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Mathematics Algebra Wolfram Language

[?] Transform an expression to a certain form?

J P

J P, Universtiy Physics Department

Posted 8 years ago

Hi, in my current project i evaluate large sums of the form: in the most cases f(i,k,n)=0 so im left with expressions of the form ba[3]a[4] + ca[4]a[3] + ... what i want are expresions of the form like: (b+c)a[3] a[4] Sometimes Simplify or FullSimplify is doing the job sometimes not... An example of what such an result look like is attached. Not my plan was to go through the expression and find all components which are proportional to a[i]a[k] and sum up the prefactors, but i cant figure out a nice way of doing that. Does someone have an idea how to put the expression in the right form? Many thanks in advance!!! Attachments:*

POSTED BY: J P

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J P

J P, Universtiy Physics Department

Posted 8 years ago

Many Thanks exactly what i was looking for!

POSTED BY: J P

Daniel Lichtblau

Daniel Lichtblau, Wolfram Research

Posted 8 years ago

e = (5 Sqrt[2/3] a^2 a[2] a[4])/(3 Sqrt[a^2 + g^2]) - ( 5 Sqrt[2/3] g^2 a[2] a[4])/(3 Sqrt[a^2 + g^2]) - ( 2 Sqrt[2/3] a g \[Pi] Sqrt[(a^2 + g^2) (4 g^2 + \[Pi]^2)] a[3] a[5])/((a^2 + g^2) (4 g^2 + \[Pi]^2)) - (a^2 a[6])/re - ( g^2 a[6])/re - (\[Pi]^2 a[6])/(3 re) + (a a[1] a[7])/Sqrt[6] + ( Sqrt[3/2] g \[Pi] a[1] a[8])/Sqrt[4 a^2 + 4 g^2 + \[Pi]^2] + ( a a[7] a[9])/Sqrt[6] + (Sqrt[3/2] g \[Pi] a[8] a[9])/Sqrt[ 4 a^2 + 4 g^2 + \[Pi]^2]; Separate out the `a` variables (but not `a` itself) and use `Collect`: avars = Cases[Variables[e], _a]; Collect[e, avars] ((5 Sqrt[2/3] a^2)/(3 Sqrt[a^2 + g^2]) - (5 Sqrt[2/3] g^2)/( 3 Sqrt[a^2 + g^2])) a[2] a[4] - ( 2 Sqrt[2/3] a g \[Pi] Sqrt[(a^2 + g^2) (4 g^2 + \[Pi]^2)] a[3] a[5])/((a^2 + g^2) (4 g^2 + \[Pi]^2)) + (-(a^2/re) - g^2/ re - \[Pi]^2/(3 re)) a[6] + a[1] ((a a[7])/Sqrt[6] + (Sqrt[3/2] g \[Pi] a[8])/Sqrt[ 4 a^2 + 4 g^2 + \[Pi]^2]) + (a a[7] a[9])/Sqrt[6] + ( Sqrt[3/2] g \[Pi] a[8] a[9])/Sqrt[4 a^2 + 4 g^2 + \[Pi]^2]

e = (5 Sqrt[2/3] a^2 a[2] a[4])/(3 Sqrt[a^2 + g^2]) - (
   5 Sqrt[2/3] g^2 a[2] a[4])/(3 Sqrt[a^2 + g^2]) - (
   2 Sqrt[2/3] a g \[Pi] Sqrt[(a^2 + g^2) (4 g^2 + \[Pi]^2)]
     a[3] a[5])/((a^2 + g^2) (4 g^2 + \[Pi]^2)) - (a^2 a[6])/re - (
   g^2 a[6])/re - (\[Pi]^2 a[6])/(3 re) + (a a[1] a[7])/Sqrt[6] + (
   Sqrt[3/2] g \[Pi] a[1] a[8])/Sqrt[4 a^2 + 4 g^2 + \[Pi]^2] + (
   a a[7] a[9])/Sqrt[6] + (Sqrt[3/2] g \[Pi] a[8] a[9])/Sqrt[
   4 a^2 + 4 g^2 + \[Pi]^2];

Separate out the a variables (but not a itself) and use Collect:

avars = Cases[Variables[e], _a];
Collect[e, avars]

((5 Sqrt[2/3] a^2)/(3 Sqrt[a^2 + g^2]) - (5 Sqrt[2/3] g^2)/(
    3 Sqrt[a^2 + g^2])) a[2] a[4] - (
 2 Sqrt[2/3] a g \[Pi] Sqrt[(a^2 + g^2) (4 g^2 + \[Pi]^2)]
   a[3] a[5])/((a^2 + g^2) (4 g^2 + \[Pi]^2)) + (-(a^2/re) - g^2/
    re - \[Pi]^2/(3 re)) a[6] + 
 a[1] ((a a[7])/Sqrt[6] + (Sqrt[3/2] g \[Pi] a[8])/Sqrt[
    4 a^2 + 4 g^2 + \[Pi]^2]) + (a a[7] a[9])/Sqrt[6] + (
 Sqrt[3/2] g \[Pi] a[8] a[9])/Sqrt[4 a^2 + 4 g^2 + \[Pi]^2]

POSTED BY: Daniel Lichtblau