[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"skill:01M6AFPWXREHJXD2YNFG93E83Z":3,"skill-same:01M6AFPWXREHJXD2YNFG93E83Z":105},{"skillNo":4,"name":5,"nameZh":6,"description":7,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":16,"categories":17,"keywords":28,"publishedAt":48,"linkOnly":49,"markdownContent":50,"markdownBody":51,"frontMatter":52,"refName":53,"commitSha":54,"skillDirectory":55,"forksCount":56,"repositoryHtmlUrl":57,"repositoryHomepageUrl":58,"ownerHtmlUrl":59,"ownerBlogUrl":60,"ownerDescription":61,"updatedAt":62,"install":63,"resources":76},"01M6AFPWXREHJXD2YNFG93E83Z","sympy",null,"Use this skill when working with symbolic mathematics in Python. This skill should be used for symbolic computation tasks including solving equations algebraically, performing calculus operations (derivatives, integrals, limits), manipulating algebraic expressions, working with matrices symbolically, physics calculations, number theory problems, geometry computations, and generating executable code from mathematical expressions. Apply this skill when the user needs exact symbolic results rather than numerical approximations, or when working with mathematical formulas that contain variables and parameters.","davila7\u002Fclaude-code-templates","davila7","https:\u002F\u002Favatars.githubusercontent.com\u002Fu\u002F6216945?v=4","01M6ADEWWFPS191NFM0Y1EX1JH","Daniel Avila","01M6ADJHGM78PHQRD3XZTFDVKK",33481,"MIT","https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Fscientific\u002Fsympy\u002FSKILL.md",[18,23],{"categoryNo":19,"categoryName":20,"taxonomyType":21,"taxonomyTypeDesc":22},"01JBSEEDCAT000000000000023","Skill与智能体开发","SCENARIO","使用场景",{"categoryNo":24,"categoryName":25,"taxonomyType":26,"taxonomyTypeDesc":27},"01JBSEEDCAT000000000000030","开发工程师","PROFESSION","适用职业",[5,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47],"with","computation","when","limits","apply","numerical","for","number","formulas","Variables","python","contain","integrals","geometry","physics","mathematics","use","code","tasks","2026-11-10 10:12:30",false,"---\nname: sympy\ndescription: Use this skill when working with symbolic mathematics in Python. This skill should be used for symbolic computation tasks including solving equations algebraically, performing calculus operations (derivatives, integrals, limits), manipulating algebraic expressions, working with matrices symbolically, physics calculations, number theory problems, geometry computations, and generating executable code from mathematical expressions. Apply this skill when the user needs exact symbolic results rather than numerical approximations, or when working with mathematical formulas that contain variables and parameters.\n---\n\n# SymPy - Symbolic Mathematics in Python\n\n## Overview\n\nSymPy is a Python library for symbolic mathematics that enables exact computation using mathematical symbols rather than numerical approximations. This skill provides comprehensive guidance for performing symbolic algebra, calculus, linear algebra, equation solving, physics calculations, and code generation using SymPy.\n\n## When to Use This Skill\n\nUse this skill when:\n- Solving equations symbolically (algebraic, differential, systems of equations)\n- Performing calculus operations (derivatives, integrals, limits, series)\n- Manipulating and simplifying algebraic expressions\n- Working with matrices and linear algebra symbolically\n- Doing physics calculations (mechanics, quantum mechanics, vector analysis)\n- Number theory computations (primes, factorization, modular arithmetic)\n- Geometric calculations (2D\u002F3D geometry, analytic geometry)\n- Converting mathematical expressions to executable code (Python, C, Fortran)\n- Generating LaTeX or other formatted mathematical output\n- Needing exact mathematical results (e.g., `sqrt(2)` not `1.414...`)\n\n## Core Capabilities\n\n### 1. Symbolic Computation Basics\n\n**Creating symbols and expressions:**\n```python\nfrom sympy import symbols, Symbol\nx, y, z = symbols('x y z')\nexpr = x**2 + 2*x + 1\n\n# With assumptions\nx = symbols('x', real=True, positive=True)\nn = symbols('n', integer=True)\n```\n\n**Simplification and manipulation:**\n```python\nfrom sympy import simplify, expand, factor, cancel\nsimplify(sin(x)**2 + cos(x)**2)  # Returns 1\nexpand((x + 1)**3)  # x**3 + 3*x**2 + 3*x + 1\nfactor(x**2 - 1)    # (x - 1)*(x + 1)\n```\n\n**For detailed basics:** See `references\u002Fcore-capabilities.md`\n\n### 2. Calculus\n\n**Derivatives:**\n```python\nfrom sympy import diff\ndiff(x**2, x)        # 2*x\ndiff(x**4, x, 3)     # 24*x (third derivative)\ndiff(x**2*y**3, x, y)  # 6*x*y**2 (partial derivatives)\n```\n\n**Integrals:**\n```python\nfrom sympy import integrate, oo\nintegrate(x**2, x)              # x**3\u002F3 (indefinite)\nintegrate(x**2, (x, 0, 1))      # 1\u002F3 (definite)\nintegrate(exp(-x), (x, 0, oo))  # 1 (improper)\n```\n\n**Limits and Series:**\n```python\nfrom sympy import limit, series\nlimit(sin(x)\u002Fx, x, 0)  # 1\nseries(exp(x), x, 0, 6)  # 1 + x + x**2\u002F2 + x**3\u002F6 + x**4\u002F24 + x**5\u002F120 + O(x**6)\n```\n\n**For detailed calculus operations:** See `references\u002Fcore-capabilities.md`\n\n### 3. Equation Solving\n\n**Algebraic equations:**\n```python\nfrom sympy import solveset, solve, Eq\nsolveset(x**2 - 4, x)  # {-2, 2}\nsolve(Eq(x**2, 4), x)  # [-2, 2]\n```\n\n**Systems of equations:**\n```python\nfrom sympy import linsolve, nonlinsolve\nlinsolve([x + y - 2, x - y], x, y)  # {(1, 1)} (linear)\nnonlinsolve([x**2 + y - 2, x + y**2 - 3], x, y)  # (nonlinear)\n```\n\n**Differential equations:**\n```python\nfrom sympy import Function, dsolve, Derivative\nf = symbols('f', cls=Function)\ndsolve(Derivative(f(x), x) - f(x), f(x))  # Eq(f(x), C1*exp(x))\n```\n\n**For detailed solving methods:** See `references\u002Fcore-capabilities.md`\n\n### 4. Matrices and Linear Algebra\n\n**Matrix creation and operations:**\n```python\nfrom sympy import Matrix, eye, zeros\nM = Matrix([[1, 2], [3, 4]])\nM_inv = M**-1  # Inverse\nM.det()        # Determinant\nM.T            # Transpose\n```\n\n**Eigenvalues and eigenvectors:**\n```python\neigenvals = M.eigenvals()  # {eigenvalue: multiplicity}\neigenvects = M.eigenvects()  # [(eigenval, mult, [eigenvectors])]\nP, D = M.diagonalize()  # M = P*D*P^-1\n```\n\n**Solving linear systems:**\n```python\nA = Matrix([[1, 2], [3, 4]])\nb = Matrix([5, 6])\nx = A.solve(b)  # Solve Ax = b\n```\n\n**For comprehensive linear algebra:** See `references\u002Fmatrices-linear-algebra.md`\n\n### 5. Physics and Mechanics\n\n**Classical mechanics:**\n```python\nfrom sympy.physics.mechanics import dynamicsymbols, LagrangesMethod\nfrom sympy import symbols\n\n# Define system\nq = dynamicsymbols('q')\nm, g, l = symbols('m g l')\n\n# Lagrangian (T - V)\nL = m*(l*q.diff())**2\u002F2 - m*g*l*(1 - cos(q))\n\n# Apply Lagrange's method\nLM = LagrangesMethod(L, [q])\n```\n\n**Vector analysis:**\n```python\nfrom sympy.physics.vector import ReferenceFrame, dot, cross\nN = ReferenceFrame('N')\nv1 = 3*N.x + 4*N.y\nv2 = 1*N.x + 2*N.z\ndot(v1, v2)  # Dot product\ncross(v1, v2)  # Cross product\n```\n\n**Quantum mechanics:**\n```python\nfrom sympy.physics.quantum import Ket, Bra, Commutator\npsi = Ket('psi')\nA = Operator('A')\ncomm = Commutator(A, B).doit()\n```\n\n**For detailed physics capabilities:** See `references\u002Fphysics-mechanics.md`\n\n### 6. Advanced Mathematics\n\nThe skill includes comprehensive support for:\n\n- **Geometry:** 2D\u002F3D analytic geometry, points, lines, circles, polygons, transformations\n- **Number Theory:** Primes, factorization, GCD\u002FLCM, modular arithmetic, Diophantine equations\n- **Combinatorics:** Permutations, combinations, partitions, group theory\n- **Logic and Sets:** Boolean logic, set theory, finite and infinite sets\n- **Statistics:** Probability distributions, random variables, expectation, variance\n- **Special Functions:** Gamma, Bessel, orthogonal polynomials, hypergeometric functions\n- **Polynomials:** Polynomial algebra, roots, factorization, Groebner bases\n\n**For detailed advanced topics:** See `references\u002Fadvanced-topics.md`\n\n### 7. Code Generation and Output\n\n**Convert to executable functions:**\n```python\nfrom sympy import lambdify\nimport numpy as np\n\nexpr = x**2 + 2*x + 1\nf = lambdify(x, expr, 'numpy')  # Create NumPy function\nx_vals = np.linspace(0, 10, 100)\ny_vals = f(x_vals)  # Fast numerical evaluation\n```\n\n**Generate C\u002FFortran code:**\n```python\nfrom sympy.utilities.codegen import codegen\n[(c_name, c_code), (h_name, h_header)] = codegen(\n    ('my_func', expr), 'C'\n)\n```\n\n**LaTeX output:**\n```python\nfrom sympy import latex\nlatex_str = latex(expr)  # Convert to LaTeX for documents\n```\n\n**For comprehensive code generation:** See `references\u002Fcode-generation-printing.md`\n\n## Working with SymPy: Best Practices\n\n### 1. Always Define Symbols First\n\n```python\nfrom sympy import symbols\nx, y, z = symbols('x y z')\n# Now x, y, z can be used in expressions\n```\n\n### 2. Use Assumptions for Better Simplification\n\n```python\nx = symbols('x', positive=True, real=True)\nsqrt(x**2)  # Returns x (not Abs(x)) due to positive assumption\n```\n\nCommon assumptions: `real`, `positive`, `negative`, `integer`, `rational`, `complex`, `even`, `odd`\n\n### 3. Use Exact Arithmetic\n\n```python\nfrom sympy import Rational, S\n# Correct (exact):\nexpr = Rational(1, 2) * x\nexpr = S(1)\u002F2 * x\n\n# Incorrect (floating-point):\nexpr = 0.5 * x  # Creates approximate value\n```\n\n### 4. Numerical Evaluation When Needed\n\n```python\nfrom sympy import pi, sqrt\nresult = sqrt(8) + pi\nresult.evalf()    # 5.96371554103586\nresult.evalf(50)  # 50 digits of precision\n```\n\n### 5. Convert to NumPy for Performance\n\n```python\n# Slow for many evaluations:\nfor x_val in range(1000):\n    result = expr.subs(x, x_val).evalf()\n\n# Fast:\nf = lambdify(x, expr, 'numpy')\nresults = f(np.arange(1000))\n```\n\n### 6. Use Appropriate Solvers\n\n- `solveset`: Algebraic equations (primary)\n- `linsolve`: Linear