繁體中文: Observe the field
繁體中文: We collect decisions from spreadsheets, paper, conversations, and experienced staff. Exceptions and hidden priorities are part of the actual operation.
繁體中文: INPUT / Current workCOMPANY & ORIGIN
繁體中文: Turn mathematics into
繁體中文: software that works
繁體中文: in the field.
繁體中文: Finite Field is named after the mathematical structure known as a finite field. We organize complex conditions into consistent models and implement them as web and app systems people can use every day.
- FOUNDED
- 繁體中文: January 6, 2022
- BASE
- 繁體中文: Usa City, Oita Prefecture
- FOCUS
- 繁體中文: From mathematical models to web and apps
INTERACTIVE / PRIME FIELDF5
2 x 3 = 6F5: 1
Legal nameFinite Field, K.K.
Business focus繁體中文: Mathematical systems development
Canonical page繁體中文: The new company profile is handled at /about/.
繁體中文: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
WHY WE EXIST
繁體中文: Before building, make the problem solvable.
繁體中文: Operational problems do not start as formulas. We first turn human judgment, exceptions, and implicit priorities into conditions and objectives that can be compared.
繁體中文: Separate constraints and goals
繁體中文: We separate hard constraints from indicators to improve, making contradictions and missing data visible before calculation.
繁體中文: MODEL / Constraints and evaluation繁體中文: Implement a usable system
繁體中文: We do not stop at a calculation result. Input, review, correction, and sharing are implemented as web and mobile apps.
繁體中文: OUTPUT / Operating system
OUR PURPOSE
繁體中文: We use mathematics to organize ambiguous judgment into systems that can be compared, explained, and used.
THE NAME
繁體中文: Finite Field means a finite mathematical field.
繁體中文: A finite field is a mathematical structure with a finite number of elements where addition, subtraction, multiplication, and division except by zero are defined. It is important in cryptography, error-correcting codes, and computer science.
DEFINITION / PLAIN LANGUAGE
繁體中文: Limited elements. Consistent rules. Results that stay inside the set.
繁體中文: In F5, the elements are 0, 1, 2, 3, and 4. After ordinary calculation, the remainder modulo 5 is used. That is why 2 × 3 becomes 1 rather than 6.
01繁體中文: Finite elements
繁體中文: The number of elements is a prime or a power of a prime.
02繁體中文: Closed under operations
繁體中文: Results return to elements in the same field.
03繁體中文: Inverses exist
繁體中文: Every nonzero element has a multiplicative inverse.
繁體中文: Important
繁體中文: This does not mean that business operations are literally finite fields. The connection here is a company metaphor for how we work.
INTERACTIVE / PRIME FIELD
F5繁體中文: Try finite-field calculation
+
=
繁體中文: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
繁體中文: See limited resources
繁體中文: People, time, vehicles, machines, and budget. We search for plans that can actually run within real limits.
繁體中文: Make rules consistent
繁體中文: We organize business rules including exceptions so contradictions and priorities can be reviewed.
繁體中文: Make results reproducible
繁體中文: The path from inputs, constraints, and evaluation to the result should not depend only on one person’s intuition.
WHAT WE DO
繁體中文: From mathematical models to business screens.
繁體中文: We are not only a mathematical consulting team, and not only a general contract developer. We design the decision logic and the software used every day as one system.
01 / MODEL
MATHEMATICAL MODEL
01 / MODEL繁體中文: What must be kept and what should improve
繁體中文: We organize constraints, objectives, priorities, exceptions, and feasibility.
02 / SOLVE
ALGORITHM
02 / SOLVE繁體中文: Search and compare candidates
繁體中文: Optimization, search, rules, and simulation are combined when appropriate.
03 / BUILD
PRODUCT ENGINEERING
03 / BUILD繁體中文: Enter, adjust, and share in the field
繁體中文: Web, iOS, Android, databases, permissions, and reports are implemented together.
INPUT
OUTPUT
OPERATING PRINCIPLES
繁體中文: Be honest before being mathematical.
繁體中文: We do not hide problems behind advanced terms or complex models. We separate what is unknown, not yet measured, and dependent on conditions.
繁體中文: Start with field language
繁體中文: We listen to actual work, decisions, and exceptions before applying terminology. A model is useful only when it explains the field.
繁體中文: Field to conditions繁體中文: Results with reasons
繁體中文: We do not stop at “the AI decided.” We show why a plan was chosen and what could not be satisfied.
