Algorithms for computer algebra
Algorithms for computer algebra
Monomial representations for Gröbner bases computations
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
A Fixed Point Method for Power Series Computation
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Infinite structures in SCRATCHPAD II
EUROCAL '87 Proceedings of the European Conference on Computer Algebra
Journal of Symbolic Computation
ACM SIGSAM Bulletin
Sparse polynomial division using a heap
Journal of Symbolic Computation
Polynomial division using dynamic arrays, heaps, and packed exponent vectors
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
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We present lazy and forgetful algorithms for multiplying and dividing multivariate polynomials. The lazy property allows us to compute the i -th term of a polynomial without doing the work required to compute all the terms. The forgetful property allows us to forget earlier terms that have been computed to save space. For example, given polynomials A ,B ,C ,D ,E we can compute the exact quotient $Q = \frac{A \times B - C \times D}{E}$ without explicitly computing the numerator A ×B *** C ×D which can be much larger than any of A ,B ,C ,D ,E and Q . As applications we apply our lazy and forgetful algorithms to reduce the maximum space needed by the Bareiss fraction-free algorithm for computing the determinant of a matrix of polynomials and the extended Subresultant algorithm for computing the inverse of an element in a polynomial quotient ring.