systems\n- `nonlinsolve`: Nonlinear systems\n- `dsolve`: Differential equations\n- `solve`: General purpose (legacy, but flexible)\n\n## Reference Files Structure\n\nThis skill uses modular reference files for different capabilities:\n\n1. **`core-capabilities.md`**: Symbols, algebra, calculus, simplification, equation solving\n   - Load when: Basic symbolic computation, calculus, or solving equations\n\n2. **`matrices-linear-algebra.md`**: Matrix operations, eigenvalues, linear systems\n   - Load when: Working with matrices or linear algebra problems\n\n3. **`physics-mechanics.md`**: Classical mechanics, quantum mechanics, vectors, units\n   - Load when: Physics calculations or mechanics problems\n\n4. **`advanced-topics.md`**: Geometry, number theory, combinatorics, logic, statistics\n   - Load when: Advanced mathematical topics beyond basic algebra and calculus\n\n5. **`code-generation-printing.md`**: Lambdify, codegen, LaTeX output, printing\n   - Load when: Converting expressions to code or generating formatted output\n\n## Common Use Case Patterns\n\n### Pattern 1: Solve and Verify\n\n```python\nfrom sympy import symbols, solve, simplify\nx = symbols('x')\n\n# Solve equation\nequation = x**2 - 5*x + 6\nsolutions = solve(equation, x)  # [2, 3]\n\n# Verify solutions\nfor sol in solutions:\n    result = simplify(equation.subs(x, sol))\n    assert result == 0\n```\n\n### Pattern 2: Symbolic to Numeric Pipeline\n\n```python\n# 1. Define symbolic problem\nx, y = symbols('x y')\nexpr = sin(x) + cos(y)\n\n# 2. Manipulate symbolically\nsimplified = simplify(expr)\nderivative = diff(simplified, x)\n\n# 3. Convert to numerical function\nf = lambdify((x, y), derivative, 'numpy')\n\n# 4. Evaluate numerically\nresults = f(x_data, y_data)\n```\n\n### Pattern 3: Document Mathematical Results\n\n```python\n# Compute result symbolically\nintegral_expr = Integral(x**2, (x, 0, 1))\nresult = integral_expr.doit()\n\n# Generate documentation\nprint(f\"LaTeX: {latex(integral_expr)} = {latex(result)}\")\nprint(f\"Pretty: {pretty(integral_expr)} = {pretty(result)}\")\nprint(f\"Numerical: {result.evalf()}\")\n```\n\n## Integration with Scientific Workflows\n\n### With NumPy\n\n```python\nimport numpy as np\nfrom sympy import symbols, lambdify\n\nx = symbols('x')\nexpr = x**2 + 2*x + 1\n\nf = lambdify(x, expr, 'numpy')\nx_array = np.linspace(-5, 5, 100)\ny_array = f(x_array)\n```\n\n### With Matplotlib\n\n```python\nimport matplotlib.pyplot as plt\nimport numpy as np\nfrom sympy import symbols, lambdify, sin\n\nx = symbols('x')\nexpr = sin(x) \u002F x\n\nf = lambdify(x, expr, 'numpy')\nx_vals = np.linspace(-10, 10, 1000)\ny_vals = f(x_vals)\n\nplt.plot(x_vals, y_vals)\nplt.show()\n```\n\n### With SciPy\n\n```python\nfrom scipy.optimize import fsolve\nfrom sympy import symbols, lambdify\n\n# Define equation symbolically\nx = symbols('x')\nequation = x**3 - 2*x - 5\n\n# Convert to numerical function\nf = lambdify(x, equation, 'numpy')\n\n# Solve numerically with initial guess\nsolution = fsolve(f, 2)\n```\n\n## Quick Reference: Most Common Functions\n\n```python\n# Symbols\nfrom sympy import symbols, Symbol\nx, y = symbols('x y')\n\n# Basic operations\nfrom sympy import simplify, expand, factor, collect, cancel\nfrom sympy import sqrt, exp, log, sin, cos, tan, pi, E, I, oo\n\n# Calculus\nfrom sympy import diff, integrate, limit, series, Derivative, Integral\n\n# Solving\nfrom sympy import solve, solveset, linsolve, nonlinsolve, dsolve\n\n# Matrices\nfrom sympy import Matrix, eye, zeros, ones, diag\n\n# Logic and sets\nfrom sympy import And, Or, Not, Implies, FiniteSet, Interval, Union\n\n# Output\nfrom sympy import latex, pprint, lambdify, init_printing\n\n# Utilities\nfrom sympy import evalf, N, nsimplify\n```\n\n## Getting Started Examples\n\n### Example 1: Solve Quadratic Equation\n```python\nfrom sympy import symbols, solve, sqrt\nx = symbols('x')\nsolution = solve(x**2 - 5*x + 6, x)\n# [2, 3]\n```\n\n### Example 2: Calculate Derivative\n```python\nfrom sympy import symbols, diff, sin\nx = symbols('x')\nf = sin(x**2)\ndf_dx = diff(f, x)\n# 2*x*cos(x**2)\n```\n\n### Example 3: Evaluate Integral\n```python\nfrom sympy import symbols, integrate, exp\nx = symbols('x')\nintegral = integrate(x * exp(-x**2), (x, 0, oo))\n# 1\u002F2\n```\n\n### Example 4: Matrix Eigenvalues\n```python\nfrom sympy import Matrix\nM = Matrix([[1, 2], [2, 1]])\neigenvals = M.eigenvals()\n# {3: 1, -1: 1}\n```\n\n### Example 5: Generate Python Function\n```python\nfrom sympy import symbols, lambdify\nimport numpy as np\nx = symbols('x')\nexpr = x**2 + 2*x + 1\nf = lambdify(x, expr, 'numpy')\nf(np.array([1, 2, 3]))\n# array([ 4,  9, 16])\n```\n\n## Troubleshooting Common Issues\n\n1. **\"NameError: name 'x' is not defined\"**\n   - Solution: Always define symbols using `symbols()` before use\n\n2. **Unexpected numerical results**\n   - Issue: Using floating-point numbers like `0.5` instead of `Rational(1, 2)`\n   - Solution: Use `Rational()` or `S()` for exact arithmetic\n\n3. **Slow performance in loops**\n   - Issue: Using `subs()` and `evalf()` repeatedly\n   - Solution: Use `lambdify()` to create a fast numerical function\n\n4. **\"Can't solve this equation\"**\n   - Try different solvers: `solve`, `solveset`, `nsolve` (numerical)\n   - Check if the equation is solvable algebraically\n   - Use numerical methods if no closed-form solution exists\n\n5. **Simplification not working as expected**\n   - Try different simplification functions: `simplify`, `factor`, `expand`, `trigsimp`\n   - Add assumptions to symbols (e.g., `positive=True`)\n   - Use `simplify(expr, force=True)` for aggressive simplification\n\n## Additional Resources\n\n- Official Documentation: https:\u002F\u002Fdocs.sympy.org\u002F\n- Tutorial: https:\u002F\u002Fdocs.sympy.org\u002Flatest\u002Ftutorials\u002Fintro-tutorial\u002Findex.html\n- API Reference: https:\u002F\u002Fdocs.sympy.org\u002Flatest\u002Freference\u002Findex.html\n- Examples: https:\u002F\u002Fgithub.com\u002Fsympy\u002Fsympy\u002Ftree\u002Fmaster\u002Fexamples\n","# SymPy - Symbolic Mathematics in Python\n\n## Overview\n\nSymPy is a Python library for symbolic mathematics that enables exact computation using mathematical symbols rather than numerical approximations. This skill provides comprehensive guidance for performing symbolic algebra, calculus, linear algebra, equation solving, physics calculations, and code generation using SymPy.\n\n## When to Use This Skill\n\nUse this skill when:\n- Solving equations symbolically (algebraic, differential, systems of equations)\n- Performing calculus operations (derivatives, integrals, limits, series)\n- Manipulating and simplifying algebraic expressions\n- Working with matrices and linear algebra symbolically\n- Doing physics calculations (mechanics, quantum mechanics, vector analysis)\n- Number theory computations (primes, factorization, modular arithmetic)\n- Geometric calculations (2D\u002F3D geometry, analytic geometry)\n- Converting mathematical expressions to executable code (Python, C, Fortran)\n- Generating LaTeX or other formatted mathematical output\n- Needing exact mathematical results (e.g., `sqrt(2)` not `1.414...`)\n\n## Core Capabilities\n\n### 1. Symbolic Computation Basics\n\n**Creating symbols and expressions:**\n```python\nfrom sympy import symbols, Symbol\nx, y, z = symbols('x y z')\nexpr = x**2 + 2*x + 1\n\n# With assumptions\nx = symbols('x', real=True, positive=True)\nn = symbols('n', integer=True)\n```\n\n**Simplification and manipulation:**\n```python\nfrom sympy import simplify, expand, factor, cancel\nsimplify(sin(x)**2 + cos(x)**2)  # Returns 1\nexpand((x + 1)**3)  # x**3 + 3*x**2 + 3*x + 1\nfactor(x**2 - 1)    # (x - 1)*(x + 1)\n```\n\n**For detailed basics:** See `references\u002Fcore-capabilities.md`\n\n### 2. Calculus\n\n**Derivatives:**\n```python\nfrom sympy import diff\ndiff(x**2, x)        # 2*x\ndiff(x**4, x, 3)     # 24*x (third derivative)\ndiff(x**2*y**3, x, y)  # 6*x*y**2 (partial derivatives)\n```\n\n**Integrals:**\n```python\nfrom sympy import integrate, oo\nintegrate(x**2, x)              # x**3\u002F3 (indefinite)\nintegrate(x**2, (x, 0, 1))      # 1\u002F3 (definite)\nintegrate(exp(-x), (x, 0, oo))  # 1 (improper)\n```\n\n**Limits and Series:**\n```python\nfrom sympy import limit, series\nlimit(sin(x)\u002Fx, x, 0)  # 1\nseries(exp(x), x, 0, 6)  # 1 + x + x**2\u002F2 + x**3\u002F6 + x**4\u002F24 + x**5\u002F120 + O(x**6)\n```\n\n**For detailed calculus operations:** See `references\u002Fcore-capabilities.md`\n\n### 3. Equation Solving\n\n**Algebraic equations:**\n```python\nfrom sympy import solveset, solve, Eq\nsolveset(x**2 - 4, x)  # {-2, 2}\nsolve(Eq(x**2, 4), x)  # [-2, 2]\n```\n\n**Systems of equations:**\n```python\nfrom sympy import linsolve, nonlinsolve\nlinsolve([x + y - 2, x - y], x, y)  # {(1, 1)} (linear)\nnonlinsolve([x**2 + y - 2, x + y**2 - 3], x, y)  # (nonlinear)\n```\n\n**Differential equations:**\n```python\nfrom sympy import Function, dsolve, Derivative\nf = symbols('f', cls=Function)\ndsolve(Derivative(f(x), x) - f(x), f(x))  # Eq(f(x), C1*exp(x))\n```\n\n**For detailed solving methods:** See `references\u002Fcore-capabilities.md`\n\n### 4. Matrices and Linear Algebra\n\n**Matrix creation and operations:**\n```python\nfrom sympy import Matrix, eye, zeros\nM = Matrix([[1, 2], [3, 4]])\nM_inv = M**-1  # Inverse\nM.det()        # Determinant\nM.T            # Transpose\n```\n\n**Eigenvalues and eigenvectors:**\n```python\neigenvals = M.eigenvals()  # {eigenvalue: multiplicity}\neigenvects = M.eigenvects()  # [(eigenval, mult, [eigenvectors])]\nP, D = M.diagonalize()  # M = P*D*P^-1\n```\n\n**Solving linear systems:**\n```python\nA = Matrix([[1, 2], [3, 4]])\nb = Matrix([5, 6])\nx = A.solve(b)  # Solve Ax = b\n```\n\n**For comprehensive linear algebra:** See `references\u002Fmatrices-linear-algebra.md`\n\n### 5. Physics and Mechanics\n\n**Classical mechanics:**\n```python\nfrom sympy.physics.mechanics import dynamicsymbols, LagrangesMethod\nfrom sympy import symbols\n\n# Define system\nq = dynamicsymbols('q')\nm, g, l = symbols('m g