{"id":3271,"date":"2023-12-10T14:41:22","date_gmt":"2023-12-10T09:11:22","guid":{"rendered":"https:\/\/www.rangakrish.com\/?p=3271"},"modified":"2023-12-10T14:41:22","modified_gmt":"2023-12-10T09:11:22","slug":"generating-polynomials-part-2","status":"publish","type":"post","link":"https:\/\/www.rangakrish.com\/index.php\/2023\/12\/10\/generating-polynomials-part-2\/","title":{"rendered":"Generating Polynomials – Part 2"},"content":{"rendered":"

In my last article<\/strong><\/em><\/a>, I showed how we can use Prolog<\/strong><\/em> to generate univariate Polynomials<\/strong><\/em>. After I finished that article, I wanted to try Lisp<\/strong><\/em> for the same task. Prolog<\/strong><\/em> is \u201cdeclarative\u201d<\/strong><\/em>, whereas Lisp<\/strong><\/em> is primarily \u201cfunctional\u201d<\/strong><\/em> (it supports OOP as well), so the implementation will exhibit that difference.<\/p>\n

Here is the primary function generate-polynomial<\/strong><\/em> along with the tester function (main<\/strong><\/em>):<\/p>\n

\"Function<\/a>
Function to Generate Polynomial<\/strong><\/figcaption><\/figure>\n

Here is sample output (polynomials of degree 4):<\/p>\n

\"Sample<\/a>
Sample Output<\/strong><\/figcaption><\/figure>\n

Generate-polynomial<\/strong><\/em> uses the following functions to generate a polynomial of given degree:<\/p>\n

\"Core<\/a>
Core Functions<\/strong><\/figcaption><\/figure>\n

A few utility<\/strong><\/em> functions are also used along the way. These are:<\/p>\n

\"Some<\/a>
Some Utility Functions<\/strong><\/figcaption><\/figure>\n

Here is another sample output:<\/p>\n

\"Another<\/a>
Another Test Run<\/strong><\/figcaption><\/figure>\n

As you can see, the output is quite random. Let us try to generate polynomials of degree 3:<\/p>\n

\"Polynomials<\/a>
Polynomials of Degree 3<\/strong><\/figcaption><\/figure>\n

Nothing fancy or surprising here. The program works as expected.<\/p>\n

Between the Prolog<\/strong><\/em> and Lisp<\/strong><\/em> implementations, I think had to write some extra code to get the Lisp implementation working. Maybe if I had used some external utility libraries, I could have saved some code, but that is no big deal. Anyway, it was a nice exercise for me!<\/p>\n

The code is implemented in LispWorks Lisp 8.0.1 Enterprise Edition for Windows 64 bit<\/a>.<\/strong><\/em> You can download the code here<\/strong><\/em><\/a>.<\/p>\n

Have a nice weekend!<\/p>\n","protected":false},"excerpt":{"rendered":"

