Taking the numerator and the denominator












6












$begingroup$


Is there any way to get the Numerator and the Denominator of an expression split in the same way that Mathematica graphically represents it.



Say I have an expression:



(a^(p1 + p2 - p3) b^(p1 - p2 + p3))/(c d)


When plugged into mathematica it gets represented with the $c$ and $d$ in the denominator but if I were to try to extract the numerator and denominator with respectively Numerator and Denominator I would not get the same split. I understand that a different (probably more sensible) choice of representation is made in Numerator and Denominator. However, is it possible to (automatically and reliably) take the denominator and numerator parts as split in the graphical representation? Mathematica must be able to determine this split since it has to decide how to graphically represent the output.






expression-manipulation







share|improve this question









$endgroup$

















    6












    $begingroup$


    Is there any way to get the Numerator and the Denominator of an expression split in the same way that Mathematica graphically represents it.



    Say I have an expression:



    (a^(p1 + p2 - p3) b^(p1 - p2 + p3))/(c d)


    When plugged into mathematica it gets represented with the $c$ and $d$ in the denominator but if I were to try to extract the numerator and denominator with respectively Numerator and Denominator I would not get the same split. I understand that a different (probably more sensible) choice of representation is made in Numerator and Denominator. However, is it possible to (automatically and reliably) take the denominator and numerator parts as split in the graphical representation? Mathematica must be able to determine this split since it has to decide how to graphically represent the output.






    expression-manipulation







    share|improve this question









    $endgroup$















      6












      6








      6





      $begingroup$


      Is there any way to get the Numerator and the Denominator of an expression split in the same way that Mathematica graphically represents it.



      Say I have an expression:



      (a^(p1 + p2 - p3) b^(p1 - p2 + p3))/(c d)


      When plugged into mathematica it gets represented with the $c$ and $d$ in the denominator but if I were to try to extract the numerator and denominator with respectively Numerator and Denominator I would not get the same split. I understand that a different (probably more sensible) choice of representation is made in Numerator and Denominator. However, is it possible to (automatically and reliably) take the denominator and numerator parts as split in the graphical representation? Mathematica must be able to determine this split since it has to decide how to graphically represent the output.






      expression-manipulation







      share|improve this question









      $endgroup$




      Is there any way to get the Numerator and the Denominator of an expression split in the same way that Mathematica graphically represents it.



      Say I have an expression:



      (a^(p1 + p2 - p3) b^(p1 - p2 + p3))/(c d)


      When plugged into mathematica it gets represented with the $c$ and $d$ in the denominator but if I were to try to extract the numerator and denominator with respectively Numerator and Denominator I would not get the same split. I understand that a different (probably more sensible) choice of representation is made in Numerator and Denominator. However, is it possible to (automatically and reliably) take the denominator and numerator parts as split in the graphical representation? Mathematica must be able to determine this split since it has to decide how to graphically represent the output.






      expression-manipulation




      expression-manipulation






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked yesterday









      KvotheKvothe

      926317




      926317






















          3 Answers
          3






          active

          oldest

          votes


















          7












          $begingroup$

          The problem is that the negative terms in the exponent are being included in the denominator. A way to workaround this is to inactivate Plus, use Numerator and Denominator, and reactivate:



          expr = (a^(p1+p2-p3) b^(p1-p2+p3))/(c d);
          

          
Activate @* Through @* {Numerator, Denominator} @* ReplaceAll[Plus->Inactive[Plus]] @ expr



          {a^(p1 + p2 - p3) b^(p1 - p2 + p3), c d}







          share|improve this answer









          $endgroup$





















            3












            $begingroup$

            So, for your particular expression (which is a single fraction), the following kluge works:



            expr = (a^(p1 + p2 - p3) b^(p1 - p2 + p3))/(c d);
            
ToExpression /@ List @@ ToBoxes@expr
            
(* {a^(p1 + p2 - p3) b^(p1 - p2 + p3), c d} *)


            This is a little tricky to automat, because you have to inspect the formatting expression that you get.




