العربية: Observe the field
العربية: We collect decisions from spreadsheets, paper, conversations, and experienced staff. Exceptions and hidden priorities are part of the actual operation.
العربية: INPUT / Current workCOMPANY & ORIGIN
العربية: Turn mathematics into
العربية: software that works
العربية: in the field.
العربية: 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
- العربية: January 6, 2022
- BASE
- العربية: Usa City, Oita Prefecture
- FOCUS
- العربية: From mathematical models to web and apps
INTERACTIVE / PRIME FIELDF5
2 x 3 = 6F5: 1
Legal nameFinite Field, K.K.
Business focusالعربية: Mathematical systems development
Canonical pageالعربية: The new company profile is handled at /about/.
العربية: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
WHY WE EXIST
العربية: Before building, make the problem solvable.
العربية: Operational problems do not start as formulas. We first turn human judgment, exceptions, and implicit priorities into conditions and objectives that can be compared.
العربية: Separate constraints and goals
العربية: We separate hard constraints from indicators to improve, making contradictions and missing data visible before calculation.
العربية: MODEL / Constraints and evaluationالعربية: Implement a usable system
العربية: We do not stop at a calculation result. Input, review, correction, and sharing are implemented as web and mobile apps.
العربية: OUTPUT / Operating system
OUR PURPOSE
العربية: We use mathematics to organize ambiguous judgment into systems that can be compared, explained, and used.
THE NAME
العربية: Finite Field means a finite mathematical field.
العربية: 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
العربية: Limited elements. Consistent rules. Results that stay inside the set.
العربية: 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.
01العربية: Finite elements
العربية: The number of elements is a prime or a power of a prime.
02العربية: Closed under operations
العربية: Results return to elements in the same field.
03العربية: Inverses exist
العربية: Every nonzero element has a multiplicative inverse.
العربية: Important
العربية: 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
F5العربية: Try finite-field calculation
+
=
العربية: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
العربية: See limited resources
العربية: People, time, vehicles, machines, and budget. We search for plans that can actually run within real limits.
العربية: Make rules consistent
العربية: We organize business rules including exceptions so contradictions and priorities can be reviewed.
العربية: Make results reproducible
العربية: The path from inputs, constraints, and evaluation to the result should not depend only on one person’s intuition.
WHAT WE DO
العربية: From mathematical models to business screens.
العربية: 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 / MODELالعربية: What must be kept and what should improve
العربية: We organize constraints, objectives, priorities, exceptions, and feasibility.
02 / SOLVE
ALGORITHM
02 / SOLVEالعربية: Search and compare candidates
العربية: Optimization, search, rules, and simulation are combined when appropriate.
03 / BUILD
PRODUCT ENGINEERING
03 / BUILDالعربية: Enter, adjust, and share in the field
العربية: Web, iOS, Android, databases, permissions, and reports are implemented together.
INPUT
OUTPUT
OPERATING PRINCIPLES
العربية: Be honest before being mathematical.
العربية: We do not hide problems behind advanced terms or complex models. We separate what is unknown, not yet measured, and dependent on conditions.
العربية: Start with field language
العربية: We listen to actual work, decisions, and exceptions before applying terminology. A model is useful only when it explains the field.
العربية: Field to conditionsالعربية: Results with reasons
العربية: We do not stop at “the AI decided.” We show why a plan was chosen and what could not be satisfied.
العربية: Result to evidenceالعربية: Verify small before growing
العربية: Before production, we test the calculation on a small portion of real data. Reasons it cannot be solved are also findings.
العربية: Hypothesis to verificationالعربية: Implement usability too
العربية: We design for input, correction, smartphone use, and multilingual operation, not only calculation speed.
العربية: Logic to adoptionWE SAYالعربية: Organize conditions and create comparable plans
WE SHOWالعربية: Inputs, constraints, evaluation, and unresolved points
WE DO NOT CLAIMالعربية: Absolutely no bugs or always one unique optimum
COMPANY JOURNEY
العربية: Deepening from implementation strength into mathematics.
العربية: Experience building business systems, mobile apps, and multilingual services connects to planning, assignment, search, and verification.
2022.01.06FOUNDATION
FOUNDATION
العربية: Finite Field, K.K. established
العربية: Established in Usa City, Oita Prefecture, with a foundation for planning, building, and operating web, app, and business systems.
BUILDIMPLEMENTATION
IMPLEMENTATION
العربية: Complex operations into usable screens
العربية: We have built systems that connect data and operations, including ordering, visit availability, and unmanned sales workflows.
NOWMATHEMATICAL SYSTEMS
MATHEMATICAL SYSTEMS
العربية: Toward automation of planning and assignment
العربية: Shift planning, visit scheduling, routing, production planning, and assignment matching are now presented as core mathematical-systems domains.
R&DVERIFY
FROM CODE TO FIELD
العربية: Show working assets, not only philosophy.
العربية: A company page alone is not enough to judge capability. Demos, business screens, case studies, and security policies are available before consultation.
01 / DEMO
العربية: Mathematical demos
العربية: Change conditions and review results and unresolved points.
العربية: Try 02 / CASESالعربية: Case studies
العربية: Implemented functions and confirmed changes are separated.
العربية: Read 03 / SECURITYالعربية: Data handling
العربية: Receipt, retention, external AI, deletion, and responsibility are explained.
العربية: Check 04 / RESEARCHMath Lab
العربية: Research-stage technology is separated from completed products.
العربية: ViewCOMPANY PROFILE
Finite Field, K.K.
العربية: Based in Usa City, Oita Prefecture, we design and build mathematical models, algorithms, web systems, and mobile apps.
BASE / JAPANالعربية: Usa City, Oita Prefecture
FINITE FIELDالعربية: Usa City, Oita Prefecture
BASE / JAPAN
العربية: From a regional base, we use software to address complex operational problems.
- العربية: Legal name
- Finite Field, K.K. / 株式会社ファイナイトフィールド
- العربية: Japanese name
- 株式会社ファイナイトフィールド
- العربية: Address
- 879-0151 Oita, Usa, Miyaguma 550, اليابان
- العربية: Established
- العربية: January 6, 2022
- العربية: Capital
- العربية: JPY 3,000,000
- العربية: Officers
- المدير الممثل Toshiya Kazuyoshi مسؤولة Yoshie Kazuyoshi مسؤول Hikaru Ono
- العربية: Major client
- Matsuhisa Japan Co., Ltd.
- العربية: Business domains
- العربية: Mathematical systems development Web and mobile app development Business systems and R&D
INFORMATION POLICY
العربية: 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
العربية: About the company and the name
العربية: A short explanation of the relationship between a mathematical term and the actual service.
01العربية: What is a finite field?
العربية: 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.
02العربية: How does the name relate to business systems?
العربية: 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.
03العربية: Can we start with a mathematical consultation only?
العربية: 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.
04العربية: Can you develop the actual system too?
العربية: 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
العربية: What does your team think through every time?
العربية: Shifts, visits, routes, production, and assignments. We start from your current spreadsheets and rules to identify what can be modeled.