Ready to supercharge your AI agents?

Install any skill in seconds. Free to start, no credit card required.

Get Started Free →

Numerical Stability · FreedomIntelligence | DecimalAI

Scienceby FreedomIntelligence

Numerical Stability

Analyze and enforce numerical stability for time-dependent PDE simulations.

SkillScore

SkillScore36/100

Test results 36

Safety

3/3 safety checks passed

Code scan
Intent
Content

What it changes

0%36%of test cases passed +36 pts

Without skill0 of 22

With skill8 of 22

8 fixed0 passed either way14 still failing0 broke

Measured on gemini-3.6-flash7/26/2026v120 comparable

Track record

Agent runs: 0; All time

Use this skill

Your agent runs on

Adds every file the skill has, pinned so you can update it. No account needed.

pip install "decimalai>=0.15"
decimalai skills add numerical-stability
claude --plugin-dir "$(git rev-parse --show-toplevel 2>/dev/null || pwd)/.agents"

The same install from Python, for a notebook or a setup script.

Install

pip install "decimalai>=0.15"

Add the skill

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("numerical-stability")
if result.exit_code:
    raise SystemExit(result.problems)

print("Added. Start Claude Code with the command below.")

Start Claude Code with it

claude --plugin-dir "$(git rev-parse --show-toplevel 2>/dev/null || pwd)/.agents"

Type these in a Claude Code session. No account or API key. It writes the skill and any files it bundles, and asks first when its safety rating isn't Passed.

Add the DecimalAI plugin, once

/plugin marketplace add decimal-labs/decimalai-claude-plugins
/plugin install decimalai@decimalai

Install this skill

/decimalai:install numerical-stability

The plugin needs python3 and curl on your machine.

No Python or account. Claude Code picks it up in its next session.

Save it into your project

curl -fsSL --create-dirs -o .claude/skills/numerical-stability/SKILL.md https://app.decimal.ai/s/numerical-stability/SKILL.md

Copy SKILL.md

Save it in your project, as

.claude/skills/numerical-stability/SKILL.md

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Claude Code docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[claude-agent-sdk]"
decimalai skills add numerical-stability

Add it to your agent

import asyncio

from claude_agent_sdk import ClaudeAgentOptions
from decimalai.claude_agent_sdk import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

async def main():
    question = "Hello!"
    async with support.run(question) as run:  # one user message, one run
        async for message in run.query(options=ClaudeAgentOptions(max_turns=6)):
            print(message)

# In a notebook or async code: await main()
asyncio.run(main())

Prefer its own loader? ClaudeAgentOptions(plugins=[skills_plugin()], skills="all") reads the same folder. Use one or the other: a skill delivered both ways reaches the prompt twice.

The same install from Python, for a notebook or a setup script. agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[claude-agent-sdk]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("numerical-stability")
if result.exit_code:
    raise SystemExit(result.problems)

import asyncio

from claude_agent_sdk import ClaudeAgentOptions
from decimalai.claude_agent_sdk import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

async def main():
    question = "Hello!"
    async with support.run(question) as run:  # one user message, one run
        async for message in run.query(options=ClaudeAgentOptions(max_turns=6)):
            print(message)

# In a notebook or async code: await main()
asyncio.run(main())

Prefer its own loader? ClaudeAgentOptions(plugins=[skills_plugin()], skills="all") reads the same folder. Use one or the other: a skill delivered both ways reaches the prompt twice.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/numerical-stability/SKILL.md

Give it to your agent

import asyncio
from pathlib import Path
from claude_agent_sdk import ClaudeAgentOptions, query

skill = Path(".agents/skills/numerical-stability/SKILL.md").read_text()
options = ClaudeAgentOptions(system_prompt=f"You are a helpful agent.\n\n{skill}", max_turns=6)

async def main():
    async for message in query(prompt="Hello!", options=options):
        print(message)

# In a notebook or async code: await main()
asyncio.run(main())

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Claude Agent SDK docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[openai-agents]"
decimalai skills add numerical-stability

Add it to your agent

from agents import Agent, Runner
from decimalai.openai_agents import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = Agent(
    name=support.name,
    instructions=support.instructions,  # your prompt, then the skill list
    tools=[*support.tools],             # your tools, then load_skill
)
# In a notebook or async code: result = await Runner.run(agent, "Hello!")
result = Runner.run_sync(agent, "Hello!")

