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from sentence_transformers import SentenceTransformer |
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from sklearn.metrics.pairwise import cosine_similarity |
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import gradio as gr |
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import arxiv |
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from semanticscholar import SemanticScholar |
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from duckduckgo_search import DDGS |
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model = SentenceTransformer('all-MiniLM-L6-v2') |
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DOMAINS = { |
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"Real Analysis": "Studies properties of real-valued functions, sequences, limits, continuity, differentiation, Riemann/ Lebesgue integration, and convergence in the real number system.", |
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"Complex Analysis": "Explores analytic functions of complex variables, contour integration, conformal mappings, and singularity theory.", |
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"Functional Analysis": "Deals with infinite-dimensional vector spaces, Banach and Hilbert spaces, linear operators, duality, and spectral theory in the context of functional spaces.", |
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"Measure Theory": "Studies sigma-algebras, measures, measurable functions, and integrals, forming the foundation for modern probability and real analysis.", |
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"Fourier and Harmonic Analysis": "Analyzes functions via decompositions into sines, cosines, or general orthogonal bases, often involving Fourier series, Fourier transforms, and convolution techniques.", |
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"Calculus of Variations": "Optimizes functionals over infinite-dimensional spaces, leading to Euler-Lagrange equations and applications in physics and control theory.", |
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"Metric Geometry": "Explores geometric properties of metric spaces and the behavior of functions and sequences under various notions of distance.", |
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"Ordinary Differential Equations (ODEs)": "Involves differential equations with functions of a single variable, their qualitative behavior, existence, uniqueness, and methods of solving them.", |
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"Partial Differential Equations (PDEs)": "Deals with multivariable functions involving partial derivatives, including wave, heat, and Laplace equations.", |
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"Dynamical Systems": "Studies evolution of systems over time using discrete or continuous-time equations, stability theory, phase portraits, and attractors.", |
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"Linear Algebra": "Focuses on vector spaces, linear transformations, eigenvalues, diagonalization, and matrices.", |
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"Abstract Algebra": "General study of algebraic structures such as groups, rings, fields, and modules.", |
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"Group Theory": "Investigates algebraic structures with a single binary operation satisfying group axioms, including symmetry groups and applications.", |
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"Ring and Module Theory": "Extends group theory to rings (two operations) and modules (generalized vector spaces).", |
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"Field Theory": "Studies field extensions, algebraic and transcendental elements, and classical constructions.", |
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"Galois Theory": "Connects field theory and group theory to solve polynomial equations and understand solvability.", |
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"Algebraic Number Theory": "Applies tools from abstract algebra to study integers, Diophantine equations, and number fields.", |
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"Representation Theory": "Studies abstract algebraic structures by representing their elements as linear transformations of vector spaces.", |
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"Algebraic Geometry": "Examines solutions to polynomial equations using geometric and algebraic techniques like varieties, schemes, and morphisms.", |
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"Differential Geometry": "Studies geometric structures on smooth manifolds, curvature, geodesics, and applications in general relativity.", |
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"Topology": "Analyzes qualitative spatial properties preserved under continuous deformations, including homeomorphism, compactness, and connectedness.", |
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"Geometric Topology": "Explores topological manifolds and their classification, knot theory, and low-dimensional topology.", |
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"Symplectic Geometry": "Studies geometry arising from Hamiltonian systems and phase space, central to classical mechanics.", |
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"Combinatorics": "Covers enumeration, existence, construction, and optimization of discrete structures.", |
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"Graph Theory": "Deals with the study of graphs, networks, trees, connectivity, and coloring problems.", |
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"Discrete Geometry": "Focuses on geometric objects and combinatorial properties in finite settings, such as polytopes and tilings.", |
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"Set Theory": "Studies sets, cardinality, ordinals, ZFC axioms, and independence results.", |
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"Mathematical Logic": "Includes propositional logic, predicate logic, proof theory, model theory, and recursion theory.", |
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"Category Theory": "Provides a high-level, structural framework to relate different mathematical systems through morphisms and objects.", |
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"Probability Theory": "Mathematical foundation for randomness, including random variables, distributions, expectation, and stochastic processes.", |
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"Mathematical Statistics": "Theory behind estimation, hypothesis testing, confidence intervals, and likelihood inference.", |
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"Stochastic Processes": "Studies processes that evolve with randomness over time, like Markov chains and Brownian motion.", |
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"Information Theory": "Analyzes data transmission, entropy, coding theory, and information content in probabilistic settings.", |
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"Numerical Analysis": "Designs and analyzes algorithms to approximate solutions of mathematical problems including root-finding, integration, and differential equations.", |
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"Optimization": "Studies finding best outcomes under constraints, including convex optimization, linear programming, and integer programming.", |
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"Operations Research": "Applies optimization, simulation, and probabilistic modeling to decision-making problems in logistics, finance, and industry.", |
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"Control Theory": "Mathematically models and regulates dynamic systems through feedback and optimal control strategies.", |
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"Computational Mathematics": "Applies algorithmic and numerical techniques to solve mathematical problems on computers.", |
