Íslenska: Observe the field
Íslenska: We collect decisions from spreadsheets, paper, conversations, and experienced staff. Exceptions and hidden priorities are part of the actual operation.
Íslenska: INPUT / Current workCOMPANY & ORIGIN
Íslenska: Turn mathematics into
Íslenska: software that works
Íslenska: in the field.
Íslenska: 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
- Íslenska: January 6, 2022
- BASE
- Íslenska: Usa City, Oita Prefecture
- FOCUS
- Íslenska: From mathematical models to web and apps
INTERACTIVE / PRIME FIELDF5
2 x 3 = 6F5: 1
Legal nameFinite Field, K.K.
Business focusÍslenska: Mathematical systems development
Canonical pageÍslenska: The new company profile is handled at /about/.
Íslenska: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
WHY WE EXIST
Íslenska: Before building, make the problem solvable.
Íslenska: Operational problems do not start as formulas. We first turn human judgment, exceptions, and implicit priorities into conditions and objectives that can be compared.
Íslenska: Separate constraints and goals
Íslenska: We separate hard constraints from indicators to improve, making contradictions and missing data visible before calculation.
Íslenska: MODEL / Constraints and evaluationÍslenska: Implement a usable system
Íslenska: We do not stop at a calculation result. Input, review, correction, and sharing are implemented as web and mobile apps.
Íslenska: OUTPUT / Operating system
OUR PURPOSE
Íslenska: We use mathematics to organize ambiguous judgment into systems that can be compared, explained, and used.
THE NAME
Íslenska: Finite Field means a finite mathematical field.
Íslenska: 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
Íslenska: Limited elements. Consistent rules. Results that stay inside the set.
Íslenska: 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.
01Íslenska: Finite elements
Íslenska: The number of elements is a prime or a power of a prime.
02Íslenska: Closed under operations
Íslenska: Results return to elements in the same field.
03Íslenska: Inverses exist
Íslenska: Every nonzero element has a multiplicative inverse.
Íslenska: Important
Íslenska: 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
F5Íslenska: Try finite-field calculation
+
=
Íslenska: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
Íslenska: See limited resources
Íslenska: People, time, vehicles, machines, and budget. We search for plans that can actually run within real limits.
Íslenska: Make rules consistent
Íslenska: We organize business rules including exceptions so contradictions and priorities can be reviewed.
Íslenska: Make results reproducible
Íslenska: The path from inputs, constraints, and evaluation to the result should not depend only on one person’s intuition.
WHAT WE DO
Íslenska: From mathematical models to business screens.
Íslenska: 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 / MODELÍslenska: What must be kept and what should improve
Íslenska: We organize constraints, objectives, priorities, exceptions, and feasibility.
02 / SOLVE
ALGORITHM
02 / SOLVEÍslenska: Search and compare candidates
Íslenska: Optimization, search, rules, and simulation are combined when appropriate.
03 / BUILD
PRODUCT ENGINEERING
03 / BUILDÍslenska: Enter, adjust, and share in the field
Íslenska: Web, iOS, Android, databases, permissions, and reports are implemented together.
INPUT
OUTPUT
OPERATING PRINCIPLES
Íslenska: Be honest before being mathematical.
Íslenska: We do not hide problems behind advanced terms or complex models. We separate what is unknown, not yet measured, and dependent on conditions.
Íslenska: Start with field language
Íslenska: We listen to actual work, decisions, and exceptions before applying terminology. A model is useful only when it explains the field.
Íslenska: Field to conditionsÍslenska: Results with reasons
Íslenska: We do not stop at “the AI decided.” We show why a plan was chosen and what could not be satisfied.
Íslenska: Result to evidenceÍslenska: Verify small before growing
Íslenska: Before production, we test the calculation on a small portion of real data. Reasons it cannot be solved are also findings.
Íslenska: Hypothesis to verificationÍslenska: Implement usability too
Íslenska: We design for input, correction, smartphone use, and multilingual operation, not only calculation speed.
Íslenska: Logic to adoptionWE SAYÍslenska: Organize conditions and create comparable plans
WE SHOWÍslenska: Inputs, constraints, evaluation, and unresolved points
WE DO NOT CLAIMÍslenska: Absolutely no bugs or always one unique optimum
COMPANY JOURNEY
Íslenska: Deepening from implementation strength into mathematics.
Íslenska: Experience building business systems, mobile apps, and multilingual services connects to planning, assignment, search, and verification.
2022.01.06FOUNDATION
FOUNDATION
Íslenska: Finite Field, K.K. established
Íslenska: Established in Usa City, Oita Prefecture, with a foundation for planning, building, and operating web, app, and business systems.
BUILDIMPLEMENTATION
NOWMATHEMATICAL SYSTEMS
MATHEMATICAL SYSTEMS
Íslenska: Toward automation of planning and assignment
Íslenska: Shift planning, visit scheduling, routing, production planning, and assignment matching are now presented as core mathematical-systems domains.
R&DVERIFY
FROM CODE TO FIELD
Íslenska: Show working assets, not only philosophy.
Íslenska: A company page alone is not enough to judge capability. Demos, business screens, case studies, and security policies are available before consultation.
01 / DEMO
Íslenska: Mathematical demos
Íslenska: Change conditions and review results and unresolved points.
Íslenska: Try 02 / CASESÍslenska: Case studies
Íslenska: Implemented functions and confirmed changes are separated.
Íslenska: Read 03 / SECURITYÍslenska: Data handling
Íslenska: Receipt, retention, external AI, deletion, and responsibility are explained.
Íslenska: Check 04 / RESEARCHMath Lab
Íslenska: Research-stage technology is separated from completed products.
Íslenska: ViewCOMPANY PROFILE
Finite Field, K.K.
Íslenska: Based in Usa City, Oita Prefecture, we design and build mathematical models, algorithms, web systems, and mobile apps.
BASE / JAPANÍslenska: Usa City, Oita Prefecture
FINITE FIELDÍslenska: Usa City, Oita Prefecture
BASE / JAPAN
Íslenska: From a regional base, we use software to address complex operational problems.
- Íslenska: Legal name
- Finite Field, K.K. / 株式会社ファイナイトフィールド
- Íslenska: Japanese name
- 株式会社ファイナイトフィールド
- Íslenska: Address
- Japan, 879-0151 Oita, Usa, Miyaguma 550
- Íslenska: Established
- Íslenska: January 6, 2022
- Íslenska: Capital
- Íslenska: JPY 3,000,000
- Íslenska: Officers
- Fulltrúaframkvæmdastjóri Toshiya Kazuyoshi Stjórnandi Yoshie Kazuyoshi Stjórnandi Hikaru Ono
- Íslenska: Major client
- Matsuhisa Japan Co., Ltd.
- Íslenska: Business domains
- Íslenska: Mathematical systems development Web and mobile app development Business systems and R&D
INFORMATION POLICY
Íslenska: 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
Íslenska: About the company and the name
Íslenska: A short explanation of the relationship between a mathematical term and the actual service.
01Íslenska: What is a finite field?
Íslenska: 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.
02Íslenska: How does the name relate to business systems?
Íslenska: 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.
03Íslenska: Can we start with a mathematical consultation only?
Íslenska: 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.
04Íslenska: Can you develop the actual system too?
Íslenska: 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
Íslenska: What does your team think through every time?
Íslenska: Shifts, visits, routes, production, and assignments. We start from your current spreadsheets and rules to identify what can be modeled.