Using SandboxAgent? capabilities=[Shell(), decimalai.openai_agents.sandbox_skills()] points its own loader at the same folder.

Install

pip install "decimalai[openai-agents]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("numerical-stability")
if result.exit_code:
    raise SystemExit(result.problems)

from agents import Agent, Runner
from decimalai.openai_agents import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = Agent(
    name=support.name,
    instructions=support.instructions,  # your prompt, then the skill list
    tools=[*support.tools],             # your tools, then load_skill
)
# In a notebook or async code: result = await Runner.run(agent, "Hello!")
result = Runner.run_sync(agent, "Hello!")

Using SandboxAgent? capabilities=[Shell(), decimalai.openai_agents.sandbox_skills()] points its own loader at the same folder.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/numerical-stability/SKILL.md

Give it to your agent

from pathlib import Path
from agents import Agent, Runner

skill = Path(".agents/skills/numerical-stability/SKILL.md").read_text()
agent = Agent(name="support", instructions=f"You are a helpful agent.\n\n{skill}")
# In a notebook or async code: result = await Runner.run(agent, "Hello!")
result = Runner.run_sync(agent, "Hello!")

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

OpenAI Agents docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[openai]"
decimalai skills add numerical-stability

Add it to your agent

import json

from openai import OpenAI
from decimalai.openai import agent_config

client = OpenAI()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")


def lookup_order(order_id: str) -> str:
    return f"Order {order_id} shipped yesterday."


# Your tools, as Chat Completions takes them, and what answers each.
TOOLS = [{"type": "function", "function": {
    "name": "lookup_order",
    "description": "Look up the status of an order.",
    "parameters": {"type": "object", "properties": {"order_id": {"type": "string"}},
                   "required": ["order_id"]},
}}]
FUNCTIONS = {"lookup_order": lookup_order}

question = "Where is order A1001?"
with support.run(question) as run:  # one user message, one run
    # run.system is your prompt, then the skill list.
    messages = [{"role": "system", "content": run.system}, run.message]
    while True:
        reply = client.chat.completions.create(
            model="gpt-5.4-mini",
            messages=messages,
            tools=[*TOOLS, *run.tools],  # your tools, then load_skill
        ).choices[0].message
        messages.append(reply)
        if not reply.tool_calls:
            break
        for call in reply.tool_calls:
            # load_skill is answered by the run; your own tools by FUNCTIONS.
            function = FUNCTIONS.get(call.function.name)
            messages.append(run.tool_result(call) or {
                "role": "tool", "tool_call_id": call.id,
                "content": function(**json.loads(call.function.arguments)) if function
                else f"There is no tool named {call.function.name!r}.",
            })
print(reply.content)

# The Responses API takes run.response_tools instead of run.tools.

Install

pip install "decimalai[openai]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("numerical-stability")
if result.exit_code:
    raise SystemExit(result.problems)

import json

from openai import OpenAI
from decimalai.openai import agent_config

client = OpenAI()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")


def lookup_order(order_id: str) -> str:
    return f"Order {order_id} shipped yesterday."


# Your tools, as Chat Completions takes them, and what answers each.
TOOLS = [{"type": "function", "function": {
    "name": "lookup_order",
    "description": "Look up the status of an order.",
    "parameters": {"type": "object", "properties": {"order_id": {"type": "string"}},
                   "required": ["order_id"]},
}}]
FUNCTIONS = {"lookup_order": lookup_order}

question = "Where is order A1001?"
with support.run(question) as run:  # one user message, one run
    # run.system is your prompt, then the skill list.
    messages = [{"role": "system", "content": run.system}, run.message]
    while True:
        reply = client.chat.completions.create(
            model="gpt-5.4-mini",
            messages=messages,
            tools=[*TOOLS, *run.tools],  # your tools, then load_skill
        ).choices[0].message
        messages.append(reply)
        if not reply.tool_calls:
            break
        for call in reply.tool_calls:
            # load_skill is answered by the run; your own tools by FUNCTIONS.
            function = FUNCTIONS.get(call.function.name)
            messages.append(run.tool_result(call) or {
                "role": "tool", "tool_call_id": call.id,
                "content": function(**json.loads(call.function.arguments)) if function
                else f"There is no tool named {call.function.name!r}.",
            })
print(reply.content)