l')\n\n# Lagrangian (T - V)\nL = m*(l*q.diff())**2\u002F2 - m*g*l*(1 - cos(q))\n\n# Apply Lagrange's method\nLM = LagrangesMethod(L, [q])\n```\n\n**Vector analysis:**\n```python\nfrom sympy.physics.vector import ReferenceFrame, dot, cross\nN = ReferenceFrame('N')\nv1 = 3*N.x + 4*N.y\nv2 = 1*N.x + 2*N.z\ndot(v1, v2)  # Dot product\ncross(v1, v2)  # Cross product\n```\n\n**Quantum mechanics:**\n```python\nfrom sympy.physics.quantum import Ket, Bra, Commutator\npsi = Ket('psi')\nA = Operator('A')\ncomm = Commutator(A, B).doit()\n```\n\n**For detailed physics capabilities:** See `references\u002Fphysics-mechanics.md`\n\n### 6. Advanced Mathematics\n\nThe skill includes comprehensive support for:\n\n- **Geometry:** 2D\u002F3D analytic geometry, points, lines, circles, polygons, transformations\n- **Number Theory:** Primes, factorization, GCD\u002FLCM, modular arithmetic, Diophantine equations\n- **Combinatorics:** Permutations, combinations, partitions, group theory\n- **Logic and Sets:** Boolean logic, set theory, finite and infinite sets\n- **Statistics:** Probability distributions, random variables, expectation, variance\n- **Special Functions:** Gamma, Bessel, orthogonal polynomials, hypergeometric functions\n- **Polynomials:** Polynomial algebra, roots, factorization, Groebner bases\n\n**For detailed advanced topics:** See `references\u002Fadvanced-topics.md`\n\n### 7. Code Generation and Output\n\n**Convert to executable functions:**\n```python\nfrom sympy import lambdify\nimport numpy as np\n\nexpr = x**2 + 2*x + 1\nf = lambdify(x, expr, 'numpy')  # Create NumPy function\nx_vals = np.linspace(0, 10, 100)\ny_vals = f(x_vals)  # Fast numerical evaluation\n```\n\n**Generate C\u002FFortran code:**\n```python\nfrom sympy.utilities.codegen import codegen\n[(c_name, c_code), (h_name, h_header)] = codegen(\n    ('my_func', expr), 'C'\n)\n```\n\n**LaTeX output:**\n```python\nfrom sympy import latex\nlatex_str = latex(expr)  # Convert to LaTeX for documents\n```\n\n**For comprehensive code generation:** See `references\u002Fcode-generation-printing.md`\n\n## Working with SymPy: Best Practices\n\n### 1. Always Define Symbols First\n\n```python\nfrom sympy import symbols\nx, y, z = symbols('x y z')\n# Now x, y, z can be used in expressions\n```\n\n### 2. Use Assumptions for Better Simplification\n\n```python\nx = symbols('x', positive=True, real=True)\nsqrt(x**2)  # Returns x (not Abs(x)) due to positive assumption\n```\n\nCommon assumptions: `real`, `positive`, `negative`, `integer`, `rational`, `complex`, `even`, `odd`\n\n### 3. Use Exact Arithmetic\n\n```python\nfrom sympy import Rational, S\n# Correct (exact):\nexpr = Rational(1, 2) * x\nexpr = S(1)\u002F2 * x\n\n# Incorrect (floating-point):\nexpr = 0.5 * x  # Creates approximate value\n```\n\n### 4. Numerical Evaluation When Needed\n\n```python\nfrom sympy import pi, sqrt\nresult = sqrt(8) + pi\nresult.evalf()    # 5.96371554103586\nresult.evalf(50)  # 50 digits of precision\n```\n\n### 5. Convert to NumPy for Performance\n\n```python\n# Slow for many evaluations:\nfor x_val in range(1000):\n    result = expr.subs(x, x_val).evalf()\n\n# Fast:\nf = lambdify(x, expr, 'numpy')\nresults = f(np.arange(1000))\n```\n\n### 6. Use Appropriate Solvers\n\n- `solveset`: Algebraic equations (primary)\n- `linsolve`: Linear systems\n- `nonlinsolve`: Nonlinear systems\n- `dsolve`: Differential equations\n- `solve`: General purpose (legacy, but flexible)\n\n## Reference Files Structure\n\nThis skill uses modular reference files for different capabilities:\n\n1. **`core-capabilities.md`**: Symbols, algebra, calculus, simplification, equation solving\n   - Load when: Basic symbolic computation, calculus, or solving equations\n\n2. **`matrices-linear-algebra.md`**: Matrix operations, eigenvalues, linear systems\n   - Load when: Working with matrices or linear algebra problems\n\n3. **`physics-mechanics.md`**: Classical mechanics, quantum mechanics, vectors, units\n   - Load when: Physics calculations or mechanics problems\n\n4. **`advanced-topics.md`**: Geometry, number theory, combinatorics, logic, statistics\n   - Load when: Advanced mathematical topics beyond basic algebra and calculus\n\n5. **`code-generation-printing.md`**: Lambdify, codegen, LaTeX output, printing\n   - Load when: Converting expressions to code or generating formatted output\n\n## Common Use Case Patterns\n\n### Pattern 1: Solve and Verify\n\n```python\nfrom sympy import symbols, solve, simplify\nx = symbols('x')\n\n# Solve equation\nequation = x**2 - 5*x + 6\nsolutions = solve(equation, x)  # [2, 3]\n\n# Verify solutions\nfor sol in solutions:\n    result = simplify(equation.subs(x, sol))\n    assert result == 0\n```\n\n### Pattern 2: Symbolic to Numeric Pipeline\n\n```python\n# 1. Define symbolic problem\nx, y = symbols('x y')\nexpr = sin(x) + cos(y)\n\n# 2. Manipulate symbolically\nsimplified = simplify(expr)\nderivative = diff(simplified, x)\n\n# 3. Convert to numerical function\nf = lambdify((x, y), derivative, 'numpy')\n\n# 4. Evaluate numerically\nresults = f(x_data, y_data)\n```\n\n### Pattern 3: Document Mathematical Results\n\n```python\n# Compute result symbolically\nintegral_expr = Integral(x**2, (x, 0, 1))\nresult = integral_expr.doit()\n\n# Generate documentation\nprint(f\"LaTeX: {latex(integral_expr)} = {latex(result)}\")\nprint(f\"Pretty: {pretty(integral_expr)} = {pretty(result)}\")\nprint(f\"Numerical: {result.evalf()}\")\n```\n\n## Integration with Scientific Workflows\n\n### With NumPy\n\n```python\nimport numpy as np\nfrom sympy import symbols, lambdify\n\nx = symbols('x')\nexpr = x**2 + 2*x + 1\n\nf = lambdify(x, expr, 'numpy')\nx_array = np.linspace(-5, 5, 100)\ny_array = f(x_array)\n```\n\n### With Matplotlib\n\n```python\nimport matplotlib.pyplot as plt\nimport numpy as np\nfrom sympy import symbols, lambdify, sin\n\nx = symbols('x')\nexpr = sin(x) \u002F x\n\nf = lambdify(x, expr, 'numpy')\nx_vals = np.linspace(-10, 10, 1000)\ny_vals = f(x_vals)\n\nplt.plot(x_vals, y_vals)\nplt.show()\n```\n\n### With SciPy\n\n```python\nfrom scipy.optimize import fsolve\nfrom sympy import symbols, lambdify\n\n# Define equation symbolically\nx = symbols('x')\nequation = x**3 - 2*x - 5\n\n# Convert to numerical function\nf = lambdify(x, equation, 'numpy')\n\n# Solve numerically with initial guess\nsolution = fsolve(f, 2)\n```\n\n## Quick Reference: Most Common Functions\n\n```python\n# Symbols\nfrom sympy import symbols, Symbol\nx, y = symbols('x y')\n\n# Basic operations\nfrom sympy import simplify, expand, factor, collect, cancel\nfrom sympy import sqrt, exp, log, sin, cos, tan, pi, E, I, oo\n\n# Calculus\nfrom sympy import diff, integrate, limit, series, Derivative, Integral\n\n# Solving\nfrom sympy import solve, solveset, linsolve, nonlinsolve, dsolve\n\n# Matrices\nfrom sympy import Matrix, eye, zeros, ones, diag\n\n# Logic and sets\nfrom sympy import And, Or, Not, Implies, FiniteSet, Interval, Union\n\n# Output\nfrom sympy import latex, pprint, lambdify, init_printing\n\n# Utilities\nfrom sympy import evalf, N, nsimplify\n```\n\n## Getting Started Examples\n\n### Example 1: Solve Quadratic Equation\n```python\nfrom sympy import symbols, solve, sqrt\nx = symbols('x')\nsolution = solve(x**2 - 5*x + 6, x)\n# [2, 3]\n```\n\n### Example 2: Calculate Derivative\n```python\nfrom sympy import symbols, diff, sin\nx = symbols('x')\nf = sin(x**2)\ndf_dx = diff(f, x)\n# 2*x*cos(x**2)\n```\n\n### Example 3: Evaluate Integral\n```python\nfrom sympy import symbols, integrate, exp\nx = symbols('x')\nintegral = integrate(x * exp(-x**2), (x, 0, oo))\n# 1\u002F2\n```\n\n### Example 4: Matrix Eigenvalues\n```python\nfrom sympy import Matrix\nM = Matrix([[1, 2], [2, 1]])\neigenvals = M.eigenvals()\n# {3: 1, -1: 1}\n```\n\n### Example 5: Generate Python Function\n```python\nfrom sympy import symbols, lambdify\nimport numpy as np\nx = symbols('x')\nexpr = x**2 + 2*x + 1\nf = lambdify(x, expr, 'numpy')\nf(np.array([1, 2, 3]))\n# array([ 4,  9, 16])\n```\n\n## Troubleshooting Common Issues\n\n1. **\"NameError: name 'x' is not defined\"**\n   - Solution: Always define symbols using `symbols()` before use\n\n2. **Unexpected numerical results**\n   - Issue: Using floating-point numbers like `0.5` instead of `Rational(1, 2)`\n   - Solution: Use `Rational()` or `S()` for exact arithmetic\n\n3. **Slow performance in loops**\n   - Issue: Using `subs()` and `evalf()` repeatedly\n   - Solution: Use `lambdify()` to create a fast numerical function\n\n4. **\"Can't solve this equation\"**\n   - Try different solvers: `solve`, `solveset`, `nsolve` (numerical)\n   - Check if the equation is solvable algebraically\n   - Use numerical methods if no closed-form solution exists\n\n5. **Simplification not working as expected**\n   - Try different simplification functions: `simplify`, `factor`, `expand`, `trigsimp`\n   - Add assumptions to symbols (e.g., `positive=True`)\n   - Use `simplify(expr, force=True)` for aggressive simplification\n\n## Additional Resources\n\n- Official Documentation: https:\u002F\u002Fdocs.sympy.org\u002F\n- Tutorial: https:\u002F\u002Fdocs.sympy.org\u002Flatest\u002Ftutorials\u002Fintro-tutorial\u002Findex.html\n- API Reference: https:\u002F\u002Fdocs.sympy.org\u002Flatest\u002Freference\u002Findex.html\n- Examples: https:\u002F\u002Fgithub.com\u002Fsympy\u002Fsympy\u002Ftree\u002Fmaster\u002Fexamples\n",{"name":5,"description":7},"main","2b749c82b5d11fac39d9a6e021ce3f5b8a541bd1","cli-tool\u002Fcomponents\u002Fskills\u002Fscientific\u002Fsympy",3931,"https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates","https:\u002F\u002Faitmpl.com","https:\u002F\u002Fgithub.com\u002Fdavila7","https:\u002F\u002Fdanielavila.me","Building AI dev tools with LLMs","2026-11-14 06:14:46",{"source":8,"skillName":5,"commands":64,"prompt":74,"zipAvailable":75},[65,68,71],{"tool":66,"command":67},"npx","npx skills add davila7\u002Fclaude-code-templates --skill sympy",{"tool":69,"command":70},"bunx","bunx skills add davila7\u002Fclaude-code-templates --skill sympy",{"tool":72,"command":73},"pnpm","pnpm dlx skills add davila7\u002Fclaude-code-templates --skill sympy","安装技能，技能地址：https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Fscientific\u002Fsympy\u002FSKILL.md",true,[77,83,89,93,97,101],{"path":78,"resourceType":79,"resourceTypeDesc":80,"sizeBytes":81,"sourceHtmlUrl":82},"LICENSE.txt","LICENSE","许可证",143,"https:\u002F\u002Fgithub.com\u002Fnoirelab\u002Flinux-setup\u002Fblob\u002Fmain\u002Fconfigs\u002Fcommon\u002Fclaude\u002Fskills\u002Fseo-programmatic\u002FLICENSE.txt",{"path":84,"resourceType":85,"resourceTypeDesc":86,"sizeBytes":87,"sourceHtmlUrl":88},"references\u002Fadvanced-topics.md","REFERENCE","参考文档",13132,"https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Fscientific\u002Fsympy\u002Freferences\u002Fadvanced-topics.md",{"path":90,"resourceType":85,"resourceTypeDesc":86,"sizeBytes":91,"sourceHtmlUrl":92},"references\u002Fcode-generation-printing.md",12427,"https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Fscientific\u002Fsympy\u002Freferences\u002Fcode-generation-printing.md",{"path":94,"resourceType":85,"resourceTypeDesc":86,"sizeBytes":95,"sourceHtmlUrl":96},"references\u002Fcore-capabilities.md",7754,"https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Fscientific\u002Fsympy\u002Freferences\u002Fcore-capabilities.md",{"path":98,"resourceType":85,"resourceTypeDesc":86,"sizeBytes":99,"sourceHtmlUrl":100},"references\u002Fmatrices-linear-algebra.md",9639,"https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Fscientific\u002Fsympy\u002Freferences\u002Fmatrices-linear-algebra.md",{"path":102,"resourceType":85,"resourceTypeDesc":86,"sizeBytes":103,"sourceHtmlUrl":104},"references\u002Fphysics-mechanics.md",12053,"https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Fscientific\u002Fsympy\u002Freferences\u002Fphysics-mechanics.md",[106,130,156,187,222,246],{"skillNo":107,"name":108,"nameZh":6,"description":109,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":110,"categories":111,"keywords":113,"publishedAt":48},"01M70NHBTQ8BV0A2SCAZXEPHCX","wealthville-pool-scoring","Score DeFi liquidity pools before providing liquidity. Returns a 0-100 pool score and an Enter\u002FHold\u002FExit\u002FReduce\u002FAvoid verdict with calibrated confidence for ~68,800 Solana pools and 575 EVM pools, plus a public miss-inclusive track record. Use when asked whether a pool is worth LPing into, which pools look best right now, or how accurate the scores have actually been.","https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Fweb-data\u002Fwealthville-pool-scoring\u002FSKILL.md",[112],{"categoryNo":19,"categoryName":20,"taxonomyType":21,"taxonomyTypeDesc":22},[114,115,116,117,118,35,119,120,45,31,121,29,122,123,124,125,126,127,128,129],"scoring","pool","wealthville pool scoring","liquidity","which","exit","now","reduce","record","track","verdict","evm","solana","how","public","look",{"skillNo":131,"name":132,"nameZh":6,"description":133,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":134,"categories":135,"keywords":137,"publishedAt":48},"01M70MB6VR8ERJ4EM8D5KHBMEV","technical-debt-auditor","Scans a codebase and produces a quantified technical debt report with a prioritized remediation plan. Analyzes dead code, TODO\u002FFIXME\u002FHACK markers, dependency staleness, complexity hotspots, code duplication signals, test coverage gaps, unused exports, and outdated patterns. Use this skill when the user asks to audit their codebase for tech debt, wants a health check of their code quality, says things like \"where should I focus refactoring\", \"find code smells\", \"audit my codebase\", \"what technical debt do we have\", \"prioritize cleanup work\", or asks about code quality metrics. Also trigger when the user mentions \"code rot\", \"legacy cleanup\", \"refactoring priorities\", or wants to understand the overall health of a project before a major effort. Trigger even if the user doesn't say \"technical debt\" explicitly — any request to systematically assess code quality and identify improvement priorities belongs here.","https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Fdevelopment\u002Ftechnical-debt-auditor\u002FSKILL.md",[136],{"categoryNo":19,"categoryName":20,"taxonomyType":21,"taxonomyTypeDesc":22},[138,139,140,141,142,143,144,145,146,147,148,31,46,149,150,151,152,153,154,155],"technical debt","debt","technical","technical debt auditor","auditor","coverage","complexity","markers","project","cleanup","unused","todo","work","plan","focus","signals","audit","dependency",{"skillNo":157,"name":158,"nameZh":6,"description":159,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":160,"categories":161,"keywords":169,"publishedAt":48},"01M70KPYH9QNHCNME5GJQGE22K","readonly-sql-guard","Make an agent's database access provably read-only. Use when an agent runs caller-supplied SQL against a production\u002FERP\u002Fanalytics database (a \"query\" MCP tool, text-to-SQL, an admin console), or when reviewing DB-access code for write\u002FDDL\u002Fside-effect\u002Ftransaction-escape risks. Checks what a statement CALLS, not just its