On the Role of OpenMath in Interactive Mathematical Documents

Abstract

The standard OpenMath is an enabling technology for creating an integrated computer environment in which software packages for computer algebra and for proof checking can be combined. Here we demonstrate how OpenMath can be employed for generating interactive mathematical documents containing primality proofs. Our case study takes place within a browser; once a prime number is specified, a document appears summarizing the proof in a number of assertions. By clicking an assertion regarding the truth of an arithmetic equality, a computer algebra calculation is invoked verifying the equality. By clicking an assertion regarding a specific mathematical lemma called Pocklington's Criterion, a verification of the corresponding formal proof is carried out by a proof checker. Moreover, the whole document is structured in such a way that it can be easily translated to a formal proof object. OpenMath supports the interaction between the document as it appears in the browser and the mathematical software packages. This paper begins with an introduction to OpenMath and a brief comparison with MathML.

OpenMath Technology for Interactive Mathematical Documents

“…gap> G:=Group((2,5)(3,6)(4,7),(1,5,2)(3,6,8) (4,7,9), (1,5,8,10,4)(2,6,9,3,7)); Group((2,5)(3,6)(4,7),(1,5,2)(3,6,8) (4,7,9), (1,5,8,10,4)(2,6,9,3,7)) gap> Orbit(G, [1,8],OnSets); [ [ 1,8 ], [ 3,5 ], [ 5,10 ], [ 2,6 ], [ 7,8 ], [ 2,10 ], [ 4,8 ], [ 6,9 ], [ 3,9 ], [ 1,10 ], [ 4,6 ], [ 3,7 ], [ 4,5 ], [ 1,9 ] The communication between the two packages is established using an OpenMath server. The Gap output ([1..10],[ [ 1,8 ], [ 3,5 ], …”

“…The Gap output ([1..10],[ [ 1,8 ], [ 3,5 ], [ 5,10 ], [ 2,6 ], [ 7,8 ], [ 2,10 ], [ 4,8 ], [ 6,9 ], [ 3,9 ], [ 1,10 ], [ 4,6 ], [ 3,7 ], [ 4,5 ], [ 1,9 ], [ 2,7 ] ]…”

“…In the meantime, the World Wide Web Consortium has published the recommandation for the Mathematical Markup Language (MathML) for describing mathematical notation and capturing both its structure and content [2]. Similarly, the OpenMath Society has endorsed a newer version of the OpenMath standard for representing the semantics of mathematical objects and facilitating the exchange between computer programs, the storage in knowledge bases, and the electronic publication of mathematics [15,11,9].…”

Automatic deduction in (dynamic) geometry: Loci computation

“…This is the reason why the developed Sage worksheet does not accept true/false queries. Other works related to interactive web mathematics and automatic provers using OpenMath include [31,32]. As noted in section 1.3, OpenMath is the standard for representing mathematical objects with their semantics that was taken as basis for the i2g file format.…”