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Found 7 Skills
Transform a solid geometry problem into a self-contained interactive teaching web page: step-by-step explanations using MathJax on the left, and an interactive 3D model powered by Three.js on the right (step-by-step highlighting + camera switching). Supports three entry modes—given text problems, random problem generation, and solving problems after uploading and recognizing problem images. Covers problem types such as line-plane angles, dihedral angles, angles between skew lines, distance from a point to a plane, and volume involving cubes/cuboids, pyramids/prisms, cylinders/cones. Uniformly adopts the "Coordinate System + Vector Method", driven by precise sympy calculations (answers, 3D coordinates, and step values are consistent from the same source). Other agents can also call this skill to generate such web pages. Trigger words: solid geometry, line-plane angle, dihedral angle, angle between skew lines, distance from point to plane, regular square pyramid, cube angle calculation, solve this geometry problem, generate a random solid geometry problem, solve the solid geometry problem in this image; solid geometry, line-plane angle, dihedral angle, angle between skew lines, distance to plane, interactive geometry solution page.
Turn an analytic geometry problem into a self-contained interactive teaching webpage: left column with problem statement + dynamic console (a variable parameter slider driving real-time recalculation of geometric quantities + theoretical range/fixed value indication), middle column with step-by-step explanations using KaTeX, right column with 2D Canvas dynamic geometry drawing board (ellipse/hyperbola/parabola/circle + moving lines/moving points + vectors + annotations + brush doodling). Supports three entry points—given text problems, random problem generation, and solving problems after uploading and recognizing problem images. Covers problem types such as finding standard equations, chord lengths, vector dot product ranges/fixed values, triangle area maxima/minima, fixed points, fixed values (product of slopes), loci, and eccentricities. Uses a unified method of "setting parametric line x=my+c + simultaneous equations + Vieta's formulas + substitution/constant separation", driven by sympy for precise calculations (answers, coordinates, step values, and theoretical ranges of the interactive engine are consistent from the same source). Other agents can also call this skill to generate such webpages. It parallels edu-solid-geometry in form but uses Canvas-2D + KaTeX (instead of Three.js). Trigger words: 解析几何, 圆锥曲线, 椭圆, 双曲线, 抛物线, 直线与圆锥曲线, 焦点弦, 弦长, 数量积取值范围, 向量数量积, 定点问题, 定值问题, 斜率之积, 三角形面积最值, 轨迹方程, 离心率, 解这道解析几何题, 随机出一道圆锥曲线题, 这张图里的解析几何题; analytic geometry, conic sections, ellipse, hyperbola, parabola, chord length, dot product range, fixed point, fixed value, locus, eccentricity, interactive analytic geometry solution page.
Turn a chemical reaction into a self-contained microscopic 3D interactive demonstration webpage: The left/top section features a Three.js interactive molecular animation (drag the slider to view bond breaking, bond forming, and atomic recombination with step-by-step highlighting), while the right section includes KaTeX reaction equations + step-by-step explanations + atom conservation counting + optional energy-reaction progress curves. Three entry methods are supported—given text reactions/equations, random question generation, and demonstration after image upload and recognition. It covers combustion, combination/decomposition/single displacement/double displacement reactions, redox reactions (electron transfer visualization), and organic reaction mechanisms (esterification and other reactions involving catalysts and transition states). It is precisely driven by sympy: automatically balance equations, verify atom conservation and atomic mapping, deduce bond breaking/forming, ensuring consistency between answers and geometric models. Two built-in engines are available with automatic selection: morph (atomic deformation, demonstrating atom conservation) and mechanism (mechanism keyframes, demonstrating catalysis/transition states). Hybrid geometry: uses a self-built VSEPR molecular library by default; if RDKit is installed in the environment, it can generate conformations from SMILES (never installed automatically). Other agents can also call this skill to generate such webpages. Its form is parallel to edu-solid-geometry / edu-analytic-geometry, but uses Three.js + KaTeX to demonstrate molecular reactions. Trigger words: chemical reaction, microscopic demonstration, molecular animation, combustion, methane combustion, hydrogen combustion, water electrolysis, redox reaction, electron transfer, esterification reaction, reaction mechanism, bond breaking and forming, atom conservation, mass conservation, chemical equation balancing, solve this chemical reaction, generate a random chemical reaction, the chemical reaction in this image; chemistry reaction, microscopic/molecular animation, combustion, electrolysis, redox electron transfer, esterification mechanism, bond breaking and forming, atom conservation, balance equation, interactive chemistry reaction page.
Deterministic router for math cognitive stack - maps user intent to exact CLI commands
Guide to the math cognitive stack - what tools exist and when to use each
Use when "scientific computing", "astronomy", "astropy", "bioinformatics", "biopython", "symbolic math", "sympy", "statistics", "statsmodels", "scientific Python"
Unified math capabilities - computation, solving, and explanation. I route to the right tool.