shape.","https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Fdatabase\u002Freadonly-sql-guard\u002FSKILL.md",[162,165,166],{"categoryNo":163,"categoryName":164,"taxonomyType":21,"taxonomyTypeDesc":22},"01JBSEEDCAT000000000000010","后端与接口",{"categoryNo":19,"categoryName":20,"taxonomyType":21,"taxonomyTypeDesc":22},{"categoryNo":167,"categoryName":168,"taxonomyType":26,"taxonomyTypeDesc":27},"01JBSEEDCAT000000000000033","数据分析师",[170,171,172,173,174,175,176,35,177,178,179,180,181,182,183,45,184,185,31,186],"readonly","guard","sql guard","sql","readonly sql guard","erp","effect","read-only","db","just","tool","calls","only","MCP","access","database","query",{"skillNo":188,"name":189,"nameZh":6,"description":190,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":191,"licenseFileUrl":192,"sourceHtmlUrl":193,"categories":194,"keywords":198,"publishedAt":48},"01M6AFY6F7CC2BBZP1QD6VTNVC","web-artifacts-builder","Suite of tools for creating elaborate, multi-component claude.ai HTML artifacts using modern frontend web technologies (React, Tailwind CSS, shadcn\u002Fui). Use for complex artifacts requiring state management, routing, or shadcn\u002Fui components - not for simple single-file HTML\u002FJSX artifacts.","Apache-2.0","https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Futilities\u002Fweb-artifacts-builder\u002FLICENSE.txt","https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Futilities\u002Fweb-artifacts-builder\u002FSKILL.md",[195],{"categoryNo":196,"categoryName":197,"taxonomyType":21,"taxonomyTypeDesc":22},"01JBSEEDCAT000000000000009","前端开发",[199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,35,221],"artifacts builder","web","web artifacts builder","artifacts","builder","state","routing","state management","component","css","frontend","ui","Tools","file","components","shadcn","react","Tailwind","suite","jsx","html","single-file","ui components",{"skillNo":223,"name":224,"nameZh":6,"description":225,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":191,"licenseFileUrl":226,"sourceHtmlUrl":227,"categories":228,"keywords":233,"publishedAt":48},"01M6AFWF33SFV9Z3SF4PEEE4BF","webapp-testing","Toolkit for interacting with and testing local web applications using Playwright. Supports verifying frontend functionality, debugging UI behavior, capturing browser screenshots, and viewing browser logs.","https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Fsecurity\u002Fwebapp-testing\u002FLICENSE.txt","https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Fsecurity\u002Fwebapp-testing\u002FSKILL.md",[229,232],{"categoryNo":230,"categoryName":231,"taxonomyType":21,"taxonomyTypeDesc":22},"01JBSEEDCAT000000000000008","测试与质量",{"categoryNo":196,"categoryName":197,"taxonomyType":21,"taxonomyTypeDesc":22},[234,235,236,237,238,200,239,209,210,240,241,242,243,35,244,29,245],"webapp testing","testing","webapp","browser","playwright","applications","debugging","toolkit","logs","screenshots","local","behavior",{"skillNo":247,"name":248,"nameZh":6,"description":249,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":191,"licenseFileUrl":250,"sourceHtmlUrl":251,"categories":252,"keywords":260,"publishedAt":48},"01M6AF67Q67JJJ5V51JR2P52KA","discernment-nudge","After you give a substantive answer or draft that the user may act on — advice or recommendations, drafted artifacts such as goals, plans, pitches, proposals, or emails, estimates or projections, analysis or interpretation of data, factual claims they may rely on, or a multi-step argument — invoke this skill BEFORE finalizing your reply and then, if it applies, append 2-3 short follow-up questions, each tied to something specific in what you just produced, that help the user check key facts, probe the reasoning or assumptions, and notice missing context. Do this at most once per conversation. Skip it when the user asked a trivial how-to or simple lookup, wants a purely educational explanation, asked you only to format, convert, or assemble a file from content they provided, is writing code they will run, is doing creative writing or casual chat, or already asked you to double-check, cite, or review — the skill file explains these boundaries and the exact output format.","https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Fproductivity\u002Fdiscernment-nudge\u002FLICENSE.txt","https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Fproductivity\u002Fdiscernment-nudge\u002FSKILL.md",[253,256,257],{"categoryNo":254,"categoryName":255,"taxonomyType":21,"taxonomyTypeDesc":22},"01JBSEEDCAT000000000000018","写作与文案",{"categoryNo":19,"categoryName":20,"taxonomyType":21,"taxonomyTypeDesc":22},{"categoryNo":258,"categoryName":259,"taxonomyType":26,"taxonomyTypeDesc":27},"01JBSEEDCAT000000000000036","内容创作者",[261,262,263,264,265,266,267,268,202,269,212,46,270,271,272,273,274,182,275,31,276,277,278,279,280,127,281],"discernment nudge","nudge","interpretation","help","run","reasoning","data","writing","lookup","content","review","conversation","short","up","invoke","you","analysis","claims","argument","assemble","recommendations"]