In my last article, I showed how we can use Prolog to generate univariate Polynomials. After I finished that article, I wanted to try Lisp for the same task. Prolog is \u201cdeclarative\u201d, whereas Lisp is primarily \u201cfunctional\u201d (it supports OOP as well), so the implementation will exhibit that difference. Here is the primary function generate-polynomial […]<\/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":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[18,17],"tags":[375],"class_list":["post-3271","post","type-post","status-publish","format-standard","hentry","category-lisp","category-programming","tag-polynomials"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p9OLnF-QL","jetpack-related-posts":[{"id":3260,"url":"https:\/\/www.rangakrish.com\/index.php\/2023\/11\/26\/generating-polynomials-in-prolog\/","url_meta":{"origin":3271,"position":0},"title":"Generating Polynomials in Prolog","author":"admin","date":"November 26, 2023","format":false,"excerpt":"Polynomial is an important topic in High School maths curriculum. There are many online courses that explain the topic in great details with lots of examples and sample exercises. Wouldn\u2019t it be interesting if we can generate polynomials of given degree programmatically? It turns out that this is not such\u2026","rel":"","context":"In "Programming"","block_context":{"text":"Programming","link":"https:\/\/www.rangakrish.com\/index.php\/category\/programming\/"},"img":{"alt_text":"Generating Polynomials - Main Clauses","src":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2023\/11\/Code1-300x163.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2023\/11\/Code1-300x163.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2023\/11\/Code1-300x163.jpg?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":3555,"url":"https:\/\/www.rangakrish.com\/index.php\/2024\/11\/22\/multiobjective-optimization-moo-in-lisp-and-prolog\/","url_meta":{"origin":3271,"position":1},"title":"Multiobjective Optimization (MOO) in Lisp and Prolog","author":"admin","date":"November 22, 2024","format":false,"excerpt":"Recently I came across a nice article\u00a0by Jose Crespo, where the author stresses that the future of programming revolves around the application of math concepts such as Functor, Monads, Folds, etc. In addition, he argues that familiarity with C\/C++ is essential in this modern AI age. The author goes through\u2026","rel":"","context":"In "C++"","block_context":{"text":"C++","link":"https:\/\/www.rangakrish.com\/index.php\/category\/c\/"},"img":{"alt_text":"Lisp Code for Pareto Front","src":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2024\/11\/lisp-code-249x300.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":2832,"url":"https:\/\/www.rangakrish.com\/index.php\/2022\/06\/12\/definite-clause-grammars-in-lisp-part-4\/","url_meta":{"origin":3271,"position":2},"title":"Definite Clause Grammars in Lisp – Part 4","author":"admin","date":"June 12, 2022","format":false,"excerpt":"In a series of articles\u00a0written earlier, I had shown how it is possible to model Definite Clause Grammars (DCG) in LispWorks Lisp (Enterprise Edition). We use defgrammar\u00a0in Common Prolog (available as part of KnowledgeWorks package) to define our grammar rules. Here is a toy English grammar represented using defgrammar: This\u2026","rel":"","context":"In "LISP"","block_context":{"text":"LISP","link":"https:\/\/www.rangakrish.com\/index.php\/category\/lisp\/"},"img":{"alt_text":"DCG Using Defgrammar","src":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2022\/06\/defgrammar-version-300x177.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2022\/06\/defgrammar-version-300x177.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2022\/06\/defgrammar-version-300x177.jpg?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":245,"url":"https:\/\/www.rangakrish.com\/index.php\/2016\/05\/26\/constraint-propagation-in-picat\/","url_meta":{"origin":3271,"position":3},"title":"Constraint Programming in Picat","author":"admin","date":"May 26, 2016","format":false,"excerpt":"In my last post\u00a0I briefly described how we can use the Screamer Lisp library for constraint programming in music. Another language I have been hearing a lot about, in the context of constraint programming, is Picat, a Prolog-derived language. Although I am familiar with Prolog and have been a user\u2026","rel":"","context":"In "LISP"","block_context":{"text":"LISP","link":"https:\/\/www.rangakrish.com\/index.php\/category\/lisp\/"},"img":{"alt_text":"Picat Program","src":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2016\/05\/Picat-Program.png?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":3589,"url":"https:\/\/www.rangakrish.com\/index.php\/2025\/01\/04\/word-transformation-puzzle-part-2-implementation-in-common-lisp\/","url_meta":{"origin":3271,"position":4},"title":"Word Transformation Puzzle – Part 2: Implementation in Common Lisp","author":"admin","date":"January 4, 2025","format":false,"excerpt":"In the last article\u00a0I discussed an interesting word puzzle and showed how to solve it using Prolog. Here is the problem statement: \u201cYou are given two words of the same length. You have to transform the first word into the second word, by changing only one letter at a time.\u2026","rel":"","context":"In "LISP"","block_context":{"text":"LISP","link":"https:\/\/www.rangakrish.com\/index.php\/category\/lisp\/"},"img":{"alt_text":"Getting Word Neighbors","src":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2025\/01\/code1-300x127.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2025\/01\/code1-300x127.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2025\/01\/code1-300x127.jpg?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":1659,"url":"https:\/\/www.rangakrish.com\/index.php\/2019\/08\/04\/generating-poetry-in-prolog\/","url_meta":{"origin":3271,"position":5},"title":"Generating Poetry in Prolog","author":"admin","date":"August 4, 2019","format":false,"excerpt":"In an earlier article, I showed how we can generate poetry (with limitations, of course!) using my iLangGen framework. 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