P. Burgisser, M. Clausen, and M.A. Shokrollahi. Algebraic Complexity Theory, volume 315 of Grundlehren der Mathematischen Wissenschaften. Springer Verlag, Heidelberg, 1996. M. A. Shokrollahi Home/Search Document Not in Database Summary Related Articles Check |
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Uniform Bounds for the Number of Rational Points of.. - Gaudry, Kulesz.. (2001) (Correct)
....and curves of genus 1 with a rational point are elliptic curves (see Section 2) Problem (i) and (ii) are related to the use of arithmetic circuits as data structures in computer science. Arithmetic circuits have been extensively used to modelize algebraic computations (see e.g. Par95] or [BCS97] In particular, the use of arithmetic circuits as data structures has been proved to be very useful for the design of ecient algorithms for the solution of multivariate parametric polynomial equation systems (see e.g. KP96] GHM 98] GHH 97] HKP 00] The general context of ....
....Find a short circuit with rational parameters which evaluates the polynomial f . It is well known that the vector of coecients of a univariate polynomial f 2 Q[Y ] of degree d represented by an arithmetic circuit of lenght L belongs to a Q de nable algebraic variety of C L O(1) see e.g. BCS97] Therefore, our problem can be easily restated as the search for a rational solution of a suitable algebraic variety of C L O(1) The existence of an arithmetic circuit of length L representing the given polynomial f is then equivalent to the existence of a rational solution of a suitable ....
P. Burgisser, M. Clausen, and M.A. Shokrollahi. Algebraic Complexity Theory, volume 315 of Grundlehren der mathematischen Wissenschaften. Springer, Berlin Heidelberg New York, 1997.
The Complexity of Tensor Calculus - Damm, Holzer, McKenzie (2000) (1 citation) (Correct)
....of the field (unless some of the classes coincide or some inclusions hold) On the other hand, Hastad [23] has shown that computing the rank of a tensor is at least as hard as NP regardless of the field s characteristic. Tensor rank, which is a central notion in algebraic complexity theory (see [12]) is a natural generalization of matrix rank. However, while matrix rank can be expressed efficiently in matrix calculus [28] Hastad s result together with the characterizations from Section 5 tells us that tensor rank cannot be expressed efficiently in tensor calculus. ....
P. Burgisser, M. Clausen, and M. A. Shokrollahi. Algebraic Complexity Theory, volume 315 of Grundlehren Der Mathematischen Wissenschaften. Springer Verlag, 1997.
Counting Prime Divisors on Elliptic Curves - And Multiplication In Self-citation (Shokrollahi) (Correct)
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P. Burgisser, M. Clausen, and M.A. Shokrollahi. Algebraic Complexity Theory, volume 315 of Grundlehren der Mathematischen Wissenschaften. Springer Verlag, Heidelberg, 1996. M. A. Shokrollahi
Computing Roots of Polynomials over - Function Fields Of Self-citation (Shokrollahi) (Correct)
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P. Burgisser, M. Clausen, and M.A. Shokrollahi. Algebraic Complexity Theory, volume 315 of Grundlehren der Mathematischen Wissenschaften. Springer Verlag, Heidelberg, 1996.
Fast and Precise Computations of Discrete Fourier.. - Buhler, Shokrollahi.. (1997) (1 citation) Self-citation (Shokrollahi) (Correct)
....p. The total complexity is therefore O(Ld log(d)M(log(b) b= log(b) O(b 1 ffl L) The second Chinese remainder step involves a Chinese remainder computation on r primes of length O(log(b) for each of the L components. Using fast Chinese remaindering techniques as described in [1] or in [2], we obtain a running time of O(b 2 ffl L) O(b 1 ffl L log(L) for this step. At this stage of the algorithm we have obtained a vector of length L whose entries are integral linear combinations of powers of i with coefficients bounded by M in absolute value. For each of these entries we ....
P. Burgisser, M. Clausen, and A. Shokrollahi: Algebraic Complexity Theory, Volume 315 of Grundlehren der mathematischen Wissenschaften, Springer-Verlag, 1996.