# The Responses API takes run.response_tools instead of run.tools.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/numerical-stability/SKILL.md

Give it to your agent

from pathlib import Path
from openai import OpenAI

client = OpenAI()
skill = Path(".agents/skills/numerical-stability/SKILL.md").read_text()
reply = client.chat.completions.create(
    model="gpt-5.4-mini",
    messages=[
        {"role": "system", "content": f"You are a helpful agent.\n\n{skill}"},
        {"role": "user", "content": "Hello!"},
    ],
).choices[0].message

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

OpenAI SDK docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[anthropic]"
decimalai skills add numerical-stability

Add it to your agent

import anthropic
from decimalai.anthropic import agent_config

client = anthropic.Anthropic()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

question = "Hello!"
with support.run(question) as run:  # one user message, one run
    answer = client.beta.messages.tool_runner(
        model="claude-haiku-5-5",
        max_tokens=4096,
        system=run.system,     # your prompt, then the skill list
        tools=[*run.tools],    # your tools, then load_skill
        messages=[{"role": "user", "content": question}],
    ).until_done()

Install

pip install "decimalai[anthropic]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("numerical-stability")
if result.exit_code:
    raise SystemExit(result.problems)

import anthropic
from decimalai.anthropic import agent_config

client = anthropic.Anthropic()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

question = "Hello!"
with support.run(question) as run:  # one user message, one run
    answer = client.beta.messages.tool_runner(
        model="claude-haiku-5-5",
        max_tokens=4096,
        system=run.system,     # your prompt, then the skill list
        tools=[*run.tools],    # your tools, then load_skill
        messages=[{"role": "user", "content": question}],
    ).until_done()

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/numerical-stability/SKILL.md

Give it to your agent

from pathlib import Path
import anthropic

client = anthropic.Anthropic()
skill = Path(".agents/skills/numerical-stability/SKILL.md").read_text()
reply = client.messages.create(
    model="claude-haiku-5-5",
    max_tokens=4096,
    system=f"You are a helpful agent.\n\n{skill}",
    messages=[{"role": "user", "content": "Hello!"}],
)

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Anthropic docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[google-genai]"
decimalai skills add numerical-stability

Add it to your agent

from google import genai
from google.genai import types
from decimalai.google_genai import agent_config

client = genai.Client()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")


def lookup_order(order_id: str) -> str:
    return f"Order {order_id} shipped yesterday."


# Your functions, as declarations for the model, and what answers each.
TOOLS = [{"function_declarations": [{
    "name": "lookup_order",
    "description": "Look up the status of an order.",
    "parameters_json_schema": {"type": "object", "properties": {"order_id": {"type": "string"}},
                               "required": ["order_id"]},
}]}]
FUNCTIONS = {"lookup_order": lookup_order}

question = "Where is order A1001?"
with support.run(question) as run:  # one user message, one run
    config = types.GenerateContentConfig(
        system_instruction=run.system,     # your prompt, then the skill list
        tools=[*TOOLS, *run.tool_params],  # your functions, then load_skill
    )
    contents = [{"role": "user", "parts": [{"text": run.message}]}]
    while True:
        response = client.models.generate_content(
            model="gemini-3.5-flash", contents=contents, config=config,
        )
        if not response.function_calls:
            break
        contents.append(response.candidates[0].content)
        parts = []
        for call in response.function_calls:
            # load_skill is answered by the run; your own functions by FUNCTIONS.
            # A loop of your own rather than automatic function calling, which
            # raises KeyError when the model asks for a function you did not pass.
            function = FUNCTIONS.get(call.name)
            parts.append(run.tool_result(call) or {"function_response": {
                "name": call.name, "id": call.id,
                "response": {"result": function(**(call.args or {})) if function
                             else f"There is no function named {call.name!r}."},
            }})
        contents.append({"role": "user", "parts": parts})
print(response.text)

Install

pip install "decimalai[google-genai]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("numerical-stability")
if result.exit_code:
    raise SystemExit(result.problems)

from google import genai
from google.genai import types
from decimalai.google_genai import agent_config

client = genai.Client()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")


def lookup_order(order_id: str) -> str:
    return f"Order {order_id} shipped yesterday."


