Hi Steve, >There have been a number of programs written that were capable of manipulating algebraic formulas, and some to solve isolated equations. There have also been programs to solve simultaneous *linear* equations >via array operations. In the engine I envision, every "formula" would be presumed to equal zero, and hence would be an equation, despite its missing = sign, similar to array operator implementations to solving >simultaneous linear equations. Instead of operators like "addition" or "subtraction", there would be new operators like "union" that would solve a system of simultaneous NONlinear equations, etc.
What are you talking about, solving equations and general algebraic operations algorithms are mathematically solved (for linear ones - for sure), we wouldn't be able to solve them by hand if it was not. One of the *first (some claim it's the first)* electronic computers itself was designed precisely to solve linear equations with 30 unknowns (the ABC, Atanassoff-Berry-Computer), because the other methods were too slow for the needs of John Atanassoff. The computer was conceived in 1937. Vladimir Turchin has written algebraic programs in the 60-ies with his programming language REFAL. http://www.encyclopediaofmath.org/index.php/Refal Functional and Logical Languages in general are somewhat intrinsically "algebraic", unlike procedural like C, which are more "computational/arithmetical". The "Matrix processors", the first "SIMD-MIMD" etc. and multi-processing units devices started with multiplication + addition done much quickly than general purpose computers, because that's a critical operation for scientific computation, which are largely for computation of "matrices" including solving linear equations. With the advent of video cards for PCs, then the GPU, that's now in every PC's GPU with huge parallelism, sometimes capable of many TFLOPS. In computer vision there are such equations for example when triangulating a stereo image into 3D object, and calibrating a camera parameters from taken pictures.I've written a simple program to solve such myself as a student, using the same algorithm as I'd apply manually - Mathematica solves all kinds of algebraic expressions, AFAIK it's done also in one extent or another using REFAL: http://integrals.wolfram.com/index.jsp *--- Todor "Tosh" Arnaudov --* *"Twenkid Research*" - http://research.twenkid.com *Self-Improving General Intelligence Conferenc*e Chair : http://artificial-mind.blogspot.com/2012/07/news-sigi-2012-1-first-sigi-agi.html ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-c97d2393 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-2484a968 Powered by Listbox: http://www.listbox.com
