Українська: Observe the field
Українська: We collect decisions from spreadsheets, paper, conversations, and experienced staff. Exceptions and hidden priorities are part of the actual operation.
Українська: INPUT / Current workCOMPANY & ORIGIN
Українська: Turn mathematics into
Українська: software that works
Українська: in the field.
Українська: 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
- Українська: January 6, 2022
- BASE
- Українська: Usa City, Oita Prefecture
- FOCUS
- Українська: From mathematical models to web and apps
INTERACTIVE / PRIME FIELDF5
2 x 3 = 6F5: 1
Legal nameFinite Field, K.K.
Business focusУкраїнська: Mathematical systems development
Canonical pageУкраїнська: The new company profile is handled at /about/.
Українська: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
WHY WE EXIST
Українська: Before building, make the problem solvable.
Українська: Operational problems do not start as formulas. We first turn human judgment, exceptions, and implicit priorities into conditions and objectives that can be compared.
Українська: Separate constraints and goals
Українська: We separate hard constraints from indicators to improve, making contradictions and missing data visible before calculation.
Українська: MODEL / Constraints and evaluationУкраїнська: Implement a usable system
Українська: We do not stop at a calculation result. Input, review, correction, and sharing are implemented as web and mobile apps.
Українська: OUTPUT / Operating system
OUR PURPOSE
Українська: We use mathematics to organize ambiguous judgment into systems that can be compared, explained, and used.
THE NAME
Українська: Finite Field means a finite mathematical field.
Українська: 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
Українська: Limited elements. Consistent rules. Results that stay inside the set.
Українська: 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.
01Українська: Finite elements
Українська: The number of elements is a prime or a power of a prime.
02Українська: Closed under operations
Українська: Results return to elements in the same field.
03Українська: Inverses exist
Українська: Every nonzero element has a multiplicative inverse.
Українська: Important
Українська: 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
F5Українська: Try finite-field calculation
+
=
Українська: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
Українська: See limited resources
Українська: People, time, vehicles, machines, and budget. We search for plans that can actually run within real limits.
Українська: Make rules consistent
Українська: We organize business rules including exceptions so contradictions and priorities can be reviewed.
Українська: Make results reproducible
Українська: The path from inputs, constraints, and evaluation to the result should not depend only on one person’s intuition.
WHAT WE DO
Українська: From mathematical models to business screens.
Українська: 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 / MODELУкраїнська: What must be kept and what should improve
Українська: We organize constraints, objectives, priorities, exceptions, and feasibility.
02 / SOLVE
ALGORITHM
02 / SOLVEУкраїнська: Search and compare candidates
Українська: Optimization, search, rules, and simulation are combined when appropriate.
03 / BUILD
PRODUCT ENGINEERING
03 / BUILDУкраїнська: Enter, adjust, and share in the field
Українська: Web, iOS, Android, databases, permissions, and reports are implemented together.
INPUT
OUTPUT
OPERATING PRINCIPLES
Українська: Be honest before being mathematical.
Українська: We do not hide problems behind advanced terms or complex models. We separate what is unknown, not yet measured, and dependent on conditions.
Українська: Start with field language
Українська: We listen to actual work, decisions, and exceptions before applying terminology. A model is useful only when it explains the field.
Українська: Field to conditionsУкраїнська: Results with reasons
Українська: We do not stop at “the AI decided.” We show why a plan was chosen and what could not be satisfied.
Українська: Result to evidenceУкраїнська: Verify small before growing
Українська: Before production, we test the calculation on a small portion of real data. Reasons it cannot be solved are also findings.
Українська: Hypothesis to verificationУкраїнська: Implement usability too
Українська: We design for input, correction, smartphone use, and multilingual operation, not only calculation speed.
Українська: Logic to adoptionWE SAYУкраїнська: Organize conditions and create comparable plans
WE SHOWУкраїнська: Inputs, constraints, evaluation, and unresolved points
WE DO NOT CLAIMУкраїнська: Absolutely no bugs or always one unique optimum
COMPANY JOURNEY
Українська: Deepening from implementation strength into mathematics.
Українська: Experience building business systems, mobile apps, and multilingual services connects to planning, assignment, search, and verification.
2022.01.06FOUNDATION
FOUNDATION
Українська: Finite Field, K.K. established
Українська: Established in Usa City, Oita Prefecture, with a foundation for planning, building, and operating web, app, and business systems.
BUILDIMPLEMENTATION
NOWMATHEMATICAL SYSTEMS
MATHEMATICAL SYSTEMS
Українська: Toward automation of planning and assignment
Українська: Shift planning, visit scheduling, routing, production planning, and assignment matching are now presented as core mathematical-systems domains.
R&DVERIFY
FROM CODE TO FIELD
Українська: Show working assets, not only philosophy.
Українська: A company page alone is not enough to judge capability. Demos, business screens, case studies, and security policies are available before consultation.
01 / DEMO
Українська: Mathematical demos
Українська: Change conditions and review results and unresolved points.
Українська: Try 02 / CASESУкраїнська: Case studies
Українська: Implemented functions and confirmed changes are separated.
Українська: Read 03 / SECURITYУкраїнська: Data handling
Українська: Receipt, retention, external AI, deletion, and responsibility are explained.
Українська: Check 04 / RESEARCHMath Lab
Українська: Research-stage technology is separated from completed products.
Українська: ViewCOMPANY PROFILE
Finite Field, K.K.
Українська: Based in Usa City, Oita Prefecture, we design and build mathematical models, algorithms, web systems, and mobile apps.
BASE / JAPANУкраїнська: Usa City, Oita Prefecture
FINITE FIELDУкраїнська: Usa City, Oita Prefecture
BASE / JAPAN
Українська: From a regional base, we use software to address complex operational problems.
- Українська: Legal name
- Finite Field, K.K. / 株式会社ファイナイトフィールド
- Українська: Japanese name
- 株式会社ファイナイトフィールド
- Українська: Address
- 879-0151 Oita, Usa, Miyaguma 550, Японія
- Українська: Established
- Українська: January 6, 2022
- Українська: Capital
- Українська: JPY 3,000,000
- Українська: Officers
- Представницький директор Toshiya Kazuyoshi Посадова особа Yoshie Kazuyoshi Посадова особа Hikaru Ono
- Українська: Major client
- Matsuhisa Japan Co., Ltd.
- Українська: Business domains
- Українська: Mathematical systems development Web and mobile app development Business systems and R&D
INFORMATION POLICY
Українська: 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
Українська: About the company and the name
Українська: A short explanation of the relationship between a mathematical term and the actual service.
01Українська: What is a finite field?
Українська: 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.
02Українська: How does the name relate to business systems?
Українська: 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.
03Українська: Can we start with a mathematical consultation only?
Українська: 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.
04Українська: Can you develop the actual system too?
Українська: 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
Українська: What does your team think through every time?
Українська: Shifts, visits, routes, production, and assignments. We start from your current spreadsheets and rules to identify what can be modeled.