl!
        $endgroup$
        – leastaction
        yesterday
















      $begingroup$
      Thank you, Carl!
      $endgroup$
      – leastaction
      yesterday




      $begingroup$
      Thank you, Carl!
      $endgroup$
      – leastaction
      yesterday











      5












      $begingroup$

      How about:



      list[[Ordering[list /. _Subscript -> 1]]]



      {-Subscript[x, 3] - Subscript[x, 9], -Subscript[x, 9], 0, Subscript[x, 7]}




      So basically we sort it the way it would be sorted with all subscripts == 1.






      share|improve this answer









      $endgroup$













      • $begingroup$
        Thanks! Seems to work like a charm, but can you shed some light on why?
        $endgroup$
        – leastaction
        yesterday










      • $begingroup$
        @leastaction just take a look at list /. _Subscript -> 1 and at Ordering[list /. _Subscript -> 1].
        $endgroup$
        – Kuba♦
        yesterday










      • $begingroup$
        I see, so you basically assigned the value $x_i = 1$ to each $x_i$. It works in this case, but generically, $x_i$'s may be different.
        $endgroup$
        – leastaction
        yesterday






      • 1




        $begingroup$
        @leastaction sure, which means there isn't only one correct answer and every valid within constraints is correct.
        $endgroup$
        – Kuba♦
        yesterday


















      5












      $begingroup$

      How about:



      list[[Ordering[list /. _Subscript -> 1]]]



      {-Subscript[x, 3] - Subscript[x, 9], -Subscript[x, 9], 0, Subscript[x, 7]}




      So basically we sort it the way it would be sorted with all subscripts == 1.






      share|improve this answer









      $endgroup$













      • $begingroup$
        Thanks! Seems to work like a charm, but can you shed some light on why?
        $endgroup$
        – leastaction
        yesterday










      • $begingroup$
        @leastaction just take a look at list /. _Subscript -> 1 and at Ordering[list /. _Subscript -> 1].
        $endgroup$
        – Kuba♦
        yesterday










      • $begingroup$
        I see, so you basically assigned the value $x_i = 1$ to each $x_i$. It works in this case, but generically, $x_i$'s may be different.
        $endgroup$
        – leastaction
        yesterday






      • 1




        $begingroup$
        @leastaction sure, which means there isn't only one correct answer and every valid within constraints is correct.
        $endgroup$
        – Kuba♦
        yesterday
















      5












      5








      5





      $begingroup$

      How about:



      list[[Ordering[list /. _Subscript -> 1]]]



      {-Subscript[x, 3] - Subscript[x, 9], -Subscript[x, 9], 0, Subscript[x, 7]}




      So basically we sort it the way it would be sorted with all subscripts == 1.






      share|improve this answer









      $endgroup$



      How about:



      list[[Ordering[list /. _Subscript -> 1]]]



      {-Subscript[x, 3] - Subscript[x, 9], -Subscript[x, 9], 0, Subscript[x, 7]}




      So basically we sort it the way it would be sorted with all subscripts == 1.







      share|improve this answer












      share|improve this answer



      share|improve this answer










      answered yesterday









      Kuba♦Kuba

      107k12210530




      107k12210530












      • $begingroup$
        Thanks! Seems to work like a charm, but can you shed some light on why?
        $endgroup$
        – leastaction
        yesterday










      • $begingroup$
        @leastaction just take a look at list /. _Subscript -> 1 and at Ordering[list /. _Subscript -> 1].
        $endgroup$
        – Kuba♦
        yesterday










      • $begingroup$
        I see, so you basically assigned the value $x_i = 1$ to each $x_i$. It works in this case, but generically, $x_i$'s may be different.
        $endgroup$
        – leastaction
        yesterday






      • 1




        $begingroup$
        @leastaction sure, which means there isn't only one correct answer and every valid within constraints is correct.
        $endgroup$
        – Kuba♦
        yesterday




















      • $begingroup$
        Thanks! Seems to work like a charm, but can you shed some light on why?
        $endgroup$
        – leastaction
        yesterday










      • $begingroup$
        @leastaction just take a look at list /. _Subscript -> 1 and at Ordering[list /. _Subscript -> 1].
        $endgroup$
        – Kuba♦
        yesterday










      • $begingroup$
        I see, so you basically assigned the value $x_i = 1$ to each $x_i$. It works in this case, but generically, $x_i$'s may be different.
        $endgroup$
        – leastaction
        yesterday






      • 1




        $begingroup$
        @leastaction sure, which means there isn't only one correct answer and every valid within constraints is correct.
        $endgroup$
        – Kuba♦
        yesterday


















      $begingroup$
      Thanks! Seems to work like a charm, but can you shed some light on why?
      $endgroup$
      – leastaction
      yesterday




      $begingroup$
      Thanks! Seems to work like a charm, but can you shed some light on why?
      $endgroup$
      – leastaction
      yesterday