Relative Class Number of Imaginary Abelian Fields of Prime.. - Shokrollahi (1998) Self-citation (Shokrollahi) (Correct)
....at (p Gamma 1)st roots of unity. This result is essentially due to Kummer. The very heart of our approach is a novel algorithm for evaluating this polynomial modulo a prime q at (p Gamma 1)st roots of unity. Our algorithm is based on the multiple evaluation algorithm of Borodin and Moenck [3, 5]. However, we are able to use prime divisors of (p Gamma 1) to considerably accelerate the computations. The very same method has been successfully used to compute all irregular primes below 8 million [32, 31, 4] The multiple evaluation algorithm will be applied to several primes q. Chinese ....
P. Burgisser, M. Clausen, and M.A. Shokrollahi. Algebraic Complexity Theory, volume 315 of Grundlehren der Mathematischen Wissenschaften. Springer Verlag Heidelberg, 1996.
Counting Prime Divisors on Elliptic Curves and Multiplication.. - Shokrollahi Self-citation (Shokrollahi) (Correct)
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P. Burgisser, M. Clausen, and M.A. Shokrollahi. Algebraic Complexity Theory, volume 315 of Grundlehren der Mathematischen Wissenschaften. Springer Verlag, Heidelberg, 1996. M. A. Shokrollahi
Computing Roots of Polynomials over Function Fields of Curves - Gao, Shokrollahi (1999) (7 citations) Self-citation (Shokrollahi) (Correct)
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P. Burgisser, M. Clausen, and M.A. Shokrollahi. Algebraic Complexity Theory, volume 315 of Grundlehren der Mathematischen Wissenschaften. Springer Verlag, Heidelberg, 1996.
Computing Roots Of Polynomials Over Function Fields Of Curves - Gao, Shokrollahi (1998) (7 citations) Self-citation (Shokrollahi) (Correct)
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P. Burgisser, M. Clausen, and M.A. Shokrollahi. Algebraic Complexity Theory, volume 315 of Grundlehren der Mathematischen Wissenschaften. Springer Verlag, Heidelberg, 1996.
Decoding Algebraic-Geometric Codes Beyond the.. - Shokrollahi, Wasserman (1998) (16 citations) Self-citation (Shokrollahi) (Correct)
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P. Burgisser, M. Clausen, and M.A. Shokrollahi. Algebraic Complexity Theory, volume 315 of Grundlehren der Mathematischen Wissenschaften. Springer Verlag, Heidelberg, 1996.
On the Complexity of Polynomial Matrix Computations - Giorgi, Jeannerod, Villard (2003) (Correct)
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P. Burgisser, M. Clausen, and M.A. Shokrollahi. Algebraic Complexity Theory, volume 315 of Grundlehren der mathematischen Wissenschaften. Springer-Verlag, 1997.
Lifting Procedures for Ramified Fibers and.. - Bompadre, Matera, .. (Correct)
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P. Burgisser, M. Clausen, and M.A. Shokrollahi. Algebraic Complexity Theory, volume 315 of Grundlehren der mathematischen Wissenschaften. Springer, Berlin Heidelberg New York, 1997.
On the Time-Space Complexity of Geometric Elimination.. - Heintz, Matera, Waissbein (1999) (6 citations) (Correct)
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P. Burgisser, M. Clausen, and M. Amin Shokrollahi. Algebraic Complexity Theory, volume 315 of Grundlehren der mathematischen Wissenschaften. Springer--Verlag, 1997.
The Hardness of Polynomial Equation Solving - Castro, Giusti, Heintz.. (2003) (Correct)
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P. Burgisser, M. Clausen, and M.A. Shokrollahi. Algebraic Complexity Theory, volume 315 of Grundlehren der mathematischen Wissenschaften. Springer, Berlin Heidelberg New York, 1997.
On the Complexity of Polynomial Matrix Computations - Giorgi, Jeannerod (2003) (Correct)
No context found.
P. Burgisser, M. Clausen, and M.A. Shokrollahi. Algebraic Complexity Theory, volume 315 of Grundlehren der mathematischen Wissenschaften. Springer-Verlag, 1997.
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