# Your functions, as declarations for the model, and what answers each.
TOOLS = [{"function_declarations": [{
    "name": "lookup_order",
    "description": "Look up the status of an order.",
    "parameters_json_schema": {"type": "object", "properties": {"order_id": {"type": "string"}},
                               "required": ["order_id"]},
}]}]
FUNCTIONS = {"lookup_order": lookup_order}

question = "Where is order A1001?"
with support.run(question) as run:  # one user message, one run
    config = types.GenerateContentConfig(
        system_instruction=run.system,     # your prompt, then the skill list
        tools=[*TOOLS, *run.tool_params],  # your functions, then load_skill
    )
    contents = [{"role": "user", "parts": [{"text": run.message}]}]
    while True:
        response = client.models.generate_content(
            model="gemini-3.5-flash", contents=contents, config=config,
        )
        if not response.function_calls:
            break
        contents.append(response.candidates[0].content)
        parts = []
        for call in response.function_calls:
            # load_skill is answered by the run; your own functions by FUNCTIONS.
            # A loop of your own rather than automatic function calling, which
            # raises KeyError when the model asks for a function you did not pass.
            function = FUNCTIONS.get(call.name)
            parts.append(run.tool_result(call) or {"function_response": {
                "name": call.name, "id": call.id,
                "response": {"result": function(**(call.args or {})) if function
                             else f"There is no function named {call.name!r}."},
            }})
        contents.append({"role": "user", "parts": parts})
print(response.text)

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/numerical-stability/SKILL.md

Give it to your agent

from pathlib import Path
from google import genai
from google.genai import types

client = genai.Client()
skill = Path(".agents/skills/numerical-stability/SKILL.md").read_text()
response = client.models.generate_content(
    model="gemini-3.5-flash",
    contents="Hello!",
    config=types.GenerateContentConfig(system_instruction=f"You are a helpful agent.\n\n{skill}"),
)

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Gemini API docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[langchain]" langchain-openai
decimalai skills add numerical-stability

Add it to your agent

from langchain.agents import create_agent
from decimalai.langchain import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = create_agent(
    "openai:gpt-5.4-mini",
    tools=[],                         # your tools; the middleware adds load_skill
    middleware=[support.middleware],  # your prompt, the skill list and load_skill
)
result = agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

Install

pip install "decimalai[langchain]" langchain-openai

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("numerical-stability")
if result.exit_code:
    raise SystemExit(result.problems)

from langchain.agents import create_agent
from decimalai.langchain import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = create_agent(
    "openai:gpt-5.4-mini",
    tools=[],                         # your tools; the middleware adds load_skill
    middleware=[support.middleware],  # your prompt, the skill list and load_skill
)
result = agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/numerical-stability/SKILL.md

Give it to your agent

from pathlib import Path
from langchain.agents import create_agent

skill = Path(".agents/skills/numerical-stability/SKILL.md").read_text()
agent = create_agent("openai:gpt-5.4-mini", tools=[], system_prompt=f"You are a helpful agent.\n\n{skill}")
result = agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

LangChain docs

CrewAI's own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" "crewai>=1.15.27"
decimalai skills add numerical-stability

Add it to your agent

import decimalai.crewai
from crewai import Agent, Crew, Task

agent = Agent(
    role="Support", goal="Help the customer", backstory="A support agent.",
    llm=llm,                               # your own CrewAI LLM
    skills=decimalai.crewai.skills(),      # the installed folder
    tools=decimalai.crewai.skill_tools(),  # reads a skill's files, runs its scripts
)
task = Task(description="Hello!", expected_output="an answer", agent=agent)
Crew(agents=[agent], tasks=[task]).kickoff()

The same install from Python, for a notebook or a setup script. CrewAI's own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" "crewai>=1.15.27"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("numerical-stability")
if result.exit_code:
    raise SystemExit(result.problems)

import decimalai.crewai
from crewai import Agent, Crew, Task

agent = Agent(
    role="Support", goal="Help the customer", backstory="A support agent.",
    llm=llm,                               # your own CrewAI LLM
    skills=decimalai.crewai.skills(),      # the installed folder
    tools=decimalai.crewai.skill_tools(),  # reads a skill's files, runs its scripts
)
task = Task(description="Hello!", expected_output="an answer", agent=agent)
Crew(agents=[agent], tasks=[task]).kickoff()

No DecimalAI package. CrewAI's own loader reads the folder, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/numerical-stability/SKILL.md

