Practical fast polynomial multiplication
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Sparse polynomial powering using heaps
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
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Methods are presented for taking powers of symbolic polynomials and substituting them into univariate polynomials with scalar coefficients. It is shown that the size of the result is a sharp lower bound on the number of coefficient multiplications required to raise a completely sparse polynomial to a power. Other theoretical results prove the optimality or near-optimality of the methods given, in terms of numbers of coefficient operations, under the condition of complete sparsity of the argument.