root-finding

root-finding is a skill for Claude Code from parcadei/Continuous-Claude-v3. It costs 13 tokens per session (906 once invoked), scanned A, original, MIT.

A guide to finding roots, the input values that make an equation equal to zero. It covers bracketed methods, derivative-based methods, systems of equations, and verification.

In plain words
What is it for?
Use it to find single or multiple roots with bisection, Brent's method, Newton's method, or the secant method. It also covers systems of equations and symbolic or formal checks.
Why use it?
It helps choose a method that is likely to converge for the information available. It also helps check that a computed answer is actually close to a valid root.

Skill for Claude Code

Written for Claude Code: allowed-tools in frontmatter. Also seen: reads .claude/ paths.

Good fit Use it to find single or multiple roots with bisection, Brent's method, Newton's method, or the secant method. It also covers systems of equations and symbolic or formal checks.

Compare 6 skills from other repositories ↓
Install with agentmods
npx agentmods add skills/parcadei/continuous-claude-v3/root-finding
About the project

Continuous-Claude-v3 is a Claude Code development environment that preserves working context between sessions, coordinates specialized agents, and stores project knowledge through ledgers, handoffs, and analysis tools. It is for people using Claude Code on ongoing or complex software work. Its catalogue entries are the skills, agents, hooks, plugin, and setting that provide its workflows and orchestration.

parcadei/Continuous-Claude-v3 · 3,938 stars · on GitHub

Install

Getting it into your agent

One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.

Any agent
npx skills add parcadei/Continuous-Claude-v3 --skill root-finding
Clone the repo
git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3

Made for: Claude Code.

Wrote this? Show the measurements

A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.

agentmods badge for root-finding

README.md
[![agentmods](https://agentmods.dev/badge/skills/parcadei/continuous-claude-v3/root-finding/github.svg)](https://agentmods.dev/skills/parcadei/continuous-claude-v3/root-finding)
Your own site
<a href="https://agentmods.dev/skills/parcadei/continuous-claude-v3/root-finding"><img src="https://agentmods.dev/badge/skills/parcadei/continuous-claude-v3/root-finding/github.svg" alt="Measured on agentmods" height="20"></a>

Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.

agentmods 80×15 button for root-finding

Your own site · 80×15
<a href="https://agentmods.dev/skills/parcadei/continuous-claude-v3/root-finding"><img src="https://agentmods.dev/badge/skills/parcadei/continuous-claude-v3/root-finding.svg" alt="Reviewed on agentmods" width="80" height="20"></a>
Per session 13 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 906 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. A grade says what 26 rules found in the file — not that it is safe. Third-party audits
  • NVIDIA SkillSpector warn 7 Sept 2026
SkillSpector: 1 finding, up to medium

These are SkillSpector’s own severities. On a checked sample its high-severity flags on skills were ~96% false positives — a documented command, a public API, a “never do X” rule — so we show them as a caution to read, not a verdict. Why →

  • medium Agent Snooping · line 74
    Skill enumerates or reads other installed skills. Access to other skills' SKILL.md files or the skills directory reveals prompt instructions, capabilities, and secrets that should be invisible to peer skills.
    Fix: Remove all code or instructions that list or read other skills' files or directories. Skills should operate independently; cross-skill access is a privilege escalation.
How audits are shown
Origin original No closer match found in the catalogue.
Token cost

What it costs to keep this loaded

Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.

ModelPer sessionOnce invoked
Fable 5.1 $0.00013 $0.00906
Opus 5 $0.00006 $0.00453
Sonnet 5 $0.00003 $0.00181
Haiku 4.5 $0.00001 $0.00091

Measured 9d ago against content hash 13b4444ea345, method: parsed. Prices are Anthropic first-party input rates as of 2026-09-12, from the pricing page.

Security

Grade A, and why

root-finding scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 9d ago.

A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.

Nothing flagged

None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.

.claude/skills/math/numerical-methods/root-finding/SKILL.md · 75 lines

How it starts

The opening of the file, as written. The whole thing — 75 lines — stays where its author put it; the contents beside it link to each section on GitHub.

Root Finding

When to Use

Use this skill when working on root-finding problems in numerical methods.

Decision Tree

  1. Characterize the Problem

    • Single root or multiple roots?
    • Bracketed (know interval containing root)?
    • Derivatives available?
  2. Method Selection

    Situation Method Implementation
    Bracketed, no derivatives Bisection, Brent scipy.optimize.brentq
    Derivatives available Newton-Raphson scipy.optimize.newton
    No derivatives Secant method scipy.optimize.newton (no fprime)
    System of equations scipy.optimize.fsolve Requires Jacobian ideally
  3. Implement Root Finding

    • scipy.optimize.brentq(f, a, b) - guaranteed convergence if bracketed
    • scipy.optimize.newton(f, x0, fprime=df) - quadratic convergence near root
    • For systems: scipy.optimize.fsolve(F, x0)
  4. Handle Multiple Roots