Give it to your agent

from pathlib import Path
from crewai import Agent, Crew, Task

agent = Agent(
    role="Support", goal="Help the customer", backstory="A support agent.",
    llm=llm,                         # your own CrewAI LLM
    skills=[Path(".agents/skills")],
)
task = Task(description="Hello!", expected_output="an answer", agent=agent)
Crew(agents=[agent], tasks=[task]).kickoff()

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

CrewAI docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[adk]"
decimalai skills add numerical-stability

Add it to your agent

from decimalai.adk import DecimalAIPlugin, agent_config
from google.adk.agents import LlmAgent
from google.adk.apps import App

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = LlmAgent(
    name="support",          # ADK needs a Python identifier
    model="gemini-3.5-flash",
    instruction=support.instruction,  # your prompt, then the skill list
    tools=[*support.tools],           # your tools, then load_skill
)
# DecimalAIPlugin makes each invocation of runners built from this App one trace.
app = App(name="support", root_agent=agent, plugins=[DecimalAIPlugin()])

Prefer ADK's own loader? SkillToolset(skills=decimalai.adk.skills(), ...) reads the same folder. Use one or the other: a skill delivered both ways reaches the prompt twice.

Install

pip install "decimalai[adk]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("numerical-stability")
if result.exit_code:
    raise SystemExit(result.problems)

from decimalai.adk import DecimalAIPlugin, agent_config
from google.adk.agents import LlmAgent
from google.adk.apps import App

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = LlmAgent(
    name="support",          # ADK needs a Python identifier
    model="gemini-3.5-flash",
    instruction=support.instruction,  # your prompt, then the skill list
    tools=[*support.tools],           # your tools, then load_skill
)
# DecimalAIPlugin makes each invocation of runners built from this App one trace.
app = App(name="support", root_agent=agent, plugins=[DecimalAIPlugin()])

Prefer ADK's own loader? SkillToolset(skills=decimalai.adk.skills(), ...) reads the same folder. Use one or the other: a skill delivered both ways reaches the prompt twice.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/numerical-stability/SKILL.md

Give it to your agent

from pathlib import Path
from google.adk.agents import LlmAgent

skill = Path(".agents/skills/numerical-stability/SKILL.md").read_text()
agent = LlmAgent(
    name="support",
    model="gemini-3.5-flash",
    instruction=lambda context: f"You are a helpful agent.\n\n{skill}",
)

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Google ADK docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[pydantic-ai]"
decimalai skills add numerical-stability

Add it to your agent

from pydantic_ai import Agent
from decimalai.pydantic_ai import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = Agent(
    "openai:gpt-4o-mini",
    name=support.name,
    tools=[],                 # your tools; the capability adds load_skill
    capabilities=[support],   # your prompt, the skill list and load_skill
)
# In a notebook or async code: result = await agent.run("Hello!")
result = agent.run_sync("Hello!")

On the Pydantic AI harness, decimalai.pydantic_ai_harness.skills(project) uses its own loader instead.

Install

pip install "decimalai[pydantic-ai]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("numerical-stability")
if result.exit_code:
    raise SystemExit(result.problems)

from pydantic_ai import Agent
from decimalai.pydantic_ai import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = Agent(
    "openai:gpt-4o-mini",
    name=support.name,
    tools=[],                 # your tools; the capability adds load_skill
    capabilities=[support],   # your prompt, the skill list and load_skill
)
# In a notebook or async code: result = await agent.run("Hello!")
result = agent.run_sync("Hello!")

On the Pydantic AI harness, decimalai.pydantic_ai_harness.skills(project) uses its own loader instead.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/numerical-stability/SKILL.md

Give it to your agent

from pathlib import Path
from pydantic_ai import Agent

skill = Path(".agents/skills/numerical-stability/SKILL.md").read_text()
agent = Agent("openai:gpt-4o-mini", instructions=f"You are a helpful agent.\n\n{skill}")
# In a notebook or async code: result = await agent.run("Hello!")
result = agent.run_sync("Hello!")

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Pydantic AI docs

Deep Agents' own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" deepagents
decimalai skills add numerical-stability

Add it to your agent

import decimalai.deepagents
from deepagents import create_deep_agent

agent = create_deep_agent(model=model, **decimalai.deepagents.skills())
agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

The default backend reads files but has no shell. To run a skill's scripts, pass skills(backend=LocalShellBackend(...)).

