What kinds of math problems can you solve?

I handle a broad range: arithmetic, algebra, calculus (single- and multivariable), linear algebra, probability & statistics, discrete math, number theory, differential equations, optimization, and formal proofs. I can produce symbolic manipulations, numeric solutions, visualizations, and runnable code snippets for computations.

How do you present solutions and can I get LaTeX or code?

Solutions can be presented as natural-language explanations, step-by-step derivations, formatted LaTeX, or runnable code (Python/NumPy/SymPy pseudocode). Specify the desired format up front (e.g., 'Provide LaTeX for the full derivation' or 'Give Python to reproduce the plot').

Are there limits, and how accurate are the solutions?

Accuracy is high for well-specified problems, symbolic algebra, and standard numerical methods, but complex or ambiguous prompts can cause mistakes. I may misinterpret underspecified constraints or make algebraic slip-ups; always validate critical results and request intermediate checks or alternative methods when needed.

Can you help with exams, homework, or research ethically?

Yes — for learning and research the agent is valuable: it explains concepts, shows full derivations, and helps generate examples. For assessments, follow your institution’s rules. Use the agent as a tutor (understand solutions) rather than a means to submit unauthorised work.

How do you protect privacy and manage sensitive content?

Do not submit private personal data or exam keys. Treat inputs as potentially stored according to the host site’s policy; remove identifiable data before sharing. For highly sensitive or proprietary research, use institutional secure environments or self-hosted tools designed for confidentiality.

数学解答エージェント-AI math solver

AI-powered math solver that explains solutions

数学の問題を解答します。

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数学解答エージェント — 概要と設計目的

数学解答エージェントは、学術的・実務的な数学問題を高精度かつ解釈可能な形で解決・解説することを目的とした専門対話型AIシステムです。主な設計目的は次のとおりです：1) 問題の意味論的理解（与えられた条件・目標の正確な抽象化）、2) 解法選択の最適化（代数、解析、線形代数、確率論などから適切な手法を選ぶ）、3) 計算と証明の両立（数値計算だけでなく論理的な導出過程を提示）、4) 教育的配慮（途中の解釈や直感的説明を含めることで学習効果を高める）。アーキテクチャ上は、（a）入力解析モジュール（自然言語→形式表現）、（b）戦略選択モジュール（どの定理・技法を使うか決定）、（c）計算エンジン（代数処理・数値計算・符号付計算）、（d）可視化・説明生成モジュール（図、ステップ解説、反例検討）から構成されます。具体例／シナリオ： • 大学の微分積分の宿題：ユーザーが「この収束級数の和を求め、収束条件を示してほしい」と入力すると、入力解析で級数を正規化し（一般項を抽出）、比較判定・根判定・比判定等を自動で試行、最も簡潔な証明と数値近似を組み合わせて提示します。途中で用いた不等式や補題は参照付きで解説します。 • 研究用の線形代数問題：ある行列族のスペクトル性質と対角化可能性を調べたい場合、エージェントは固有値分解、Jordan標準形の判定、対称性・正定値性のチェックを実施し、具体例（小次元行列）による検算やスクリプト生成（Python／NumPyスタイル）を提案します。 • 実務的な最適化問題：物流ルートの最短化や投資配分問題では、目的関数と制約を受け取り、凸性判定→適切な最適化アルゴリズム（線形計画法、二次計画法、勾配法、内部点法）を推薦し、必要なら擬似コードや数値例で解を導出します。

主要機能と適用例

問題の形式化とモデル化
Example
自然言語で書かれた確率問題を、確率空間・確率変数・確率質量関数／密度関数の形式に変換し、必要な仮定（独立性、同分布、可測性など）を明示する。
Scenario
ある統計課題で「2つのコイン投げが与えられたとき、少なくとも一方が表になる確率を求めよ」といった問題を、標本空間の列挙→事象の集合表現→確率計算手順に落とし込み、Venn図やベン図を用いて直感的に示す。
解析的解法の導出と証明提示
Example
微分方程式の一般解を導く際、特解の候補を立て数学解答エージェント機能る（同次・非同次分離、ラプラス変換、級数解法など）し、定理に基づく収束・一意性の論証を付ける。
Scenario
物理モデルから導かれた常微分方程式で初期値問題が与えられたとき、解の存在一意性（Picard–Lindelöf定理）や長期挙動（安定性解析）を示し、具体的な解の形と数値シミュレーション結果を並べて提示する。
数値計算・アルゴリズム実行支援
Example
数値積分、行列固有値計算、最適化アルゴリズム（勾配降下、ニュートン法）の手順と収束判定基準を示し、サンプルコード（Python風）と数値例で検証する。
Scenario
高次元データの主成分分析（PCA）を行う際、データの前処理（中心化、標準化）、特異値分解の手法選択、次元削減後の復元誤差評価を説明し、簡潔なコードスニペットと出力例を提供する。

