The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
The geobucket data structure for polynomials
Journal of Symbolic Computation
Monomial representations for Gröbner bases computations
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
A Subroutine for Computations with Rational Numbers
Journal of the ACM (JACM)
A Sorting Algorithm for Polynomial Multiplication
Journal of the ACM (JACM)
Communications of the ACM
The Altran system for rational function manipulation — a survey
Communications of the ACM
Comparing the speed of programs for sparse polynomial multiplication
ACM SIGSAM Bulletin
ACM SIGSAM Bulletin
Parallel sparse polynomial multiplication using heaps
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Parallel sparse polynomial division using heaps
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Development of TRIP: fast sparse multivariate polynomial multiplication using burst tries
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Polynomial division using dynamic arrays, heaps, and packed exponent vectors
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
Parallel sparse polynomial multiplication using heaps
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Lazy and Forgetful Polynomial Arithmetic and Applications
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Sparse polynomial multiplication and division in Maple 14
ACM Communications in Computer Algebra
Parallel and cache-efficient Hensel lifting
ACM Communications in Computer Algebra
Sparse polynomial powering using heaps
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
A cache-oblivious engineering of the G2V algorithm for computing Gröbner bases
ACM Communications in Computer Algebra
POLY: a new polynomial data structure for Maple 17
ACM Communications in Computer Algebra
On the complexity of multivariate blockwise polynomial multiplication
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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In 1974, Johnson showed how to multiply and divide sparse polynomials using a binary heap. This paper introduces a new algorithm that uses a heap to divide with the same complexity as multiplication. It is a fraction-free method that also reduces the number of integer operations for divisions of polynomials with integer coefficients over the rationals. Heap-based algorithms use very little memory and do not generate garbage. They can run in the CPU cache and achieve high performance. We compare our C implementation of sparse polynomial multiplication and division with integer coefficients to the routines of the Magma, Maple, Pari, Singular and Trip computer algebra systems.