The same install from Python, for a notebook or a setup script. Deep Agents' own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" deepagents

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("numerical-stability")
if result.exit_code:
    raise SystemExit(result.problems)

import decimalai.deepagents
from deepagents import create_deep_agent

agent = create_deep_agent(model=model, **decimalai.deepagents.skills())
agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

The default backend reads files but has no shell. To run a skill's scripts, pass skills(backend=LocalShellBackend(...)).

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/numerical-stability/SKILL.md

Give it to your agent

from pathlib import Path
from deepagents import create_deep_agent

skill = Path(".agents/skills/numerical-stability/SKILL.md").read_text()
agent = create_deep_agent(model=model, system_prompt=f"You are a helpful agent.\n\n{skill}")
agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Deep Agents docs

Its own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" agent-framework
decimalai skills add numerical-stability

Add it to your agent

import asyncio

from agent_framework import Agent
from decimalai.agent_framework import skills

agent = Agent(client=client, instructions="You are a helpful agent.", context_providers=[skills()])
asyncio.run(agent.run("Hello!"))

It caches skills by default, so restart the process after decimalai skills update.

The same install from Python, for a notebook or a setup script. Its own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" agent-framework

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("numerical-stability")
if result.exit_code:
    raise SystemExit(result.problems)

import asyncio

from agent_framework import Agent
from decimalai.agent_framework import skills

agent = Agent(client=client, instructions="You are a helpful agent.", context_providers=[skills()])
asyncio.run(agent.run("Hello!"))

It caches skills by default, so restart the process after decimalai skills update.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/numerical-stability/SKILL.md

Give it to your agent

import asyncio
from pathlib import Path
from agent_framework import Agent

skill = Path(".agents/skills/numerical-stability/SKILL.md").read_text()
agent = Agent(client=client, instructions=f"You are a helpful agent.\n\n{skill}")
asyncio.run(agent.run("Hello!"))

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Microsoft Agent Framework docs

Strands' own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" strands-agents
decimalai skills add numerical-stability

Add it to your agent

from decimalai.strands import skills
from strands import Agent
from strands.vended_tools import file_editor, shell

agent = Agent(
    model=model,                # always pass one: the default is Amazon Bedrock
    system_prompt="You are a helpful agent.",
    tools=[file_editor, shell],
    plugins=[skills()],
)
agent("Hello!")

Strands loads an agent's skills once, so build the agent again after decimalai skills update.

The same install from Python, for a notebook or a setup script. Strands' own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" strands-agents

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("numerical-stability")
if result.exit_code:
    raise SystemExit(result.problems)

from decimalai.strands import skills
from strands import Agent
from strands.vended_tools import file_editor, shell

agent = Agent(
    model=model,                # always pass one: the default is Amazon Bedrock
    system_prompt="You are a helpful agent.",
    tools=[file_editor, shell],
    plugins=[skills()],
)
agent("Hello!")

Strands loads an agent's skills once, so build the agent again after decimalai skills update.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/numerical-stability/SKILL.md

Give it to your agent

from pathlib import Path
from strands import Agent

skill = Path(".agents/skills/numerical-stability/SKILL.md").read_text()
agent = Agent(model=model, system_prompt=f"You are a helpful agent.\n\n{skill}")
agent("Hello!")

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Strands docs

Adds every file the skill has, pinned so you can update it. Cursor, Copilot, Cline and Warp read this folder by themselves.

pip install "decimalai>=0.15"
decimalai skills add numerical-stability

No Python or account. Cursor, Copilot, Cline and Warp read this folder by themselves.

Save it into your project

curl -fsSL --create-dirs -o .agents/skills/numerical-stability/SKILL.md https://app.decimal.ai/s/numerical-stability/SKILL.md

Copy SKILL.md

Save it in your project, as

.agents/skills/numerical-stability/SKILL.md

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Cursor and other editors docs

Fetch the file and give its text to your model as instructions. No account or package needed.

Get the file

curl -fsSL https://app.decimal.ai/s/numerical-stability/SKILL.md

Read the summary as JSON

curl -fsSL https://app.decimal.ai/s/numerical-stability.json

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Other setups docs

You don't need a DecimalAI account.