            This uses the visual formatting in the following way. ToBoxes converts the output to front-end formatting:



            ToBoxes@expr
            
(* FractionBox[
            
    RowBox[{SuperscriptBox["a", RowBox[{"p1", "+", "p2", "-", "p3"}]], " ", SuperscriptBox["b", RowBox[{"p1", "-", "p2", "+", "p3"}]]}],
            
    RowBox[{"c", " ", "d"}]
            
   ]  *)


            Then, noting that the numerator and the denominator are the first and second elements of the the FractionBox expression, we replace FractionBox with List using List@@, and then convert the remaining formatting expression to Mathematica input expressions using ToExpression.






            share|improve this answer









            $endgroup$





















              0












              $begingroup$

              Here is another option using TeXForm.



              expr = (a^(p1 + p2 - p3) b^(p1 - p2 + p3))/(c d);
              
t = ToString[TeXForm[expr]]
              

              
  (* frac{a^{text{p1}+text{p2}-text{p3}} b^{text{p1}-text{p2}+text{p3}}}{c d} *)


              Numerator:



              ToExpression[StringCases[t, RegularExpression["frac{(.+)}{(.+)}$"] -> "$1"][[1]], TeXForm]
              

              
  (* a^(p1 + p2 - p3) b^(p1 - p2 + p3) *)


              Denominator:



              ToExpression[StringCases[t, RegularExpression["frac{(.+)}{(.+)}$"] -> "$2"][[1]], TeXForm]
              

              
  (* cd *)





              share|improve this answer









              $endgroup$













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                3 Answers
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                active

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                active

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                7












                $begingroup$

                The problem is that the negative terms in the exponent are being included in the denominator. A way to workaround this is to inactivate Plus, use Numerator and Denominator, and reactivate:



                expr = (a^(p1+p2-p3) b^(p1-p2+p3))/(c d);
                

                
Activate @* Through @* {Numerator, Denominator} @* ReplaceAll[Plus->Inactive[Plus]] @ expr



                {a^(p1 + p2 - p3) b^(p1 - p2 + p3), c d}







                share|improve this answer









                $endgroup$


















                  7












                  $begingroup$

                  The problem is that the negative terms in the exponent are being included in the denominator. A way to workaround this is to inactivate Plus, use Numerator and Denominator, and reactivate:



                  expr = (a^(p1+p2-p3) b^(p1-p2+p3))/(c d);
                  

                  
Activate @* Through @* {Numerator, Denominator} @* ReplaceAll[Plus->Inactive[Plus]] @ expr



                  {a^(p1 + p2 - p3) b^(p1 - p2 + p3), c d}







                  share|improve this answer









                  $endgroup$
















                    7












                    7








                    7





                    $begingroup$

                    The problem is that the negative terms in the exponent are being included in the denominator. A way to workaround this is to inactivate Plus, use Numerator and Denominator, and reactivate:



                    expr = (a^(p1+p2-p3) b^(p1-p2+p3))/(c d);
                    

                    
Activate @* Through @* {Numerator, Denominator} @* ReplaceAll[Plus->Inactive[Plus]] @ expr



                    {a^(p1 + p2 - p3) b^(p1 - p2 + p3), c d}







                    share|improve this answer









                    $endgroup$



                    The problem is that the negative terms in the exponent are being included in the denominator. A way to workaround this is to inactivate Plus, use Numerator and Denominator, and reactivate:



                    expr = (a^(p1+p2-p3) b^(p1-p2+p3))/(c d);
                    

                    
Activate @* Through @* {Numerator, Denominator} @* ReplaceAll[Plus->Inactive[Plus]] @ expr



                    {a^(p1 + p2 - p3) b^(p1 - p2 + p3), c d}








                    share|improve this answer












                    share|improve this answer



                    share|improve this answer










                    answered yesterday









                    Carl WollCarl Woll

                    70.9k394184




                    70.9k394184























                        3












                        $begingroup$

                        So, for your particular expression (which is a single fraction), the following kluge works:



                        expr = (a^(p1 + p2 - p3) b^(p1 - p2 + p3))/(c d);
                        
ToExpression /@ List @@ ToBoxes@expr
                        
(* {a^(p1 + p2 - p3) b^(p1 - p2 + p3), c d} *)


                        This is a little tricky to automat, because you have to inspect the formatting expression that you get.




