What is the primary purpose of the CRACK package in REDUCE?

CRACK is designed to solve overdetermined systems of algebraic, ordinary, or partial differential equations, which is a core requirement for Lie symmetry analysis.

Does this skill help with Docker-based REDUCE environments?

Yes, it includes built-in diagnostics for Docker and Colima to ensure the symbolic math engine is accessible to the AI agent.

Can I use this skill for interactive mathematical troubleshooting?

Yes, the skill supports switching from batch mode to interactive mode, allowing you to manually inspect equations and choose specific solving modules step-by-step.

Why does this skill emphasize 'depend' declarations?

In REDUCE, unknown functions must have their dependencies explicitly declared so the solver can correctly compute derivatives and identify independent variables.

REDUCE CRACK Equation Solver

Name: REDUCE CRACK Equation Solver
Author: hinsley

byhinsley

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データサイエンスとML

Solves overdetermined algebraic, ODE, and PDE systems using the CRACK package in the REDUCE computer algebra system.

概要

This skill provides a specialized workflow for utilizing the CRACK package within REDUCE, specifically designed for finding Lie symmetries and solving complex differential equation systems. It guides users through critical setup steps like functional dependency declarations, manages transitions between batch and interactive solving modes, and provides structured natural language interpretations of mathematical outputs. Whether you are performing similarity reductions or deriving conservation laws, this skill helps navigate case splits, free functions, and symbolic constraints to ensure rigorous mathematical results.

主な機能

Automated functional dependency management using REDUCE depend declarations
Integration with ReLie for staged Lie group method pipelines
Natural language interpretation of symmetry generators and solution sets
Switching between batch and interactive solving for complex case splits
Docker and Colima environment readiness checks for symbolic CAS workflows
1 GitHub stars

ユースケース

Interpreting infinite-dimensional symmetry families and similarity reductions
Solving determining equations for Lie symmetries of differential equations
Analyzing overdetermined systems of algebraic or partial differential equations

概要

主な機能

Automated functional dependency management using REDUCE depend declarations
Integration with ReLie for staged Lie group method pipelines
Natural language interpretation of symmetry generators and solution sets
Switching between batch and interactive solving for complex case splits
Docker and Colima environment readiness checks for symbolic CAS workflows
1 GitHub stars

ユースケース

Interpreting infinite-dimensional symmetry families and similarity reductions
Solving determining equations for Lie symmetries of differential equations
Analyzing overdetermined systems of algebraic or partial differential equations