Version: v1, tested 7/26/2026
Source: FreedomIntelligence/OpenClaw-Medical-Skills ↗
License: Not recorded

Manage it in DecimalAI

Saved prompts and skills, pinned versions, and traces of this skill in your runs. DecimalAI does not run your agent.

Claude Code reads files from your project, so DecimalAI config does not apply there.

On Claude Agent SDK: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On OpenAI Agents: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On OpenAI SDK: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On Anthropic: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On Gemini API: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On LangChain: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On CrewAI: set DECIMAL_API_KEY and add decimalai.init(crewai=True) to record runs and skill use. The skill version stays in your repo.

On Google ADK: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On Pydantic AI: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On Deep Agents: set DECIMAL_API_KEY and add decimalai.init(langchain=True) to record runs and skill use. The skill version stays in your repo.

On Microsoft Agent Framework: set DECIMAL_API_KEY and add decimalai.init(otel=True, agent_name="support") to record runs and skill use. The skill version stays in your repo.

On Strands: set DECIMAL_API_KEY and add decimalai.init(otel=True, agent_name="support") to record runs and skill use. The skill version stays in your repo.

Editors read files from your project, so DecimalAI config does not apply there.

Anywhere else: record a use with decimalai.log_skill_activation() inside a trace.

Use this skill

SKILL.md

Numerical Stability

Goal

Provide a repeatable checklist and script-driven checks to keep time-dependent simulations stable and defensible.

Requirements

Python 3.8+
NumPy (for matrix_condition.py and von_neumann_analyzer.py)
See scripts/requirements.txt for dependencies

Inputs to Gather

Input	Description	Example
Grid spacing `dx`	Spatial discretization	`0.01 m`
Time step `dt`	Temporal discretization	`1e-4 s`
Velocity `v`	Advection speed	`1.0 m/s`
Diffusivity `D`	Thermal/mass diffusivity	`1e-5 m²/s`
Reaction rate `k`	First-order rate constant	`100 s⁻¹`
Dimensions	1D, 2D, or 3D	`2`
Scheme type	Explicit or implicit	`explicit`

Decision Guidance

Choosing Explicit vs Implicit

Is the problem stiff (fast + slow dynamics)?
├── YES → Use implicit or IMEX scheme
│         └── Check conditioning with matrix_condition.py
└── NO → Is CFL/Fourier satisfied with reasonable dt?
    ├── YES → Use explicit scheme (cheaper per step)
    └── NO → Consider implicit or reduce dx

Stability Limit Quick Reference

Physics	Number	Explicit Limit (1D)	Formula
Advection	CFL	C ≤ 1	`C = v·dt/dx`
Diffusion	Fourier	Fo ≤ 0.5	`Fo = D·dt/dx²`
Reaction	Reaction	R ≤ 1	`R = k·dt`

Multi-dimensional correction: For d dimensions, diffusion limit is Fo ≤ 1/(2d).

Script Outputs (JSON Fields)

Script	Key Outputs
`scripts/cfl_checker.py`	`metrics.cfl`, `metrics.fourier`, `recommended_dt`, `stable`
`scripts/von_neumann_analyzer.py`	`results.max_amplification`, `results.stable`
`scripts/matrix_condition.py`	`results.condition_number`, `results.is_symmetric`
`scripts/stiffness_detector.py`	`results.stiffness_ratio`, `results.stiff`, `results.recommendation`

Workflow

Identify dominant physics (advection vs diffusion vs reaction)
Run CFL checker with scripts/cfl_checker.py
Compare to limits and adjust dt if needed
Check stiffness with scripts/stiffness_detector.py if multiple scales
Analyze custom schemes with scripts/von_neumann_analyzer.py
Check conditioning with scripts/matrix_condition.py for implicit solves
Document the stability verdict and recommended time step

Conversational Workflow Example

User: My phase-field simulation is blowing up after 100 steps. I'm using explicit Euler with dx=0.01, dt=1e-4, and diffusivity D=1e-3.

