scholarly journals Computer Algebra Recipes for Mathematical Physics

2005 ◽  
Keyword(s):  
Computer Algebra ◽  
Mathematical Physics

Dodgson condensation, alternating signs and square ice

2006 ◽  
Vol 364 (1849) ◽  
pp. 3183-3198 ◽  
Author(s):  
Andrew N.W Hone
Keyword(s):  
Number Theory ◽  
Computer Algebra ◽  
Statistical Physics ◽  
Mathematical Physics ◽  
Algebraic Combinatorics ◽  
General Scientific ◽  
Dodgson Condensation

Starting with the numbers 1,2,7,42,429,7436, what is the next term in the sequence? This question arose in the area of mathematics called algebraic combinatorics, which deals with the precise counting of sets of objects, but it goes back to Lewis Carroll's work on determinants. The resolution of the problem was only achieved at the end of the last century, and with two completely different approaches: the first involved extensive verification by computer algebra and a huge posse of referees, while the second relied on an unexpected connection with the theory of ‘square ice’ in statistical physics. This paper, aimed at a general scientific audience, explains the background to this problem and how subsequent developments are leading to a fruitful interplay between algebraic combinatorics, mathematical physics and number theory.

Solving some problems of algebra, analysis, and mathematical physics using computer algebra systems

Cybernetics ◽  
1991 ◽  
Vol 27 (2) ◽  
pp. 189-198
Author(s):  
N. M. Glazunov ◽  
F. G. Karpinskii ◽  
V. V. Kornyak
Keyword(s):  
Computer Algebra ◽  
Mathematical Physics ◽  
Computer Algebra Systems

Variational Principles in Mathematical Physics, Geometry, and Economics

2009 ◽  
Author(s):  
Alexandru Kristaly ◽  
Vicentiu D. Radulescu ◽  
Csaba Varga
Keyword(s):  
Variational Principles ◽  
Mathematical Physics
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