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"Game Theory": "Analyzes strategic interaction among rational agents using payoff matrices and equilibrium concepts.", |
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"Machine Learning Theory": "Explores the mathematical foundation of algorithms that learn from data, covering generalization, VC dimension, and convergence.", |
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"Spectral Theory": "Studies the spectrum (eigenvalues) of linear operators, primarily in Hilbert/Banach spaces, relevant to quantum mechanics and PDEs.", |
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"Operator Theory": "Focuses on properties of linear operators on function spaces and their classification.", |
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"Mathematical Physics": "Uses advanced mathematical tools to solve and model problems in physics, often involving differential geometry and functional analysis.", |
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"Financial Mathematics": "Applies stochastic calculus and optimization to problems in pricing, risk, and investment.", |
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"Mathematics Education": "Focuses on teaching methods, learning theories, and curriculum design in mathematics.", |
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"History of Mathematics": "Studies the historical development of mathematical concepts, theorems, and personalities.", |
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"Others / Multidisciplinary": "Covers problems that span multiple mathematical areas or do not fall neatly into a traditional domain." |
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} |
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domain_names = list(DOMAINS.keys()) |
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domain_texts = list(DOMAINS.values()) |
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domain_embeddings = model.encode(domain_texts) |
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def fetch_arxiv_refs(query, max_results=5): |
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refs = [] |
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try: |
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search = arxiv.Search(query=query, max_results=max_results) |
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for r in search.results(): |
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refs.append({ |
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"title": r.title, |
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"authors": ", ".join(a.name for a in r.authors[:3]), |
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"year": r.published.year, |
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"url": r.entry_id, |
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"source": "arXiv" |
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}) |
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except: |
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pass |
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return refs |
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def fetch_duckduckgo_links(query, max_results=10): |
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links = [] |
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try: |
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with DDGS() as ddgs: |
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results = ddgs.text(query, max_results=max_results) |
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count = 0 |
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for res in results: |
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url = res['href'] |
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if ".edu" in url or ".org" in url: |
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links.append({ |
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"title": res['title'], |
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"url": url, |
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"snippet": res['body'], |
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"source": "DuckDuckGo" |
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}) |
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count += 1 |
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if count >= 3: |
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break |
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except: |
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pass |
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return links |
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def classify_math_question(question): |
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q_embed = model.encode([question]) |
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scores = cosine_similarity(q_embed, domain_embeddings)[0] |
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sorted_indices = scores.argsort()[::-1] |
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major = domain_names[sorted_indices[0]] |
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minor = domain_names[sorted_indices[1]] |
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major_reason = DOMAINS[major] |
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minor_reason = DOMAINS[minor] |
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out = f"<b>Major Domain:</b> {major}<br><i>Reason:</i> {major_reason}<br><br>" |
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out += f"<b>Minor Domain:</b> {minor}<br><i>Reason:</i> {minor_reason}<br><br>" |
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refs = fetch_arxiv_refs(question, max_results=5) |
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links = fetch_duckduckgo_links(question, max_results=3) |
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if refs: |
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out += "<b>Top Academic References (arXiv):</b><ul>" |
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for p in refs: |
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out += f"<li><b>{p['title']}</b> ({p['year']}) - <i>{p['authors']}</i><br><a href='{p['url']}' target='_blank'>{p['url']}</a></li>" |
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out += "</ul>" |
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else: |
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out += "<i>No academic references found.</i><br>" |
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if links: |
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out += "<b>Top Web Resources (DuckDuckGo):</b><ul>" |
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for link in links: |
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out += f"<li><b>{link['title']}</b><br>{link['snippet']}<br><a href='{link['url']}' target='_blank'>{link['url']}</a></li>" |
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out += "</ul>" |
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else: |
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out += "<i>No web links found.</i>" |
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return out |
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iface = gr.Interface( |
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fn=classify_math_question, |
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inputs=gr.Textbox(lines=5, label="Enter Math Question (LaTeX supported)"), |
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outputs=gr.HTML(label="Predicted Domains + References"), |
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title="⚡ Fast Math Domain Classifier with arXiv + DuckDuckGo", |
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description="Classifies math problems into major/minor domains and fetches fast references from arXiv + DuckDuckGo." |
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) |
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iface.launch() |