繁體中文: Result to evidence繁體中文: Verify small before growing
繁體中文: Before production, we test the calculation on a small portion of real data. Reasons it cannot be solved are also findings.
繁體中文: Hypothesis to verification繁體中文: Implement usability too
繁體中文: We design for input, correction, smartphone use, and multilingual operation, not only calculation speed.
繁體中文: Logic to adoptionWE SAY繁體中文: Organize conditions and create comparable plans
WE SHOW繁體中文: Inputs, constraints, evaluation, and unresolved points
WE DO NOT CLAIM繁體中文: Absolutely no bugs or always one unique optimum
COMPANY JOURNEY
繁體中文: Deepening from implementation strength into mathematics.
繁體中文: Experience building business systems, mobile apps, and multilingual services connects to planning, assignment, search, and verification.
2022.01.06FOUNDATION
FOUNDATION
繁體中文: Finite Field, K.K. established
繁體中文: Established in Usa City, Oita Prefecture, with a foundation for planning, building, and operating web, app, and business systems.
BUILDIMPLEMENTATION
NOWMATHEMATICAL SYSTEMS
MATHEMATICAL SYSTEMS
繁體中文: Toward automation of planning and assignment
繁體中文: Shift planning, visit scheduling, routing, production planning, and assignment matching are now presented as core mathematical-systems domains.
R&DVERIFY
FROM CODE TO FIELD
繁體中文: Show working assets, not only philosophy.
繁體中文: A company page alone is not enough to judge capability. Demos, business screens, case studies, and security policies are available before consultation.
01 / DEMO
繁體中文: Mathematical demos
繁體中文: Change conditions and review results and unresolved points.
繁體中文: Try 02 / CASES繁體中文: Case studies
繁體中文: Implemented functions and confirmed changes are separated.
繁體中文: Read 03 / SECURITY繁體中文: Data handling
繁體中文: Receipt, retention, external AI, deletion, and responsibility are explained.
繁體中文: Check 04 / RESEARCHMath Lab
繁體中文: Research-stage technology is separated from completed products.
繁體中文: ViewCOMPANY PROFILE
Finite Field, K.K.
繁體中文: Based in Usa City, Oita Prefecture, we design and build mathematical models, algorithms, web systems, and mobile apps.
BASE / JAPAN繁體中文: Usa City, Oita Prefecture
FINITE FIELD繁體中文: Usa City, Oita Prefecture
BASE / JAPAN
繁體中文: From a regional base, we use software to address complex operational problems.
- 繁體中文: Legal name
- Finite Field, K.K. / 株式会社ファイナイトフィールド
- 繁體中文: Japanese name
- 株式会社ファイナイトフィールド
- 繁體中文: Address
- 日本 879-0151 大分縣宇佐市宮熊550
- 繁體中文: Established
- 繁體中文: January 6, 2022
- 繁體中文: Capital
- 繁體中文: JPY 3,000,000
- 繁體中文: Officers
- 代表董事 Toshiya Kazuyoshi 董事 Yoshie Kazuyoshi 董事 Hikaru Ono
- 繁體中文: Major client
- Matsuhisa Japan Co., Ltd.
- 繁體中文: Business domains
- 繁體中文: Mathematical systems development Web and mobile app development Business systems and R&D
INFORMATION POLICY
繁體中文: Only information aligned with official company facts is shown. Unconfirmed employee count, sales, certification status, and similar claims are not listed.
PAGE DATA REVIEWED / 2026.06FAQ
繁體中文: About the company and the name
繁體中文: A short explanation of the relationship between a mathematical term and the actual service.
01繁體中文: What is a finite field?
繁體中文: A finite field is a mathematical structure with a finite number of elements. Addition, subtraction, multiplication, and division except by zero are defined, and the result stays inside the same set. This page visualizes prime fields Fp for prime p.
02繁體中文: How does the name relate to business systems?
繁體中文: It does not mean that business operations are literally finite fields. The name reflects how we work with limited resources, consistent rules, and reproducible results.
03繁體中文: Can we start with a mathematical consultation only?
繁體中文: Yes. We can begin by checking whether operational judgments, assignments, orders, and plans can be modeled. A small calculation prototype can verify the idea first.
04繁體中文: Can you develop the actual system too?
繁體中文: Yes. We design and build mathematical models, calculation logic, databases, web admin screens, and iOS and Android apps as one delivery path.
START WITH THE PROBLEM
繁體中文: What does your team think through every time?
繁體中文: Shifts, visits, routes, production, and assignments. We start from your current spreadsheets and rules to identify what can be modeled.