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I’d like to use the TrigReduce function on a sum of n sinusoids to any power, and am running into an issue with Mathematica’s default ordering of symbols. Is there a way that I can specify an order of f symbols for TrigReduce, such that f1 < f2 < f3 {…}, while keeping notation symbolic?

For example, using numeric values work nicely:

enter image description here

But if symbols are used alone, I want to specify that f2 is the larger value in this example, so instead of f1-f2, TrigReduce would ideally yield the term f2-f1.

enter image description here

For perspective, the end goal is the general formula will output a list pairing each calculated numeric value with its associated symbolic f relationship (with f1 < f2 < f3 < f4, etc), but as it is, TrigReduce's symbol ordering doesn't always work as it doesn't know my preference for ascending values.

Thanks in advance!

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It isn't TrigReduce doing this. Mathematica automatically sorts expressions into canonical order. The sort is basically structural/lexical, so knowledge of symbolic inequalities isn't applicable.

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  • $\begingroup$ Is there a way to provide symbolic inequalities for functions though? How would I use TrigReduce so it would yield the expression with the desired relationship? $\endgroup$ – TikiTiki Mar 6 '18 at 0:50
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    $\begingroup$ Forget TrigReduce. It is not the cause of your problem. To see what's happening, type Cos[x]-1. Mathematica will automatically rearrange it. You could Hold your expression and then rearrange it internally, but that's complicated and requires a great deal of Mathematica expertise to do correctly. $\endgroup$ – John Doty Mar 6 '18 at 14:35
  • $\begingroup$ One possibility is to make your output into a List with a substitution like Plus->List. Then sort that. $\endgroup$ – John Doty Mar 6 '18 at 14:40

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