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Automatic understanding of the intended meaning of computer programs is a very hard problem, requiring intelligence and reasoning. In this abstract we discuss a new method for program analysis, called symbol elimination. Symbol elimination uses first-order theorem proving techniques to automatically discover non-trivial program properties, such as loop invariants and loop bounds. Moreover, symbol...
The Inverse matrix of Vandermonde Matrix has been considered to be one of the key components of symbolic computation. In this paper, based on the linear equations theory, a constructive proof of the Lagrange interpolation formula has been given. In the inference process, solving the inverse matrix of Vandermonde matrix is a key point. And then, using the generalized Yang Hui triangle theory, an explicit...
Computational methods for manipulating sets of polynomial equations are becoming of greater importance due to the use of polynomial in various applications. Dixon resultant algorithm provides one of the most efficient methods for solving the system of polynomial equations or eliminating variables. When computing Dixon resultant, we first construct the Dixon polynomial for input polynomial system....
Earlier work has presented algorithms to factor and compute GCDs of symbolic Laurent polynomials, that is multivariate polynomials whose exponents are themselves integer-valued polynomials. This article extends the notion of univariate polynomial decomposition to symbolic polynomials and presents an algorithm to compute these decompositions. For example, the symbolic polynomial f(X) = 2Xn2+n - 4X...
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