想定される主要ユーザー層

大学生・大学院生（理工系）
基礎から応用まで幅広い数学を学ぶ学習者。宿題・演習問題の解法が欲しい場合に、厳密な証明手順と直感的説明を同時に受け取れるため学習効率が向上する。例えば、解析学の収束判定や線形代数の理論的証明、確率統計の推定手法の導出などで有用。
研究者・エンジニア（応用数学・データサイエンス・最適化）
実験データ解析、モデル設計、アルゴリズム選定が求められる専門家。数学解答エージェントは理論的根拠の提示、数値検証、擬似コード／スクリプト生成を組み合わせて提供するため、モデルの妥当性確認やプロトタイプ実装の初期段階で特に有益である。

How to use 数学解答エージェント

Visit aichatonline.org for a free trial — no login, no ChatGPT Plus required.
Open aichatonline.org and start the free trial immediately; no account creation or ChatGPT Plus subscription is necessary to try the core functionality.
Provide the problem clearly and include context
Paste or type the exact math problem (include diagrams as images or LaTeX where relevant), state the level (e.g., high school, undergraduate), and specify desired output (full solution, final answer, step-by-step explanation, or LaTeX). Clear context (course, constraints, known variables) improves accuracy.
Choose style and depth of response
Select whether you want an intuitive explanation, rigorous proof, numeric computation, code (Python/Mathematica), or a short answer. For multi-step problems ask for numbered steps, intermediate checks, or error estimates to match your learning goals.
Use iterative prompts for refinement
If an answer needs clarification, request targeted follow-ups (e.g., 'show algebraic simplification of step 3Using 数学解答エージェント', 'explain the substitution used', or 'convert to LaTeX'). Provide corrections or extra constraints rather than restarting; the agent adapts quickly.
Verify results and export
Cross-check critical results (numeric checks, special cases). Export solutions in preferred formats (LaTeX, PNG of steps, code snippets). For assessments, follow institutional rules about AI use and cite the tool when required.

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Common questions about 数学解答エージェント

What kinds of math problems can you solve?
I handle a broad range: arithmetic, algebra, calculus (single- and multivariable), linear algebra, probability & statistics, discrete math, number theory, differential equations, optimization, and formal proofs. I can produce symbolic manipulations, numeric solutions, visualizations, and runnable code snippets for computations.
How do you present solutions and can I get LaTeX or code?
Solutions can be presented as natural-language explanations, step-by-step derivations, formatted LaTeX, or runnable code (Python/NumPy/SymPy pseudocode). Specify the desired format up front (e.g., 'Provide LaTeX for the full derivation' or 'Give Python to reproduce the plot').
Are there limits, and how accurate are the solutions?
Accuracy is high for well-specified problems, symbolic algebra, and standard numerical methods, but complex or ambiguous prompts can cause mistakes. I may misinterpret underspecified constraints or make algebraic slip-ups; always validate critical results and request intermediate checks or alternative methods when needed.
Can you help with exams, homework, or research ethically?
Yes — for learning and research the agent is valuable: it explains concepts, shows full derivations, and helps generate examples. For assessments, follow your institution’s rules. Use the agent as a tutor (understand solutions) rather than a means to submit unauthorised work.
How do you protect privacy and manage sensitive content?
Do not submit private personal data or exam keys. Treat inputs as potentially stored according to the host site’s policy; remove identifiable data before sharing. For highly sensitive or proprietary research, use institutional secure environments or self-hosted tools designed for confidentiality.