Imagine Maple, Maxima or Mathematica, in which the rules of the work are encyclopedic articles, and, conversely, an encyclopedia, by adding which you improve the performance of the computer algebra system. This idea is the basis of the Galois / Wiki
(Galois / Wiki) - a mathematical encyclopedia with intelligent search.
The approach is very simple: thanks to semantic markup, the system “knows” which formula in the article is an equation, and which is its solution. In addition to this information, you can specify which variable is a parameter in the article on a parametrized family of equations, and then this article can be found (and with it the solution) using any equation from this family. This approach is illustrated in the picture.
In addition to articles about equations and their solutions, the system supports articles about mathematical objects and their properties, as well as about mathematical expressions.
The Galois / Wiki project develops as a spin off of the mathematical search engine Uniquation
, which I already wrote about in Habré: “Mathematical search system Uniquation”
and “Mathematical search system with visual input of formulas”
Why produce encyclopedias when you can supplement Wikipedia?
Unfortunately, in Wikipedia you cannot embed and control your metadata, and the functionality of the project depends on them.
On the other hand, Wikipedia articles describe general mathematical concepts, such as the classification of differential equations or integral calculus, but not specific equations or equalities.
Why create Galois / Wiki when there are already computer algebra systems (CAS)?
CAS can answer the formulated question, so they are useful when you know what you want to find. But when there is no clear question and if you want to know the properties of an object, then computer algebra systems are not suitable.
Another advantage is that not all problems have algorithms for symbolic calculations, so if something cannot be calculated automatically, this does not mean that the answer cannot be found.
Thirdly, even if you know exactly what you want to find, sometimes it is difficult to express it in CAS. In the case of a search, simply enter the object you want to know about and view the results.
But the most important advantage is openness for editing, and, therefore, the fact that tomorrow the system will be better than today. For example, let's try to find in Wolframalpha information about the recursive sequence 'f (x) = 5 f (x-1) (1 - f (x-1))' ( results
) it can be seen that there are no valuable results. While a search in Galois / Wiki gives some information about the object ( results
) Of course, I added this note before writing about it on Habré, but this is an advantage.
What I have described is a technology that is already working, but in terms of filling it is not an encyclopedia, or even a reference book. Therefore, the plan, first of all, is filling in the Galois / Wiki as a reference book. I hope to find the first alpha testers that will help in this (you can start with wiki integrals - Lists of integrals
Then you need to add social functionality, such as discussing / commenting on articles and so on, to try to create a community around the site and turn the reference book into an encyclopedia.