Symbolics.jl: simplification of expressions with trigonometric terms

General Usage
1

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(2x)/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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2

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)

3

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.

2 Likes
4

Bah I cant believed I missed that

2 Likes
5

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.

6

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, and its documentation (there’s also a link on the page I just mentioned) is here.

7

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.

8

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…]

9

They just need better docs.

1 Like
10

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?