Slovenčina: Observe the field
Slovenčina: We collect decisions from spreadsheets, paper, conversations, and experienced staff. Exceptions and hidden priorities are part of the actual operation.
Slovenčina: INPUT / Current workCOMPANY & ORIGIN
Slovenčina: Turn mathematics into
Slovenčina: software that works
Slovenčina: in the field.
Slovenčina: 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
- Slovenčina: January 6, 2022
- BASE
- Slovenčina: Usa City, Oita Prefecture
- FOCUS
- Slovenčina: From mathematical models to web and apps
INTERACTIVE / PRIME FIELDF5
2 x 3 = 6F5: 1
Legal nameFinite Field, K.K.
Business focusSlovenčina: Mathematical systems development
Canonical pageSlovenčina: The new company profile is handled at /about/.
Slovenčina: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
WHY WE EXIST
Slovenčina: Before building, make the problem solvable.
Slovenčina: Operational problems do not start as formulas. We first turn human judgment, exceptions, and implicit priorities into conditions and objectives that can be compared.
Slovenčina: Separate constraints and goals
Slovenčina: We separate hard constraints from indicators to improve, making contradictions and missing data visible before calculation.
Slovenčina: MODEL / Constraints and evaluationSlovenčina: Implement a usable system
Slovenčina: We do not stop at a calculation result. Input, review, correction, and sharing are implemented as web and mobile apps.
Slovenčina: OUTPUT / Operating system
OUR PURPOSE
Slovenčina: We use mathematics to organize ambiguous judgment into systems that can be compared, explained, and used.
THE NAME
Slovenčina: Finite Field means a finite mathematical field.
Slovenčina: 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
Slovenčina: Limited elements. Consistent rules. Results that stay inside the set.
Slovenčina: 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.
01Slovenčina: Finite elements
Slovenčina: The number of elements is a prime or a power of a prime.
02Slovenčina: Closed under operations
Slovenčina: Results return to elements in the same field.
03Slovenčina: Inverses exist
Slovenčina: Every nonzero element has a multiplicative inverse.
Slovenčina: Important
Slovenčina: 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
F5Slovenčina: Try finite-field calculation
+
=
Slovenčina: For clarity, this demo shows prime fields Fp for prime p. General finite fields can also have p^n elements.
Slovenčina: See limited resources
Slovenčina: People, time, vehicles, machines, and budget. We search for plans that can actually run within real limits.
Slovenčina: Make rules consistent
Slovenčina: We organize business rules including exceptions so contradictions and priorities can be reviewed.
Slovenčina: Make results reproducible
Slovenčina: The path from inputs, constraints, and evaluation to the result should not depend only on one person’s intuition.
WHAT WE DO
Slovenčina: From mathematical models to business screens.
Slovenčina: 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 / MODELSlovenčina: What must be kept and what should improve
Slovenčina: We organize constraints, objectives, priorities, exceptions, and feasibility.
02 / SOLVE
ALGORITHM
02 / SOLVESlovenčina: Search and compare candidates
Slovenčina: Optimization, search, rules, and simulation are combined when appropriate.
03 / BUILD
PRODUCT ENGINEERING
03 / BUILDSlovenčina: Enter, adjust, and share in the field
Slovenčina: Web, iOS, Android, databases, permissions, and reports are implemented together.
INPUT
OUTPUT
OPERATING PRINCIPLES
Slovenčina: Be honest before being mathematical.
Slovenčina: We do not hide problems behind advanced terms or complex models. We separate what is unknown, not yet measured, and dependent on conditions.
Slovenčina: Start with field language
Slovenčina: We listen to actual work, decisions, and exceptions before applying terminology. A model is useful only when it explains the field.
Slovenčina: Field to conditionsSlovenčina: Results with reasons
Slovenčina: We do not stop at “the AI decided.” We show why a plan was chosen and what could not be satisfied.
Slovenčina: Result to evidenceSlovenčina: Verify small before growing
Slovenčina: Before production, we test the calculation on a small portion of real data. Reasons it cannot be solved are also findings.
