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P-adic algorithm for univariate partial fractions

โœ Scribed by Wang.

Book ID
127399420
Tongue
English
Weight
131 KB
Category
Library

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๐Ÿ“œ SIMILAR VOLUMES

Efficient p-adic Cell Decompositions for
Efficient p-adic Cell Decompositions for Univariate Polynomials
โœ Michael Maller; Jennifer Whitehead ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 177 KB

Cell decompositions are constructed for polynomials f (x) # Z p [x] of degree n, such that n< p, using O(n 2 ) cells. When f is square-free this yields a polynomialtime algorithm for counting and approximating roots in Z p . These results extend to give a polynomial-time algorithm in the bit model f

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A p-adic algorithm for computing the inverse of integer matrices
โœ H. Haramoto; M. Matsumoto ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 270 KB

A method for computing the inverse of an (n ร— n) integer matrix A using p-adic approximation is given. The method is similar to Dixon's algorithm, but ours has a quadratic convergence rate. The complexity of this algorithm (without using FFT or fast matrix multiplication) is O(n 4 (log n) 2 ), the s