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Present computer algebra systems base their interactive sessions on a very simple model of mathematical discourse. The user's input to the system is a line containing a mathematical expression (an operation, a formula, a set of equations, etc) and the system's response to the user is an output...
The recent years have seen the development of automatic methods for the resolution of nonlinear equations systems. The standard numerical approach, when faced with a nonlinear equation system, is to solve it by Newton-Raphson method, that requires the expensive calculation of the Jacobian matrix...
In this paper, a new simple AI language is described, which ties up Logic Programming and Algebraic Programming concepts, and, to our mind, may take the same place in the AI languages family as Basic language --- in the conventional programming languages family.The main (and slightly unusual for...
Let A, B , and Q be multivariate polynomials satisfying A = QB. Given A and B , we can calculate Q by recursive multivariate power-series division. In this division some higher degree terms of A and B are not needed at all. A simple and useful degree bound for the significant terms of A and B is...
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