Slovenčina: Hypothesis to verificationSlovenčina: Implement usability too
Slovenčina: We design for input, correction, smartphone use, and multilingual operation, not only calculation speed.
Slovenčina: Logic to adoptionWE SAYSlovenčina: Organize conditions and create comparable plans
WE SHOWSlovenčina: Inputs, constraints, evaluation, and unresolved points
WE DO NOT CLAIMSlovenčina: Absolutely no bugs or always one unique optimum
COMPANY JOURNEY
Slovenčina: Deepening from implementation strength into mathematics.
Slovenčina: Experience building business systems, mobile apps, and multilingual services connects to planning, assignment, search, and verification.
2022.01.06FOUNDATION
FOUNDATION
Slovenčina: Finite Field, K.K. established
Slovenčina: Established in Usa City, Oita Prefecture, with a foundation for planning, building, and operating web, app, and business systems.
BUILDIMPLEMENTATION
IMPLEMENTATION
Slovenčina: Complex operations into usable screens
Slovenčina: We have built systems that connect data and operations, including ordering, visit availability, and unmanned sales workflows.
NOWMATHEMATICAL SYSTEMS
MATHEMATICAL SYSTEMS
Slovenčina: Toward automation of planning and assignment
Slovenčina: Shift planning, visit scheduling, routing, production planning, and assignment matching are now presented as core mathematical-systems domains.
R&DVERIFY
VERIFY
Slovenčina: Researching ways to check correctness
Slovenčina: Theorem proving, formal verification, and inspectable calculation results are treated as research areas and clearly separated from production use.
FROM CODE TO FIELD
Slovenčina: Show working assets, not only philosophy.
Slovenčina: A company page alone is not enough to judge capability. Demos, business screens, case studies, and security policies are available before consultation.
01 / DEMO
Slovenčina: Mathematical demos
Slovenčina: Change conditions and review results and unresolved points.
Slovenčina: Try 02 / CASESSlovenčina: Case studies
Slovenčina: Implemented functions and confirmed changes are separated.
Slovenčina: Read 03 / SECURITYSlovenčina: Data handling
Slovenčina: Receipt, retention, external AI, deletion, and responsibility are explained.
Slovenčina: Check 04 / RESEARCHMath Lab
Slovenčina: Research-stage technology is separated from completed products.
Slovenčina: ViewCOMPANY PROFILE
Finite Field, K.K.
Slovenčina: Based in Usa City, Oita Prefecture, we design and build mathematical models, algorithms, web systems, and mobile apps.
BASE / JAPANSlovenčina: Usa City, Oita Prefecture
FINITE FIELDSlovenčina: Usa City, Oita Prefecture
BASE / JAPAN
Slovenčina: From a regional base, we use software to address complex operational problems.
- Slovenčina: Legal name
- Finite Field, K.K. / 株式会社ファイナイトフィールド
- Slovenčina: Japanese name
- 株式会社ファイナイトフィールド
- Slovenčina: Address
- 879-0151 Oita, Usa, Miyaguma 550, Japonsko
- Slovenčina: Established
- Slovenčina: January 6, 2022
- Slovenčina: Capital
- Slovenčina: JPY 3,000,000
- Slovenčina: Officers
- Zastupujúci riaditeľ Toshiya Kazuyoshi Členka vedenia Yoshie Kazuyoshi Člen vedenia Hikaru Ono
- Slovenčina: Major client
- Matsuhisa Japan Co., Ltd.
- Slovenčina: Business domains
- Slovenčina: Mathematical systems development Web and mobile app development Business systems and R&D
INFORMATION POLICY
Slovenčina: 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
Slovenčina: About the company and the name
Slovenčina: A short explanation of the relationship between a mathematical term and the actual service.
01Slovenčina: What is a finite field?
Slovenčina: 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.
02Slovenčina: How does the name relate to business systems?
Slovenčina: 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.
03Slovenčina: Can we start with a mathematical consultation only?
Slovenčina: 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.
04Slovenčina: Can you develop the actual system too?
Slovenčina: 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
Slovenčina: What does your team think through every time?
Slovenčina: Shifts, visits, routes, production, and assignments. We start from your current spreadsheets and rules to identify what can be modeled.