{"id":552,"date":"2008-08-10T16:00:55","date_gmt":"2008-08-10T23:00:55","guid":{"rendered":"https:\/\/www.reenigne.org\/blog\/?p=552"},"modified":"2008-05-30T14:29:03","modified_gmt":"2008-05-30T21:29:03","slug":"computer-algebra-system","status":"publish","type":"post","link":"https:\/\/www.reenigne.org\/blog\/computer-algebra-system\/","title":{"rendered":"Computer algebra system"},"content":{"rendered":"

At some point in the future I'd like to write a computer algebra system, like Maple or Mathematica, just because I think it would be really fun piece of software to write. The basic idea is that you can tell the computer things you know (e.g. \"x+2=3\") and ask it questions (like \"x?\") and the computer would attempt to give the simplest possible answer by searching its database of facts. When printing formulae on the screen it would use algorithms from TeX<\/a> to give attractive output.<\/p>\n

Another nice feature would be the ability to directly manipulate formulae, for example rearranging terms of an equation by dragging them with the mouse or expanding multiplications by clicking on them (the program, of course, would prevent manipulations that aren't mathematically correct). These kinds of manipulations can be very tedious to do by hand.<\/p>\n

Yet another feature that I want is the ability to create animated, interactive proofs. Rather than just presenting a static sequence of \"X implies Y implies Z\" on a page, the program could actually create an animation of X turning into Y. And if, at some stage, a derivation is unclear, the user could right-click on it, select \"Why?\" and the program would attempt to explain. That sounds difficult to do but I think much of this is really quite mechanical. When studying mathematics at university, I often wished that the proofs were presented like this - it would have made things much easier.<\/p>\n

As well as an interactive algebra and mathematical presentation system, this program would also contain a big database of mathematical facts, both to aid in the program's own proofs and as an (interactive) mathematics textbook in its own right. Mathematicians using the software could contribute their discoveries to this database\/textbook in addition to (or even instead of) the traditional distribution method of writing papers.<\/p>\n","protected":false},"excerpt":{"rendered":"

At some point in the future I'd like to write a computer algebra system, like Maple or Mathematica, just because I think it would be really fun piece of software to write. The basic idea is that you can tell the computer things you know (e.g. \"x+2=3\") and ask it questions (like \"x?\") and the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,5],"tags":[],"class_list":["post-552","post","type-post","status-publish","format-standard","hentry","category-computer","category-maths"],"_links":{"self":[{"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/posts\/552","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/comments?post=552"}],"version-history":[{"count":0,"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/posts\/552\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/media?parent=552"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/categories?post=552"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/tags?post=552"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}