September 6, 2010 at 11:58Wolframalpha + Wikipedia = Galois / Wiki
Imagine a Maple, Maxima or Mathematica, in which the rules of work are encyclopedic articles, and, conversely, an encyclopedia, supplementing which, you improve the work of computer algebra. This idea underlies 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, it is possible to indicate which variable is a parameter in an article on a parametrized family of equations, and then this article can be found (and with it a solution) by 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 on the Habr: “Mathematical search engine Uniquation” and “Mathematical search system with visual input of formulas”
Unfortunately, in Wikipedia you can’t implement and control your metadata, and the functionality of the project depends on them.
Wikipedia articles, on the other hand, describe general mathematical concepts, such as classification of differential equations or integral calculus, but not specific equations or equalities.
CAS can provide an answer to 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 algorithms have symbolic computation algorithms, 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, you just need to enter the object that you want to find out about and view the results.
But the main advantage is openness for editing, and, therefore, that tomorrow the system will be better than today. For example, let’s try in Wolframalpha to find 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 the search in Galois / Wiki gives some information about the object ( results ) Of course, I added this note before writing about it on the hub, but this is an advantage.
What I described is a technology that already works, but by level of filling this is not an encyclopedia, or even a reference. Therefore, the plan, first of all, is filling in the Galois / Wiki as a reference. I hope to find the first alpha testers on the hub who will help in this (you can start with the integrals from the wiki - Lists of integrals ).
Then you need to add social functionality, such as discussion / commenting on articles and so on, to try to create a community around the site and turn the guide into an encyclopedia.
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, it is possible to indicate which variable is a parameter in an article on a parametrized family of equations, and then this article can be found (and with it a solution) by 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 on the Habr: “Mathematical search engine Uniquation” and “Mathematical search system with visual input of formulas”
Why create an encyclopedia when you can complement Wikipedia?
Unfortunately, in Wikipedia you can’t implement and control your metadata, and the functionality of the project depends on them.
Wikipedia articles, on the other hand, describe general mathematical concepts, such as classification of differential equations or integral calculus, but not specific equations or equalities.
Why create a Galois / Wiki when you already have a computer algebra system (CAS)?
CAS can provide an answer to 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 algorithms have symbolic computation algorithms, 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, you just need to enter the object that you want to find out about and view the results.
But the main advantage is openness for editing, and, therefore, that tomorrow the system will be better than today. For example, let’s try in Wolframalpha to find 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 the search in Galois / Wiki gives some information about the object ( results ) Of course, I added this note before writing about it on the hub, but this is an advantage.
Plans
What I described is a technology that already works, but by level of filling this is not an encyclopedia, or even a reference. Therefore, the plan, first of all, is filling in the Galois / Wiki as a reference. I hope to find the first alpha testers on the hub who will help in this (you can start with the integrals from the wiki - Lists of integrals ).
Then you need to add social functionality, such as discussion / commenting on articles and so on, to try to create a community around the site and turn the guide into an encyclopedia.