                        This uses the visual formatting in the following way. ToBoxes converts the output to front-end formatting:



                        ToBoxes@expr
                        
(* FractionBox[
                        
    RowBox[{SuperscriptBox["a", RowBox[{"p1", "+", "p2", "-", "p3"}]], " ", SuperscriptBox["b", RowBox[{"p1", "-", "p2", "+", "p3"}]]}],
                        
    RowBox[{"c", " ", "d"}]
                        
   ]  *)


                        Then, noting that the numerator and the denominator are the first and second elements of the the FractionBox expression, we replace FractionBox with List using List@@, and then convert the remaining formatting expression to Mathematica input expressions using ToExpression.






                        share|improve this answer









                        $endgroup$


















                          3












                          $begingroup$

                          So, for your particular expression (which is a single fraction), the following kluge works:



                          expr = (a^(p1 + p2 - p3) b^(p1 - p2 + p3))/(c d);
                          
ToExpression /@ List @@ ToBoxes@expr
                          
(* {a^(p1 + p2 - p3) b^(p1 - p2 + p3), c d} *)


                          This is a little tricky to automat, because you have to inspect the formatting expression that you get.




                          This uses the visual formatting in the following way. ToBoxes converts the output to front-end formatting:



                          ToBoxes@expr
                          
(* FractionBox[
                          
    RowBox[{SuperscriptBox["a", RowBox[{"p1", "+", "p2", "-", "p3"}]], " ", SuperscriptBox["b", RowBox[{"p1", "-", "p2", "+", "p3"}]]}],
                          
    RowBox[{"c", " ", "d"}]
                          
   ]  *)


                          Then, noting that the numerator and the denominator are the first and second elements of the the FractionBox expression, we replace FractionBox with List using List@@, and then convert the remaining formatting expression to Mathematica input expressions using ToExpression.






                          share|improve this answer









                          $endgroup$
















                            3












                            3








                            3





                            $begingroup$

                            So, for your particular expression (which is a single fraction), the following kluge works:



                            expr = (a^(p1 + p2 - p3) b^(p1 - p2 + p3))/(c d);
                            
ToExpression /@ List @@ ToBoxes@expr
                            
(* {a^(p1 + p2 - p3) b^(p1 - p2 + p3), c d} *)


                            This is a little tricky to automat, because you have to inspect the formatting expression that you get.




                            This uses the visual formatting in the following way. ToBoxes converts the output to front-end formatting:



                            ToBoxes@expr
                            
(* FractionBox[
                            
    RowBox[{SuperscriptBox["a", RowBox[{"p1", "+", "p2", "-", "p3"}]], " ", SuperscriptBox["b", RowBox[{"p1", "-", "p2", "+", "p3"}]]}],
                            
    RowBox[{"c", " ", "d"}]
                            
   ]  *)


                            Then, noting that the numerator and the denominator are the first and second elements of the the FractionBox expression, we replace FractionBox with List using List@@, and then convert the remaining formatting expression to Mathematica input expressions using ToExpression.






                            share|improve this answer









                            $endgroup$



                            So, for your particular expression (which is a single fraction), the following kluge works:



                            expr = (a^(p1 + p2 - p3) b^(p1 - p2 + p3))/(c d);
                            
ToExpression /@ List @@ ToBoxes@expr
                            
(* {a^(p1 + p2 - p3) b^(p1 - p2 + p3), c d} *)


                            This is a little tricky to automat, because you have to inspect the formatting expression that you get.




                            This uses the visual formatting in the following way. ToBoxes converts the output to front-end formatting:



                            ToBoxes@expr
                            
(* FractionBox[
                            
    RowBox[{SuperscriptBox["a", RowBox[{"p1", "+", "p2", "-", "p3"}]], " ", SuperscriptBox["b", RowBox[{"p1", "-", "p2", "+", "p3"}]]}],
                            
    RowBox[{"c", " ", "d"}]
                            
   ]  *)


                            Then, noting that the numerator and the denominator are the first and second elements of the the FractionBox expression, we replace FractionBox with List using List@@, and then convert the remaining formatting expression to Mathematica input expressions using ToExpression.