    • Deflation: divide out found roots
    • Multiple starting points
    • sympy_compute.py solve "f(x)" --var x for symbolic solutions
  5. Verify Solutions

    • Check |f(root)| < tolerance
    • Verify root is in expected domain
    • z3_solve.py prove "f(root) == 0"

Tool Commands

Scipy_Brentq

uv run python -c "from scipy.optimize import brentq; root = brentq(lambda x: x**2 - 2, 0, 2); print('Root:', root)"

Scipy_Newton

uv run python -c "from scipy.optimize import newton; root = newton(lambda x: x**2 - 2, 1.0, fprime=lambda x: 2*x); print('Root:', root)"

Sympy_Solve

uv run python -m runtime.harness scripts/sympy_compute.py solve "x**3 - x - 1" --var x

Key Techniques

From indexed textbooks:

  • [Numerical analysis (Burden R.L., Fair... (Z-Library)] How accurate was his approximation? C H A P T E R 2 Solutions of Equations in One Variable 2. Survey of Methods and Software In this chapter we have considered the problem of solving the equation f (x) = 0, where f is a given continuous function.
  • [An Introduction to Numerical Analysis... (Z-Library)] Computational Solution of Nonlinear Operator Equations. Methods for Solving Systems of Nonlinear Equations. Society for Industrial and Applied Mathematics, Philadelphia.
  • [An Introduction to Numerical Analysis... (Z-Library)] General polynomial rootfinding methods There are a large number of rootfind ing algorithms designed especially for polynomials. Many of these are taken up in detail in the books Dejon and Henrici (1969), Henrici (1974, chap. There are far too many types of such methods to attempt to describe them all here.
  • [An Introduction to Numerical Analysis... (Z-Library)] J n Consider the product a 0 a 1 ••• am, where a 0 , a1, ••• , am are m + 1 num bers stored in a computer that uses n digit base fJ arithmetic. What is a rigorous bound for w? What is a statistical estimate for the size of w?
  • [An Introduction to Numerical Analysis... (Z-Library)] Discussion of the Literature There is a large literature on methods for calculating the roots of a single equation. See the books by Householder (1970), Ostrowski (1973), and Traub (1964) for a more extensive development than has been given here. Newton's method is one of the most widely used methods, and its development is due to many people.

Read the full file on GitHub · 75 lines

Changes

What this file has done since we first saw it

Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.

  1. 9d ago First seen · 75 lines · 13 tokens per session scan A 13b4444ea345

Subscribe to this mod's changes

root-finding is a skill published in the GitHub repository parcadei/Continuous-Claude-v3 (3,938 stars, last pushed 7mo ago), licensed MIT. It adds 13 tokens to every session and 906 once invoked, about $0.0001 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-09-03.

Related

Other skills, from other repositories

paper-discover

Use when searching for academic papers related to a topic, finding papers similar to one already in the vault, or discovering research gaps. Triggers on "find papers", "related papers", "paper search", "literature", "what papers should I read about X".

tuan3w/obsidian-vault-agent · 58 tokens

fizzy-workflow

Use for guided Fizzy.do workflows: "set up Fizzy", "configure Fizzy for this project", "sync my work to Fizzy", "review my Fizzy progress", "end of session cleanup". Provides step-by-step guidance for common operations.

keskinonur/claude-plugin-fizzy · 57 tokens

tooluniverse-pharmacogenomics

Pharmacogenomics (PGx) research — drug-gene interactions (CPIC, PharmGKB), CPIC dosing guidelines, variant-drug-response associations, ethnic-allele-frequency considerations, and metabolizer-status scoring. Use for PGx-informed dosing recommendations, CYP/HLA pharmacogenomic allele interpretation, and…

mims-harvard/ToolUniverse · 80 tokens

tooluniverse-variant-analysis

VCF and variant analysis — parsing, annotation, classification (synonymous, missense, frameshift, stopgained), VAF filtering, coding vs non-coding categorization, multi-condition variant comparison. Use for VCF parsing, variant fraction calculations (denominator = coding subset only, NOT all variants), and per-sample…

mims-harvard/ToolUniverse · 77 tokens

tooluniverse-variant-to-mechanism

End-to-end variant-to-mechanism analysis — trace a variant (rsID/coordinates) through regulatory context, target gene(s), molecular pathway(s), and phenotypic consequences. Integrates 7+ databases across 3 evidence layers (regulatory, molecular, disease) for a mechanistic model. Use for GWAS-hit-to-mechanism…

mims-harvard/ToolUniverse · 97 tokens

tooluniverse-epidemiological-analysis

End-to-end observational epidemiology analysis — from research question (PECO Population/Exposure/Comparator/Outcome) to publication-ready statistical report. Covers cohort/case-control/cross-sectional design, regression with confounders, propensity scoring, sensitivity analysis. Writes Python code for every step. Use…

mims-harvard/ToolUniverse · 85 tokens