• Corpus ID: 238583593

On sets of linear forms of maximal complexity

@article{Kaminski2021OnSO,
  title={On sets of linear forms of maximal complexity},
  author={Michael Kaminski and Igor E. Shparlinski and Michel Waldschmidt},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.04657}
}
We present a uniform description of sets of m linear forms in n variables over the field of rational numbers whose computation requires m(n− 1) additions. 

Figures from this paper

References

SHOWING 1-10 OF 14 REFERENCES
Sets of Linear Forms Which Are Hard to Compute
TLDR
This work presents a uniform description of sets of m linear forms in n variables over the field of rational numbers whose computation requires m(n − 1) additions and an effective form of the Lindemann–Weierstrass theorem.
Mathematics for computer algebra
TLDR
This textbook deals with arithmetical operations on large integers and elementary results in number theory and describes the factorization of polynomials with integer coefficients.
An Algorithm for the Computation of Linear Forms
  • J. Savage
  • Mathematics, Computer Science
    SIAM J. Comput.
  • 1974
TLDR
An algorithm is presented here which implies that every polynomial of degree n with at most s distinct coefficients can be realized with O(n/\log _s n) operations.
Integral Points of Small Height Outside of a Hypersurface
Abstract.Let F be a non-zero polynomial with integer coefficients in N variables of degree M. We prove the existence of an integral point of small height at which F does not vanish. Our basic bound
Vermeidung von Divisionen.
The extent to whieh the use of divisions may speed up the evaluation of polynomials is estimated from above. In particular it is shown that for multiplying general matrices the use of divisions does
The Design and Analysis of Computer Algorithms
TLDR
This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
Algebraic Complexity Theory
  • V. Strassen
  • Mathematics, Computer Science
    Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity
  • 1990
TLDR
This chapter discusses algebraic complexity theory, which unites two quite different traditions, that of straight-line program or arithmetic circuit or computation sequence and that of computation tree.
Computational Commutative and Non-Commutative Algebraic Geometry
This publication gives a good insight in the interplay between commutative and non-commutative algebraic geometry. The theoretical and computational aspects are the central theme in this study. The
The Design and Analysis of Computer Algorithms
TLDR
This course presents fundamental techniques for designing efficient computer algorithms, proving their correctness, and analyzing their performance in graph algorithms.
Algebra, I, Die Grundlagen
...
1
2
...