                            share|improve this answer












                            share|improve this answer



                            share|improve this answer










                            answered yesterday









                            marchmarch

                            17.4k22769




                            17.4k22769























                                0












                                $begingroup$

                                Here is another option using TeXForm.



                                expr = (a^(p1 + p2 - p3) b^(p1 - p2 + p3))/(c d);
                                
t = ToString[TeXForm[expr]]
                                

                                
  (* frac{a^{text{p1}+text{p2}-text{p3}} b^{text{p1}-text{p2}+text{p3}}}{c d} *)


                                Numerator:



                                ToExpression[StringCases[t, RegularExpression["frac{(.+)}{(.+)}$"] -> "$1"][[1]], TeXForm]
                                

                                
  (* a^(p1 + p2 - p3) b^(p1 - p2 + p3) *)


                                Denominator:



                                ToExpression[StringCases[t, RegularExpression["frac{(.+)}{(.+)}$"] -> "$2"][[1]], TeXForm]
                                

                                
  (* cd *)





                                share|improve this answer









                                $endgroup$


















                                  0












                                  $begingroup$

                                  Here is another option using TeXForm.



                                  expr = (a^(p1 + p2 - p3) b^(p1 - p2 + p3))/(c d);
                                  
t = ToString[TeXForm[expr]]
                                  

                                  
  (* frac{a^{text{p1}+text{p2}-text{p3}} b^{text{p1}-text{p2}+text{p3}}}{c d} *)


                                  Numerator:



                                  ToExpression[StringCases[t, RegularExpression["frac{(.+)}{(.+)}$"] -> "$1"][[1]], TeXForm]
                                  

                                  
  (* a^(p1 + p2 - p3) b^(p1 - p2 + p3) *)


                                  Denominator:



                                  ToExpression[StringCases[t, RegularExpression["frac{(.+)}{(.+)}$"] -> "$2"][[1]], TeXForm]
                                  

                                  
  (* cd *)





                                  share|improve this answer









                                  $endgroup$
















                                    0












                                    0








                                    0





                                    $begingroup$

                                    Here is another option using TeXForm.



                                    expr = (a^(p1 + p2 - p3) b^(p1 - p2 + p3))/(c d);
                                    
t = ToString[TeXForm[expr]]
                                    

                                    
  (* frac{a^{text{p1}+text{p2}-text{p3}} b^{text{p1}-text{p2}+text{p3}}}{c d} *)


                                    Numerator:



                                    ToExpression[StringCases[t, RegularExpression["frac{(.+)}{(.+)}$"] -> "$1"][[1]], TeXForm]
                                    

                                    
  (* a^(p1 + p2 - p3) b^(p1 - p2 + p3) *)


                                    Denominator:



                                    ToExpression[StringCases[t, RegularExpression["frac{(.+)}{(.+)}$"] -> "$2"][[1]], TeXForm]
                                    

                                    
  (* cd *)





                                    share|improve this answer









                                    $endgroup$



                                    Here is another option using TeXForm.



                                    expr = (a^(p1 + p2 - p3) b^(p1 - p2 + p3))/(c d);
                                    
t = ToString[TeXForm[expr]]
                                    

                                    
  (* frac{a^{text{p1}+text{p2}-text{p3}} b^{text{p1}-text{p2}+text{p3}}}{c d} *)


                                    Numerator:



                                    ToExpression[StringCases[t, RegularExpression["frac{(.+)}{(.+)}$"] -> "$1"][[1]], TeXForm]
                                    

                                    
  (* a^(p1 + p2 - p3) b^(p1 - p2 + p3) *)


                                    Denominator:



                                    ToExpression[StringCases[t, RegularExpression["frac{(.+)}{(.+)}$"] -> "$2"][[1]], TeXForm]
                                    

                                    
  (* cd *)






                                    share|improve this answer












                                    share|improve this answer



                                    share|improve this answer










                                    answered yesterday









                                    MelaGoMelaGo

                                    2163




                                    2163






























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