Agent workflow:

Check stability criteria:

python3 scripts/cfl_checker.py --dx 0.01 --dt 1e-4 --diffusivity 1e-3 --dimensions 2 --json

Interpret results:
- Fourier number: Fo = 1e-3 × 1e-4 / (0.01)² = 1.0
- 2D limit: Fo ≤ 0.25
- Violation: Fo = 1.0 > 0.25, unstable!
Recommend fix:
- Reduce dt to 2.5e-5 (to get Fo = 0.25)
- Or increase dx, or switch to implicit

Pre-Simulation Stability Checklist

Identify dominant physics and nondimensional groups
Compute CFL/Fourier/Reaction numbers with cfl_checker.py
If explicit and limit violated, reduce dt or change scheme
If stiffness ratio > 1000, select implicit/stiff integrator
For custom schemes, verify amplification factor ≤ 1
Document stability reasoning with inputs and outputs

CLI Examples

# Check CFL/Fourier for 2D diffusion-advection
python3 scripts/cfl_checker.py --dx 0.1 --dt 0.01 --velocity 1.0 --diffusivity 0.1 --dimensions 2 --json

# Von Neumann analysis for custom 3-point stencil
python3 scripts/von_neumann_analyzer.py --coeffs 0.2,0.6,0.2 --dx 1.0 --nk 128 --json

# Detect stiffness from eigenvalue estimates
python3 scripts/stiffness_detector.py --eigs=-1,-1000 --json

# Check matrix conditioning for implicit system
python3 scripts/matrix_condition.py --matrix A.npy --norm 2 --json

Error Handling

Error	Cause	Resolution
`dx and dt must be positive`	Zero or negative values	Provide valid positive numbers
`No stability criteria applied`	Missing velocity/diffusivity	Provide at least one physics parameter
`Matrix file not found`	Invalid path	Check matrix file exists
`Could not compute eigenvalues`	Singular or ill-formed matrix	Check matrix validity

Interpretation Guidance

Scenario	Meaning	Action
`stable: true`	All checked criteria satisfied	Proceed with simulation
`stable: false`	At least one limit violated	Reduce dt or change scheme
`stable: null`	No criteria could be applied	Provide more physics inputs
Stiffness ratio > 1000	Problem is stiff	Use implicit integrator
Condition number > 10⁶	Ill-conditioned	Use scaling/preconditioning

Limitations

Explicit schemes only for CFL/Fourier checks (implicit is unconditionally stable)
Von Neumann analysis assumes linear, constant-coefficient, periodic BCs
Stiffness detection requires eigenvalue estimates from user

References

references/stability_criteria.md - Decision thresholds and formulas
references/common_pitfalls.md - Frequent failure modes and fixes
references/scheme_catalog.md - Stability properties of common schemes

Version History

v1.1.0 (2024-12-24): Enhanced documentation, decision guidance, examples
v1.0.0: Initial release with 4 stability analysis scripts

When it activates

Automatically, when a task matches. Use when selecting time steps, choosing explicit/implicit schemes, diagnosing numerical blow-up, checking CFL/Fourier criteria, von Neumann analysis, matrix conditioning, or detecting stiffness in advection/diffusion/reaction problems.

About this skill

Automatic

Research pack

SkillSafety

✓ 3 of 3 passed

Code scan15 of 15 checks clean

0 critical · 0 warning · 0 info — scanner v4 — 7/30/2026

View 15 scanner checks

live_secretremote_code_executionreverse_shelldata_exfiltrationssrf_metadataagent_snoopinganti_refusaldestructive_commandsobfuscated_unicodeunicode_homoglyphopaque_blobsuspicious_urltool_overreachtrigger_abuseprompt_injection_phrasing

IntentSafe

LLM judge · does the skill do what it claims

ContentClean

LLM judge · policy & harmful-content review

Source

Imported

FreedomIntelligence / OpenClaw-Medical-Skills

skills/numerical-stability/SKILL.md

View on GitHub ↗

Imported 8/1/2026Version v1Bundled 8 files · scripts

Illustrative Want to see what numerical-stability would put in front of your model? Preview the rendered body and check its trigger phrases — no LLM call, no signup.

Related skills

Skills that do similar work, with their headline benchmark lift.

From the same source and nearby in the catalogue.

Ready to supercharge your AI agents?

SkillScore

Safety

What it changes

Track record

Use this skill

Numerical Stability

Goal

Requirements

Inputs to Gather

Decision Guidance

Choosing Explicit vs Implicit

Stability Limit Quick Reference

Script Outputs (JSON Fields)

Workflow

Conversational Workflow Example

Pre-Simulation Stability Checklist

CLI Examples

Error Handling

Interpretation Guidance

Limitations

References

Version History

When it activates

SkillSafety

Source

Related skills

More in the registry