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
Topological Properties of Real Normed Space
Nakasho, Kazuhisa, Futa, Yuichi, Shidama, Yasunari
Matrix of ℤ-module1
Futa, Yuichi, Okazaki, Hiroyuki, Shidama, Yasunari
Quotient Module of Z-module
Futa, Yuichi, Okazaki, Hiroyuki, Shidama, Yasunari
Embedded Lattice and Properties of Gram Matrix
Futa, Yuichi, Shidama, Yasunari
Torsion Z-module and Torsion-free Z-module
Futa, Yuichi, Okazaki, Hiroyuki, Nakasho, Kazuhisa, Shidama, Yasunari
Formalization of Integral Linear Space
Futa, Yuichi, Okazaki, Hiroyuki, Shidama, Yasunari