How to simplify tensor expression with symbolic coeficients?

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7
down vote

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I can use Vectors to simplify the following expression:



$Assumptions = (a | b | c) ∈ Vectors[3];
TensorReduce[3 b.a[Cross]c - 3 c.b[Cross]a]


which gives me 0, and correct.



However, if I change the value "3" into a symbol "g", it fails:



$Assumptions = (a | b | c) ∈ Vectors[3];
TensorReduce[g b.a[Cross]c - g c.b[Cross]a]


Or



$Assumptions = (a | b | c) ∈ Vectors[3];
$Assumptions = g ∈ Reals;
TensorReduce[g b.a[Cross]c - g c.b[Cross]a]


Mathematica gives me $g b.atimes c-g c.btimes a$, which should be 0 as well.



How can I do this simplification in Mathematica?






vector tensors







share|improve this question



























    up vote
    7
    down vote

    favorite












    I can use Vectors to simplify the following expression:



    $Assumptions = (a | b | c) ∈ Vectors[3];
    TensorReduce[3 b.a[Cross]c - 3 c.b[Cross]a]


    which gives me 0, and correct.



    However, if I change the value "3" into a symbol "g", it fails:



    $Assumptions = (a | b | c) ∈ Vectors[3];
    TensorReduce[g b.a[Cross]c - g c.b[Cross]a]


    Or



    $Assumptions = (a | b | c) ∈ Vectors[3];
    $Assumptions = g ∈ Reals;
    TensorReduce[g b.a[Cross]c - g c.b[Cross]a]


    Mathematica gives me $g b.atimes c-g c.btimes a$, which should be 0 as well.



    How can I do this simplification in Mathematica?






    vector tensors







    share|improve this question

























      up vote
      7
      down vote

      favorite









      up vote
      7
      down vote

      favorite











      I can use Vectors to simplify the following expression:



      $Assumptions = (a | b | c) ∈ Vectors[3];
      TensorReduce[3 b.a[Cross]c - 3 c.b[Cross]a]


      which gives me 0, and correct.



      However, if I change the value "3" into a symbol "g", it fails:



      $Assumptions = (a | b | c) ∈ Vectors[3];
      TensorReduce[g b.a[Cross]c - g c.b[Cross]a]


      Or



      $Assumptions = (a | b | c) ∈ Vectors[3];
      $Assumptions = g ∈ Reals;
      TensorReduce[g b.a[Cross]c - g c.b[Cross]a]


      Mathematica gives me $g b.atimes c-g c.btimes a$, which should be 0 as well.



      How can I do this simplification in Mathematica?






      vector tensors







      share|improve this question















      I can use Vectors to simplify the following expression:



      $Assumptions = (a | b | c) ∈ Vectors[3];
      TensorReduce[3 b.a[Cross]c - 3 c.b[Cross]a]


      which gives me 0, and correct.



      However, if I change the value "3" into a symbol "g", it fails:



      $Assumptions = (a | b | c) ∈ Vectors[3];
      TensorReduce[g b.a[Cross]c - g c.b[Cross]a]


      Or



      $Assumptions = (a | b | c) ∈ Vectors[3];
      $Assumptions = g ∈ Reals;
      TensorReduce[g b.a[Cross]c - g c.b[Cross]a]


      Mathematica gives me $g b.atimes c-g c.btimes a$, which should be 0 as well.



      How can I do this simplification in Mathematica?






      vector tensors




      vector tensors






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited Aug 26 at 6:51









      kglr

      161k8185385




      161k8185385










      asked Aug 26 at 6:36









      ZHANG Juenjie

      489212




      489212




















          2 Answers
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          $Assumptions = (a 

          TensorReduce[g b.a[Cross]c - g c.b[Cross]a]



          0







          share|improve this answer



























            up vote
            5
            down vote













            $Assumptions=(a|b|c) ∈ Vectors[3] && g ∈ Reals

            TensorReduce[g b.a[Cross]c-g c.b[Cross]a]
            (*0*)


            g doesn't have to be Reals. Complexes works too. It just can't be something totally undefined.






            share|improve this answer




















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              2 Answers
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              active

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              2 Answers
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              active

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              active

              oldest

              votes








              up vote
              7
              down vote



              accepted










              $Assumptions = (a 

              TensorReduce[g b.a[Cross]c - g c.b[Cross]a]



              0







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                up vote
                7
                down vote



                accepted










                $Assumptions = (a 

                TensorReduce[g b.a[Cross]c - g c.b[Cross]a]



                0







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                  up vote
                  7
                  down vote



                  accepted







                  up vote
                  7
                  down vote



                  accepted






                  $Assumptions = (a 

                  TensorReduce[g b.a[Cross]c - g c.b[Cross]a]



                  0







                  share|improve this answer












                  $Assumptions = (a 

                  TensorReduce[g b.a[Cross]c - g c.b[Cross]a]



                  0








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                  answered Aug 26 at 6:49









                  kglr

                  161k8185385




                  161k8185385




















                      up vote
                      5
                      down vote













                      $Assumptions=(a|b|c) ∈ Vectors[3] && g ∈ Reals

                      TensorReduce[g b.a[Cross]c-g c.b[Cross]a]
                      (*0*)


                      g doesn't have to be Reals. Complexes works too. It just can't be something totally undefined.






                      share|improve this answer
























                        up vote
                        5
                        down vote













                        $Assumptions=(a|b|c) ∈ Vectors[3] && g ∈ Reals

                        TensorReduce[g b.a[Cross]c-g c.b[Cross]a]
                        (*0*)


                        g doesn't have to be Reals. Complexes works too. It just can't be something totally undefined.






                        share|improve this answer






















                          up vote
                          5
                          down vote










                          up vote
                          5
                          down vote









                          $Assumptions=(a|b|c) ∈ Vectors[3] && g ∈ Reals

                          TensorReduce[g b.a[Cross]c-g c.b[Cross]a]
                          (*0*)


                          g doesn't have to be Reals. Complexes works too. It just can't be something totally undefined.






                          share|improve this answer












                          $Assumptions=(a|b|c) ∈ Vectors[3] && g ∈ Reals

                          TensorReduce[g b.a[Cross]c-g c.b[Cross]a]
                          (*0*)


                          g doesn't have to be Reals. Complexes works too. It just can't be something totally undefined.







                          share|improve this answer












                          share|improve this answer



                          share|improve this answer










                          answered Aug 26 at 6:54









                          Bill Watts

                          2,0381414




                          2,0381414



























                               

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