convergence
by parcadei
Context management for Claude Code. Hooks maintain state via ledgers and handoffs. MCP execution without context pollution. Agent orchestration with isolated context windows.
Run in ManusUse Cases
MCP Server Integration
AI tool integration using Model Context Protocol. Using convergence.
API Integration
Easily build API integrations with external services.
Data Synchronization
Automatically sync data between multiple systems.
Webhook Setup
Enable event-driven integrations with webhooks.
SKILL.md
name: convergence description: "Problem-solving strategies for convergence in real analysis" allowed-tools: [Bash, Read]
Convergence
When to Use
Use this skill when working on convergence problems in real analysis.
Decision Tree
-
Identify Sequence/Series Type
- Geometric series: |r| < 1 converges
- p-series: p > 1 converges
- Alternating series: check decreasing + limit 0
-
Apply Convergence Tests
- Ratio test:
sympy_compute.py limit "a_{n+1}/a_n" - Root test:
sympy_compute.py limit "a_n^(1/n)" - Comparison test: find bounding series
- Ratio test:
-
Verify Bounds
- Use
z3_solve.py provefor inequality bounds - Check monotonicity with derivatives
- Use
-
Compute Sum (if convergent)
sympy_compute.py sum "a_n" --var n --from 0 --to oo
Tool Commands
Sympy_Limit
uv run python -m runtime.harness scripts/sympy_compute.py limit "a_n" --var n --at oo
Sympy_Sum
uv run python -m runtime.harness scripts/sympy_compute.py sum "1/n**2" --var n --from 1 --to oo
Z3_Prove
uv run python -m runtime.harness scripts/z3_solve.py prove "series_bounded"
Cognitive Tools Reference
See .claude/skills/math-mode/SKILL.md for full tool documentation.
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