# Symbolics.jl: simplification of expressions with trigonometric terms
**URL:** https://discourse.julialang.org/t/symbolics-jl-simplification-of-expressions-with-trigonometric-terms/59904
**Category:** General Usage
**Created:** [April 23, 2021, 10:00pm UTC](https://discourse.julialang.org/t/symbolics-jl-simplification-of-expressions-with-trigonometric-terms/59904 "2021-04-23T22:00:46Z")
**Posts on this page:** 10
**Page:** 1
### Author:  [@cnf](https://discourse.julialang.org/u/cnf)
#### Post date: [April 23, 2021, 10:00pm UTC](https://discourse.julialang.org/t/symbolics-jl-simplification-of-expressions-with-trigonometric-terms/59904/1 "2021-04-23T22:00:46Z")
I am using the Symbolics.jl package with julia 1.5.2 running on a linux machine.
Any assistance with the following would be appreciated.
(1) How can I simplify expressions with trigonometric terms?
For example, I applied simplify() to various expressions but it could not transform sin(x)_cos(x) to sin(2_x)/2, and cos(x)^2-sin(x)^2 to cos(2\*x).
How can these simplifications be achieved?
(2) Are there expand() and factor() simplification functions?
(3) Where can I obtain pdf file documentation for the
Symbolics.jl package?
I looked in the table of contents of the julia 1.5.2 manual but could not see anything about the Symbolics.jl package?
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### Author:  [@lstagner](https://discourse.julialang.org/u/lstagner)
#### Post date: [April 23, 2021, 10:35pm UTC](https://discourse.julialang.org/t/symbolics-jl-simplification-of-expressions-with-trigonometric-terms/59904/2 "2021-04-23T22:35:24Z")
I wonder what the criterion is for “simpler”. For instance `sin(x)cos(x)` just has two function calls but `sin(2x)/2` has three function calls.
Granted `cos(x)^2 - sin(x)^2` should simplify to `cos(2x)`
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### Author:  [@DNF](https://discourse.julialang.org/u/DNF)
#### Post date: [April 23, 2021, 11:09pm UTC](https://discourse.julialang.org/t/symbolics-jl-simplification-of-expressions-with-trigonometric-terms/59904/3 "2021-04-23T23:09:13Z")
> [@lstagner](#):
>
> `sin(x)cos(x)` just has two function calls but `sin(2x)/2` has three function calls.
Ahem, both of those have three function calls, and not all functions are equal. A `cos` call is far more expensive than a simple multiply or divide. I expect there are a lot of multiplications and divisions going on inside `sin` and `cos`.
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### Author:  [@lstagner](https://discourse.julialang.org/u/lstagner)
#### Post date: [April 24, 2021, 1:16am UTC](https://discourse.julialang.org/t/symbolics-jl-simplification-of-expressions-with-trigonometric-terms/59904/4 "2021-04-24T01:16:54Z")
Bah I cant believed I missed that
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### Author:  [@cnf](https://discourse.julialang.org/u/cnf)
#### Post date: [April 24, 2021, 12:09pm UTC](https://discourse.julialang.org/t/symbolics-jl-simplification-of-expressions-with-trigonometric-terms/59904/5 "2021-04-24T12:09:42Z")
Thank you for the interest and comments. If at all possible please respond to my other questions as well or refer to a colleague who may be able to assist. I would like to explore further the Symbolics.jl package but need more information.
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### Author:  [@magister-ludi](https://discourse.julialang.org/u/magister-ludi)
#### Post date: [April 24, 2021, 12:56pm UTC](https://discourse.julialang.org/t/symbolics-jl-simplification-of-expressions-with-trigonometric-terms/59904/6 "2021-04-24T12:56:49Z")
Symbolics.jl is not part of Julia itself, so you won’t find any reference to it in the Julia manual. The Symbolics.jl codebase is [here](https://github.com/JuliaSymbolics/Symbolics.jl), and its documentation (there’s also a link on the page I just mentioned) is [here](https://symbolics.juliasymbolics.org/stable/).
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### Author:  [@cnf](https://discourse.julialang.org/u/cnf)
#### Post date: [April 24, 2021, 4:52pm UTC](https://discourse.julialang.org/t/symbolics-jl-simplification-of-expressions-with-trigonometric-terms/59904/7 "2021-04-24T16:52:40Z")
Yes, I visited this website previously but other than simplify() I
could not find
any additional simplification functions, eg. factor(), expand(), etc. I assume
that they are not available yet?
Also, I could not find some linear algebra functions for symbolic matrices, eg.
reduced row echelon form, etc.
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### Author:  [@BLI](https://discourse.julialang.org/u/BLI)
#### Post date: [April 24, 2021, 6:25pm UTC](https://discourse.julialang.org/t/symbolics-jl-simplification-of-expressions-with-trigonometric-terms/59904/8 "2021-04-24T18:25:44Z")
I don’t know if it helps, but `Symbolics.jl` uses some routines in package `SymbolicUtils.jl`, and the `simplify` functionality is better explained in the documentation for `SymbolicUtils.jl`. [At least last time I checked…]
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### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [April 29, 2021, 3:22pm UTC](https://discourse.julialang.org/t/symbolics-jl-simplification-of-expressions-with-trigonometric-terms/59904/9 "2021-04-29T15:22:56Z")
> [@cnf](#):
>
> any additional simplification functions, eg. factor(), expand(), etc. I assume
> that they are not available yet?
They just need better docs.
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### Author:  [@cnf](https://discourse.julialang.org/u/cnf)
#### Post date: [April 29, 2021, 8:19pm UTC](https://discourse.julialang.org/t/symbolics-jl-simplification-of-expressions-with-trigonometric-terms/59904/10 "2021-04-29T20:19:00Z")
If they are available then I would like to try them. Please let me know
as soon as the documentation is available.
I noticed that the julia command names(Symbolics) and names(Symbolics,
all=true) provides the user with some information as to all the methods that
are available in the package Symbolics.
Are there julia commands for listing the contents of a specified method in
the Symbolics package or any julia package?