Operations of Points on Elliptic Curve in Projective Coordinates
Futa, Yuichi, Okazaki, Hiroyuki, Mizushima, Daichi, Shidama, Yasunari
Gaussian Integers
Futa, Yuichi, Okazaki, Hiroyuki, Mizushima, Daichi, Shidama, Yasunari
Torsion Z-module and Torsion-free Z-module
Futa, Yuichi, Okazaki, Hiroyuki, Nakasho, Kazuhisa, Shidama, Yasunari
Divisible ℤ-modules
Futa, Yuichi, Shidama, Yasunari
Dual Lattice of ℤ-module Lattice
Futa, Yuichi, Shidama, Yasunari
Isomorphism Theorem on Vector Spaces over a Ring
Futa, Yuichi, Shidama, Yasunari
Implicit Function Theorem. Part I
Nakasho, Kazuhisa, Futa, Yuichi, Shidama, Yasunari
Maximum Number of Steps Taken by Modular Exponentiation and Euclidean Algorithm
Okazaki, Hiroyuki, Nagao, Koh-ichi, Futa, Yuichi
Polynomially Bounded Sequences and Polynomial Sequences
Okazaki, Hiroyuki, Futa, Yuichi
Inverse Function Theorem. Part I1
Nakasho, Kazuhisa, Futa, Yuichi
Isomorphism between Spaces of Multilinear Maps and Nested Compositions over Real Normed Vector Spaces
Nakasho, Kazuhisa, Futa, Yuichi
Z-modules
Futa, Yuichi, Okazaki, Hiroyuki, Shidama, Yasunari