Modern computer algebra

By Joachim von zur Gathen, Jürgen Gerhard. SIGA, 2002

2,117 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/8d94ef5c931ca436fa67155faa0b09dfbe0fd68b

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Citations in the corpus

A unified approach to solving the harmonic elimination equations in multilevel converters (2004, methodology): “In contrast to iterative methods, the approach here is based on solving polynomial equations using the theory of resultants which produces all possible solutions [8], [ 13 ].”
Identifying the Matrix Ring: Algorithms for Quaternion Algebras and Quadratic Forms (2010, background): “A domain R which is the localization of a ring which is finitely generated over its prime ring is computable by the theory of Gröbner bases [13].”
A new approach to solving the harmonic elimination equations for a multilevel converter (2003, methodology): “Previous work in [1][2] has shown that the transcendental equations characterizing the harmonic content can be converted into polynomial equations which are then solved using the method of resultants from elimination theory [3][4].”
A New Algorithm for Decoding Reed-Solomon Codes (2003, methodology): “Fortunately, all these operations can be computed via fast Fourier transforms (FFT) (see for instance [ 7 ]).”
HEPCloud: An FPGA-Based Multicore Processor for FV Somewhat Homomorphic Function Evaluation (2018, methodology): “The reduction of the result modulo f(x) follows the Newton iteration method Newton iteration method [39].”
Succinct Non-Interactive Zero Knowledge Arguments from Span Programs and Linear Error-Correcting Codes (2013, methodology): “If d is a power of 2 and rj = ω j d, where ωd is the dth primitive root of unity, then both operations can be done in time O(d log d) by using Fast Fourier Transform [12].”
Unconditionally Secure Constant Round Multi-Party Computation for Equality, Comparison, Bits and Exponentiation (2006, background): “The coecien ts of i(X) only depend on the set P and on the modulus q. Computing the coecien ts of F (X) takes O(k2d log2 d log log d) bit operations [ GG99 , Chap.10].”
Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data (2004, methodology): “Each convolution can be performed asymptotically in time O ( δ log δ log log δ ) (see, e.g., [vzGG03]), and the total time required to ﬁnd σ gets reduced to O ( δ log 2 δ log log δ ) operation in F .”
Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes (2010, background): “15 of [6]) that the polynomials S and T are given by S = ∑N−1 i=0 six i and T = ∑M−1 i=0 tix , where the si and ti are the solutions of”
High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams (2004, background): “Step 1 discards trinomials that are squares (see Theorem 4.1 below).”
The Use of Power Sums to Solve the Harmonic Elimination Equations for Multilevel Converters (2005, methodology): “, elimi-nating x2 (See [14-15] for a discussion of elimination theory and resultants).”
A fast isomorphism test for groups whose Lie algebra has genus 2 (2017, methodology): “We refer the reader to [vzGG] for further information on these matters.”