      $begingroup$
      @leastaction just take a look at list /. _Subscript -> 1 and at Ordering[list /. _Subscript -> 1].
      $endgroup$
      – Kuba♦
      yesterday




      $begingroup$
      @leastaction just take a look at list /. _Subscript -> 1 and at Ordering[list /. _Subscript -> 1].
      $endgroup$
      – Kuba♦
      yesterday












      $begingroup$
      I see, so you basically assigned the value $x_i = 1$ to each $x_i$. It works in this case, but generically, $x_i$'s may be different.
      $endgroup$
      – leastaction
      yesterday




      $begingroup$
      I see, so you basically assigned the value $x_i = 1$ to each $x_i$. It works in this case, but generically, $x_i$'s may be different.
      $endgroup$
      – leastaction
      yesterday




      1




      1




      $begingroup$
      @leastaction sure, which means there isn't only one correct answer and every valid within constraints is correct.
      $endgroup$
      – Kuba♦
      yesterday






      $begingroup$
      @leastaction sure, which means there isn't only one correct answer and every valid within constraints is correct.
      $endgroup$
      – Kuba♦
      yesterday













      4












      $begingroup$

      Sort[list, TrueQ@Simplify[#1 < #2, _Subscript > 0] &]
      

      
(* Out: {-Subscript[x, 3] - Subscript[x, 9], -Subscript[x, 9], 0, Subscript[x, 7]} *)





      share|improve this answer









      $endgroup$


















        4












        $begingroup$

        Sort[list, TrueQ@Simplify[#1 < #2, _Subscript > 0] &]
        

        
(* Out: {-Subscript[x, 3] - Subscript[x, 9], -Subscript[x, 9], 0, Subscript[x, 7]} *)





        share|improve this answer









        $endgroup$
















          4












          4








          4





          $begingroup$

          Sort[list, TrueQ@Simplify[#1 < #2, _Subscript > 0] &]
          

          
(* Out: {-Subscript[x, 3] - Subscript[x, 9], -Subscript[x, 9], 0, Subscript[x, 7]} *)





          share|improve this answer









          $endgroup$



          Sort[list, TrueQ@Simplify[#1 < #2, _Subscript > 0] &]
          

          
(* Out: {-Subscript[x, 3] - Subscript[x, 9], -Subscript[x, 9], 0, Subscript[x, 7]} *)






          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered yesterday









          MarcoBMarcoB

          37.7k556113




          37.7k556113























              4












              $begingroup$

              In this case, we can use RankedMin and FullSimplify to get the answer you seek



              Assuming[
              
 Subscript[x, 3] > 0 && Subscript[x, 7] > 0 && Subscript[x, 9] > 0, 
              
 FullSimplify[Table[RankedMin[list, i], {i, 1, Length[list]}]]]
              
(* {-Subscript[x, 3] - Subscript[x, 9], -Subscript[x, 9], 0, Subscript[x, 7]} *)


              This has the advantage of not returning a (potentially) wrong answer if the sort order is uncertain.






              share|improve this answer











              $endgroup$


















                4












                $begingroup$

                In this case, we can use RankedMin and FullSimplify to get the answer you seek



                Assuming[
                
 Subscript[x, 3] > 0 && Subscript[x, 7] > 0 && Subscript[x, 9] > 0, 
                
 FullSimplify[Table[RankedMin[list, i], {i, 1, Length[list]}]]]
                
(* {-Subscript[x, 3] - Subscript[x, 9], -Subscript[x, 9], 0, Subscript[x, 7]} *)


                This has the advantage of not returning a (potentially) wrong answer if the sort order is uncertain.






                share|improve this answer











                $endgroup$
















                  4












                  4








                  4





                  $begingroup$

                  In this case, we can use RankedMin and FullSimplify to get the answer you seek



                  Assuming[
                  
 Subscript[x, 3] > 0 && Subscript[x, 7] > 0 && Subscript[x, 9] > 0, 
                  
 FullSimplify[Table[RankedMin[list, i], {i, 1, Length[list]}]]]
                  
(* {-Subscript[x, 3] - Subscript[x, 9], -Subscript[x, 9], 0, Subscript[x, 7]} *)


                  This has the advantage of not returning a (potentially) wrong answer if the sort order is uncertain.






                  share|improve this answer











                  $endgroup$



                  In this case, we can use RankedMin and FullSimplify to get the answer you seek



                  Assuming[
                  
 Subscript[x, 3] > 0 && Subscript[x, 7] > 0 && Subscript[x, 9] > 0, 
                  
 FullSimplify[Table[RankedMin[list, i], {i, 1, Length[list]}]]]
                  
(* {-Subscript[x, 3] - Subscript[x, 9], -Subscript[x, 9], 0, Subscript[x, 7]} *)


                  This has the advantage of not returning a (potentially) wrong answer if the sort order is uncertain.







                  share|improve this answer














                  share|improve this answer



                  share|improve this answer








                  edited yesterday

























                  answered yesterday









                  mikadomikado

                  6,7171929




                  6,7171929






























                      draft saved

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