{"id":285,"date":"2016-07-22T05:27:00","date_gmt":"2016-07-22T05:27:00","guid":{"rendered":"http:\/\/www.rangakrish.com\/?p=285"},"modified":"2016-09-11T15:20:24","modified_gmt":"2016-09-11T15:20:24","slug":"using-julia-to-interact-with-mathematica","status":"publish","type":"post","link":"https:\/\/www.rangakrish.com\/index.php\/2016\/07\/22\/using-julia-to-interact-with-mathematica\/","title":{"rendered":"Using Julia to Interact with Mathematica"},"content":{"rendered":"

Mathematica<\/a> is a powerful environment for symbolic and numerical computation. I have been using it for many years now. In this post<\/a>\u00a0I had explained how we can use Mathematica bundled with Raspberry distribution to control littleBits devices.<\/p>\n

When I saw that there is support in Julia for interacting with Mathematica, I decided to investigate it further. Please note that for this to work, you must have a local copy of Mathematica; Julia does not replace Mathematica.<\/p>\n

The package Mathematica.jl<\/strong><\/a> is required for this interaction.\u00a0I found out that this package has dependency on a couple of other files (MathLink<\/strong>) that\u00a0are not automatically installed by Julia\u2019s package manager. The files are located here: https:\/\/github.com\/MikeInnes\/MathLink.jl<\/a>.\u00a0So I manually downloaded the ZIP file and extracted the SRC files to my local directory.<\/p>\n

For convenience in launching Julia from the Terminal on my iMac (that is where I have my Mathematica installation), I set up an alias:<\/p>\n

alias julia=”\/Applications\/Julia-0.4.6.app\/Contents\/Resources\/julia\/bin\/julia”<\/strong><\/p>\n

Launch Julia on the Terminal by typing julia<\/strong>.<\/p>\n

We have to install the Mathematica.jl<\/strong> package just once through Julia\u2019s package manager. In my case, I had already installed it in an earlier session. The next important step is to tell Julia where it can locate the MathLink<\/strong> dependency files. See the following image:<\/p>\n

\"Julia<\/a>
Julia Session<\/figcaption><\/figure>\n

 <\/p>\n

Now we are all set to interact with Mathematica. The nice thing is that we need not launch Mathematica manually for this interaction to work.<\/p>\n

Let us start by calculating the Nth prime number, where N is 10^10:<\/p>\n

julia> <\/b>Prime(10^10)<\/b><\/p>\n

252097800623<\/b><\/p>\n

Note that the answer is coming from Mathematica, not Julia.<\/p>\n

Next, let us create an array of Lucas numbers for N = 10 to 20:<\/p>\n

julia> <\/b>res = [LucasL(n) for n = 10:20]<\/b><\/p>\n

11-element Array{Any,1}:<\/b><\/p>\n

\u00a0\u00a0 123<\/b><\/p>\n

\u00a0\u00a0 199<\/b><\/p>\n

\u00a0\u00a0 322<\/b><\/p>\n

\u00a0\u00a0 521<\/b><\/p>\n

\u00a0\u00a0 843<\/b><\/p>\n

\u00a0 1364<\/b><\/p>\n

\u00a0 2207<\/b><\/p>\n

\u00a0 3571<\/b><\/p>\n

\u00a0 5778<\/b><\/p>\n

\u00a0 9349<\/b><\/p>\n

\u00a015127<\/b><\/p>\n

What is interesting\u00a0is that the result is a Julia expression, so we can access the elements of the returned array.<\/p>\n

julia> <\/b>res[1] + res[2]<\/b><\/p>\n

322<\/b><\/p>\n

Because the syntax of Mathematica and Julia are different, one way to execute an actual Mathematica expression in Julia is to represent it as a String and call Mathematica\u2019s ToExpression<\/strong> function on the String.<\/p>\n

As an example, let us use Mathematica to play some music – the notes C4 and D4, each lasting 1 second:<\/p>\n

julia> <\/b>ToExpression(“””EmitSound[Sound[{SoundNote[“C4”], SoundNote[“D4″]}]]”””)<\/b><\/p>\n

When you execute the above code, you can hear Mathematica playing music.<\/p>\n

A slight variation of the above is to play a Chord using notes C4-E4-G4, for 0.5 second using Violin:<\/p>\n

julia> <\/b>ToExpression(“””EmitSound[Sound[SoundNote[{“C4”, “E4”, “G4”}, 0.5, “Violin”]]]”””)<\/b><\/p>\n

As the final example, I can define my own Mathematica function and execute it:<\/p>\n

julia> <\/b>ToExpression(“MyFunction[a_] = a ^ 34;MyFunction[2]”)<\/b><\/p>\n

17179869184<\/b><\/p>\n

So it is quite remarkable\u00a0that we can interact with Mathematica and take advantage of its vast computational power from within Julia. I am sure that as Julia evolves, further enhancements to the Mathematica.jl<\/strong> package will be made.<\/p>\n","protected":false},"excerpt":{"rendered":"

Mathematica is a powerful environment for symbolic and numerical computation. I have been using it for many years now. In this post\u00a0I had explained how we can use Mathematica bundled with Raspberry distribution to control littleBits devices. When I saw that there is support in Julia for interacting with Mathematica, I decided to investigate it […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[63,72,17],"tags":[64,43],"class_list":["post-285","post","type-post","status-publish","format-standard","hentry","category-julia","category-mathematica","category-programming","tag-julia","tag-mathematica"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p9OLnF-4B","jetpack-related-posts":[{"id":2947,"url":"https:\/\/www.rangakrish.com\/index.php\/2022\/11\/24\/using-julia-from-mathematica\/","url_meta":{"origin":285,"position":0},"title":"Using Julia from Mathematica","author":"admin","date":"November 24, 2022","format":false,"excerpt":"In an earlier article, I had shown how it is possible to interact with Mathematica from Julia. 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Python Cells Let us start with the simplest way to\u2026","rel":"","context":"In "Mathematica"","block_context":{"text":"Mathematica","link":"https:\/\/www.rangakrish.com\/index.php\/category\/mathematica\/"},"img":{"alt_text":"Function References","src":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2019\/05\/External-Evaluate-4.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2019\/05\/External-Evaluate-4.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2019\/05\/External-Evaluate-4.png?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":3626,"url":"https:\/\/www.rangakrish.com\/index.php\/2025\/02\/21\/using-openai-from-mathematica-part-3\/","url_meta":{"origin":285,"position":4},"title":"Using OpenAI from Mathematica: Part-3","author":"admin","date":"February 21, 2025","format":false,"excerpt":"Let us continue our discussion on using Mathematica to interact with OpenAI (you may want to go through the earlier article as well). 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