I did some digging about FullSimplify but did not find something concrete about my problems and I think they are too elementary to pass.


1)This example is not problematic but I will use it as the prototype.

Input1: -((2 k^2)/3) + 8 k^4 M^2 - 12 k^2 M^2 \[Omega]^2 // FullSimplify.

Output1: 2/3 k^2 (-1 + 6 M^2 (2 k^2 - 3 \[Omega]^2))

which is just fine and what I actually need. Notice that M^2 gets factored.

2)Now a slightly modified version of 1)

Input2: -2 k^2 + 12 k^4 M^2 - 18 k^2 M^2 \[Omega]^2 // FullSimplify

Output2: 2 k^2 (-1 + 6 k^2 M^2 - 9 M^2 \[Omega]^2)

Now this is problematic, notice that M^2 did not get factored in this case as in Output1 and therefore the expression is not fully simplified.

3)A simpler problematic example.

Input3: (2 k^2)/3 - 4 k^4 // FullSimplify

Output3: (2 k^2)/3 - 4 k^4 M^2

In this case no simplification was performed whatsoever, even if you try Simplify Output3 is again the same. For the sake of clarity by simplification I mean that the output should have k^2 factored from both terms.



1)Does anyone have any idea why is this happening in Output2 in contrast to Output1?

2)What about Output3? Isn't it too trivial for FullSimplify to fail?

3)Any possible fixes?

  • $\begingroup$ Output 3 has the same leaf count as the result you were expecting.Output 2 has either the same, or one less, depending on exactly where minus signs get placed. These details will affect the eventual result. $\endgroup$ – Daniel Lichtblau Apr 20 at 14:36

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