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We propose a new search algorithm to solve the equation x3+y3 + z3 = n for a fixed value of n > 0. By parametrizing |x| =min(|x|, |y|, |z|), this algorithm obtains |y| and |z| (if they exist) byâ€¦ (More)

- Yumi Nakajima, Yasuhito Kawano, Hiroshi Sekigawa
- Quantum Information & Computation
- 2006

We provide a new algorithm that translates a unitary matrix into a quantum circuit according to the G = KAK theorem in Lie group theory. With our algorithm, any matrix decomposition corresponding toâ€¦ (More)

- Kiyoshi Shirayanagi, Hiroshi Sekigawa
- Theor. Comput. Sci.
- 2008

We propose a new method for converting a GrÃ¶bner basis w.r.t. one term order into a GrÃ¶bner basis w.r.t. another term order by using the algorithm stabilization techniques proposed by Shirayanagi andâ€¦ (More)

- Hiroshi Sekigawa
- ISSAC
- 2007

For a real multivariate interval polynomial <i>P</i> and a real multivariate polynomial <i>f</i>, we provide a rigorous method for deciding whether there exists a polynomial <i>p</i> in <i>P</i> suchâ€¦ (More)

- Hiroshi Sekigawa, Kiyoshi Shirayanagi
- Mathematics in Computer Science
- 2007

Given a univariate complex interval polynomial F , we provide a rigorous method for deciding whether there exists a pseudozero of F in a prescribed closed complex domain D. Here a pseudozero of F isâ€¦ (More)

- Pramook Khungurn, Hiroshi Sekigawa, Kiyoshi Shirayanagi
- ISSAC
- 2007

Shirayanagi and Sweedler proved that a large class of algorithms over the reals can be modified slightly so that they also work correctly on fixed-precision oating-point numbers. Their main theoremâ€¦ (More)

- Hiroshi Sekigawa, Kiyoshi Shirayanagi
- ISSAC
- 2006

For a real interval polynomial <i>F</i>, we provide a rigorous method for deciding whether there exists a polynomial in <i>F</i> that has a multiple zero in a prescribed interval in <i>R</i>. We showâ€¦ (More)

This article explains the technologies and applications of lossless audio coding. NTT started research on lossless coding of audio signals and proposed the initiation of international standardizationâ€¦ (More)

- Kiyoshi Shirayanagi, Hiroshi Sekigawa
- SNC
- 2009

For a certain class of algebraic algorithms, we propose a new method that reduces the number of exact computational steps needed for obtaining exact results. This method is the floating-pointâ€¦ (More)

- Hiroshi Sekigawa, Kenji Koyama
- Math. Comput.
- 1999

We obtain nonexistence conditions of a solution for of the congruence x1 + Â· Â· Â· + xs â‰¡ N (mod pn), where k â‰¥ 2, s â‰¥ 2 and N are integers, and pn is a prime power. We give nonexistence conditions ofâ€¦ (More)