Sparse polynomial division using a heap

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 existing computer algebra systems.

• Type: Journal
• Year: 2011
• Where: JSC
• Authors: Michael B. Monagan, Roman Pearce
• Keywords: Computer Algebra Systems, JSC 2011, Polynomial Multiplication, Sparse Polynomials