analytic-functions
Problem-solving strategies for analytic functions in complex analysis
Profile →npx skills add parcadei/Continuous-Claude-v3 --skill analytic-functions --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Analytic Functions ## When to Use Use this skill when working on analytic-functions problems in complex analysis. ## Decision Tree 1. **Is f analytic at z0?** - Check Cauchy-Riemann equations: du/dx = dv/dy, du/dy = -dv/dx - Check if f has power series expansion around z0 - Check if f is differentiable in neighborhood of z0 - `sympy_compute.py diff "u" --var x` and `sympy_compute.py diff "v" --var y` 2. **Cauchy-Riemann Verification** - Write f(z) = u(x,y) + iv(x,y) - Compute partial derivatives - Verify: du/dx = dv/dy AND du/dy = -dv/dx - `z3_solve.py prove "cauchy_riemann"` 3. **Power Series** - f(z) = sum_{n=0}^{inf} a_n (z - z0)^n - Radius of convergence: R = 1/limsup |a_n|^(1/n) - `sympy_compute.py series "f(z)" --var z --at z0` 4. **Analytic Continuation** - Extend f beyond original domain via power series - Identity theorem: if f = g on set with limit point, then f = g everywhere ## Tool Commands ### Sympy_Diff_U ```bash uv run python -m runtime.harness scripts/sympy_compute.py diff "u(x,y)" --var x ``` ### Sympy_Diff_V ```bash uv run python -m runtime.harness scripts/sympy_compute.py diff "v(x,y)" --var y ``` ### Sympy_Series ```bash uv run python -m runtime.harness scrip
- When to Use
- Decision Tree
- Tool Commands
- SympyDiffU
- SympyDiffV
- SympySeries
- Z3CauchyRiemann
- Key Techniques
- Cognitive Tools Reference
uv run python -m runtime.harness scripts/sympy_compute.py diff "u(x,y)" --var x uv run python -m runtime.harness scripts/sympy_compute.py diff "v(x,y)" --var y uv run python -m runtime.harness scripts/sympy_compute.py series "exp(z)" --var z --at 0 uv run python -m runtime.harness scripts/z3_solve.py prove "diff(u,x) == diff(v,y)"
What does the analytic-functions skill do?
Problem-solving strategies for analytic functions in complex analysis
How do I install it?
Run `npx skills add parcadei/Continuous-Claude-v3 --skill analytic-functions --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From parcadei/Continuous-Claude-v3, a repository with 3,879 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.