How to factor out known multipliers in algebraic expressions in mathematica

Questions
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1

Hi There,

I have some very complicated expressions in the form of F[x,y,z,A,B,C]/(x^2 - y^2 - z^2) . Here F[ ] is a very long function of x,y,z as well as some other terms, A,B,C. There are places in F where (x^2 - y^2 - z^2) could be completely canceled out, however, no matter what algebraic manipulation I try in mathematica (Simplify,Cancel,Factor, etc), I cannot get these terms to cancel!

What I want is a way to say: rewrite F in terms of groupings of (x^2 - y^2 - z^2) wherever you can (even if it makes F look overall messier). Note I’ve tried “Collect” and doesn’t seem to work in this sense.

Can anybody suggest a good thing to try? I can send the expression for F in a notebook, but I warn you it’s very VERY long :).

Thanks,

Alissa

2

You might try mapping `Factor` over the sum of terms obtained from using `Expand` on the expression.

3

Thanks for the suggestion. Applying ‘Factor’ to the 'Expand’ed form seems to just mix up the terms of F more, i.e. it sort of multiplies everything out. But I may be mistaking what you mean by mapping Factor?

Thanks either way for the reply!

4

By “map Factor over…” I mean something like this (which maybe is what you did):

Map[Factor, Expand[F[x,y,z,A,B,C]/(x^2 - y^2 - z^2]

This way Factor is used on each term separately.

5

You might want to try:

Simplify[F,R==(x^2 - y^2 - z^2)]
6

Alissa, even thought your expressions are large, do you think it is possible to find a compact sub-expression that illustrates the nature of the problem?

7

Thanks! Simplify[ F, R==(x^2 - y^2 - z^2)] helps a lot, I believe it’s grouping all the factors of (x^2 - y^2 - z^2) into ‘R’ which makes it very easy for me to cancel it out.

Wow, this forum is really a great tool. Thanks everybody!

8

Like I said Simplify[ F, R==(x^2 - y^2 - z^2)] seems to mostly do the job, but here a notebook to illustrate the problem in case people have other suggestions.

Basically, I know that part of “Denom” can be factored out of “F” , the output I’m really interested in is F/Denom, but I’m aiming cancel out Denom every place I can. Does that make sense?
Again, thanks to everyone for replying!

F := (m r (K^2)[r] \[Sigma][r] \[CapitalSigma][
     r]^2 (bz^2 r^(2 nz) + 
      c[r]^2 \[CapitalSigma][r]) (-bz^2 r^(2 nz) - 
      c[r]^2 \[CapitalSigma][r] + 
      r^2 \[Sigma][r]^2 \[CapitalSigma][r]) + 
   2 \[CapitalOmega][
     r] (-I bz^5 b\[Theta]g r^(1 + 5 nz)
        Derivative[1][\[CapitalSigma]][r] + 
      bz^3 r^(3 nz) \[CapitalSigma][
        r] (I bz^2 b\[Theta]g (1 + nz) r^(2 nz) - 
         3 I b\[Theta]g r c[r]^2 Derivative[1][\[CapitalSigma]][r] + 
         r^2 (2 I b\[Theta]g r + bz m r^nz) \[Sigma][r]^2 Derivative[
           1][\[CapitalSigma]][r]) - 
      m r c[r] \[Sigma][r] \[CapitalSigma][
        r]^4 (2 r^3 \[Sigma][r]^3 Derivative[1][c][r] + 
         r^2 c[r] \[Sigma][
           r]^2 (\[Sigma][r] + 2 \[CapitalOmega][r] + 
            r Derivative[1][\[CapitalOmega]][r]) - 
         c[r]^3 (3 \[Sigma][r] + 2 \[CapitalOmega][r] + 
            3 r Derivative[1][\[CapitalOmega]][r])) + 
      bz r^nz \[CapitalSigma][
        r]^2 (-2 I b\[Theta]g r c[r]^4 Derivative[1][\[CapitalSigma]][
           r] + c[r]^2 (I bz^2 b\[Theta]g (2 + 3 nz) r^(2 nz) + 
            2 r^2 (I b\[Theta]g r + bz m r^nz) \[Sigma][
              r]^2 Derivative[1][\[CapitalSigma]][r]) + 
         bz^2 r^(1 + 2 nz) \[Sigma][
           r] ((-I b\[Theta]g (-1 + 3 nz) r + 3 bz m r^nz) \[Sigma][
              r] + 2 (I b\[Theta]g r + bz m r^nz) \[CapitalOmega][r] +
             r (2 I b\[Theta]g r + 3 bz m r^nz) Derivative[
              1][\[CapitalOmega]][r])) + \[CapitalSigma][
        r]^3 (-2 I bz b\[Theta]g r^(3 + nz)
           c[r] \[Sigma][r]^2 Derivative[1][c][r] + 
         c[r]^4 (I bz b\[Theta]g (1 + 2 nz) r^nz + 
            m r^2 \[Sigma][r]^2 Derivative[1][\[CapitalSigma]][r]) - 
         bz r^(3 + nz) \[Sigma][
           r]^3 (bz m (1 + 2 nz) r^nz \[Sigma][r] + 
            2 I b\[Theta]g r \[CapitalOmega][r] + 
            2 bz m r^nz \[CapitalOmega][r] + 
            bz m r^(1 + nz) Derivative[1][\[CapitalOmega]][r]) + 
         r c[r]^2 \[Sigma][
           r] (bz r^
             nz (-I b\[Theta]g (-1 + 2 nz) r + 6 bz m r^nz) \[Sigma][
              r] - m r^3 \[Sigma][r]^3 Derivative[1][\[CapitalSigma]][
              r] + 2 bz r^
             nz ((I b\[Theta]g r + 2 bz m r^nz) \[CapitalOmega][r] + 
               r (I b\[Theta]g r + 3 bz m r^nz) Derivative[
                 1][\[CapitalOmega]][r])))))

Denom := (2 m c[r]^2 \[Sigma][r]^2 \[CapitalSigma][
    r]^3 (bz^2 r^(2 nz) + c[r]^2 \[CapitalSigma][r] - 
     r^2 \[Sigma][r]^2 \[CapitalSigma][r]) \[CapitalOmega][r])


(*here the (x^2-y^2-z^2) -> (bz^2 r^(2 nz)+c[r]^2 \
\[CapitalSigma][r]-r^2 \[Sigma][r]^2 \[CapitalSigma][r]) *)

(*I am looking for a for sure way to cancel (bz^2 r^(2 nz)+c[r]^2 \
\[CapitalSigma][r]-r^2 \[Sigma][r]^2 \[CapitalSigma][r]) from parts \
of F, so I guess I want every term that doesn't have to be over that \
denomator to not be over that denomenator  *)
9

Okay, also I have no idea of the best way to express mathematica notebooks in this forum, my paste job up there seems pretty messy. Can I just attach the notebook somehow?

10

We are considering this functionality, but at the moment you could use any free upload services and provide a link for large notebooks. But anyway - your paste job looks good to me :wink: