sympy

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.

1.12x

Quality

75%

Does it follow best practices?

Impact

89%

1.12x

Average score across 6 eval scenarios

Securityby

Passed

No known issues

Optimize this skill with Tessl

npx tessl skill review --optimize ./scientific-skills/sympy/SKILL.md

Evaluation results

78%

Filter Transfer Function Audit

Exact arithmetic and equation solving

Criteria

Without context

With context

Exact fraction encoding

100%

Symbol definition

100%

Primary solver solveset

Limit at removable singularity

100%

Limit at infinity

100%

Expression simplification

100%

Symbol assumptions

Numerical approximation

100%

Output file written

100%

Efficient Electromagnetic Field Evaluation

Lambdify and performance optimization

Criteria

Without context

With context

lambdify for vectorization

100%

numpy backend

100%

All variables in lambdify

100%

Common subexpression elimination

100%

No subs/evalf loop

100%

NumPy grid creation

100%

Output field_data.npz

100%

Output performance_log.txt

100%

90%

18%

N-Body Simulation Kernel Generation

C code generation and LaTeX documentation

Criteria

Without context

With context

codegen import and use

100%

C language argument

100%

CSE before codegen

100%

53%

latex() for documentation

100%

nbody_kernel.c generated

100%

formulas.tex generated

100%

Symbol assumptions

100%

70%

Symbolic differentiation

100%

Damped Oscillator Transient Analysis

ODE solving with initial conditions and series expansion

Criteria

Without context

With context

Function symbol cls=Function

100%

dsolve() used

100%

ics parameter for initial conditions

100%

series() for Taylor expansion

100%

removeO() on series result

100%

Symbol assumptions applied

100%

evalf() for numerical output

100%

Results file written

100%

71%

33%

Vibration Mode Analysis for a Multi-Story Building

Matrix eigenvalue analysis and decompositions

Criteria

Without context

With context

Symbol k with assumption

100%

Matrix() construction

100%

eigenvals() called

14%

100%

eigenvects() called

diagonalize() called

Diagonalization verified

70%

QRdecomposition() called

25%

100%

linsolve or A.solve for linear system

21%

100%

Results file written

87%

100%

96%

Insurance Risk Modeling with Exact Probability Calculations

Symbolic probability and statistics with sympy.stats

Criteria

Without context

With context

Normal random variable defined

100%

density() for PDF

100%

P() for probability

100%

66%

E() for expected value

100%

variance() for variance

100%

Poisson random variable defined

100%

Symbolic parameters with assumptions

50%

100%

evalf() for numerical output

100%

Report file written

100%

Repository: K-Dense-AI/claude-scientific-skills
Commit: b58ad7e

Evaluated: 27 days ago
Agent: Claude Code
Model: Claude Sonnet 4.6

Table of Contents

Filter Transfer Function Audit Efficient Electromagnetic Field Evaluation N-Body Simulation Kernel Generation Damped Oscillator Transient Analysis Vibration Mode Analysis for a Multi-Story Building Insurance Risk Modeling with Exact Probability Calculations

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