# How to factor out known multipliers in algebraic expressions in mathematica

Posted 10 years ago
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 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
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Posted 10 years ago
 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 ;)
Posted 10 years ago
 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?
Posted 10 years ago
 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[\[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[\[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[c][r] +          r^2 c[r] \[Sigma][           r]^2 (\[Sigma][r] + 2 \[CapitalOmega][r] +             r Derivative[\[CapitalOmega]][r]) -          c[r]^3 (3 \[Sigma][r] + 2 \[CapitalOmega][r] +             3 r Derivative[\[CapitalOmega]][r])) +       bz r^nz \[CapitalSigma][        r]^2 (-2 I b\[Theta]g r c[r]^4 Derivative[\[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[\[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[c][r] +          c[r]^4 (I bz b\[Theta]g (1 + 2 nz) r^nz +             m r^2 \[Sigma][r]^2 Derivative[\[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[\[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[\[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  *)
Posted 10 years ago
 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?
Posted 10 years ago
 You might want to try:Simplify[F,R==(x^2 - y^2 - z^2)]
Posted 10 years ago
 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!
Posted 10 years ago
 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.
Posted 10 years ago
 You might try mapping Factor over the sum of terms obtained from using Expand on the expression.
Posted 10 years ago
 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!