Operations of Points on Elliptic Curve in Affine Coordinates
Futa, Yuichi, Okazaki, Hiroyuki, Shidama, Yasunari
Isomorphism between Spaces of Multilinear Maps and Nested Compositions over Real Normed Vector Spaces
Nakasho, Kazuhisa, Futa, Yuichi
Set of Points on Elliptic Curve in Projective Coordinates
Futa, Yuichi, Okazaki, Hiroyuki, Shidama, Yasunari
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
Matrix of ℤ-module1
Futa, Yuichi, Okazaki, Hiroyuki, Shidama, Yasunari
Divisible ℤ-modules
Futa, Yuichi, Shidama, Yasunari
Embedded Lattice and Properties of Gram Matrix
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