Interface with Isabelle/HOL for classical mathematics formalization

Numerical methods for ordinary differential equations

Robust statistical methods resistant to outliers

SageMath for comprehensive mathematical computation

Symbolic computation using SymPy for Python-based mathematical analysis

Interface with zbMATH Open database

Skill for HVAC system design and analysis per ASHRAE standards including load calculations, equipment selection, and energy efficiency analysis

Skill for dimensional tolerance analysis and stack-up calculations

Workflow automation skill for orchestrating multi-technique characterization sequences

NanoHUB tool interface skill for accessing educational and research nanoscience simulations

VASP DFT calculation skill for electronic structure, geometry optimization, and property prediction of nanomaterials

AFLOW automatic materials discovery skill for high-throughput DFT calculations and materials database queries

emcee MCMC skill for Bayesian parameter estimation and posterior sampling in physics applications

Kwant quantum transport skill for mesoscopic physics, scattering matrix calculations, and nanostructure modeling

Monte Carlo simulation skill for statistical physics, particle transport, and stochastic processes

PySCF quantum chemistry skill for molecular calculations, coupled cluster, and multireference methods

Quantum ESPRESSO DFT skill for plane-wave pseudopotential calculations and materials simulation

QuTiP/quimb tensor network skill for quantum many-body simulations and entanglement analysis

SpinW spin wave simulation skill for magnetic materials, magnon dispersions, and neutron scattering analysis

VASP DFT calculation skill for electronic structure, band structures, and materials property predictions

Wannier90 skill for maximally localized Wannier functions and tight-binding model construction

Zemax optical design skill for lens systems, imaging optics, and tolerancing analysis

PySCF quantum chemistry interface for classical electronic structure calculations

Qiskit Nature skill for quantum chemistry and materials science applications

Hamiltonian simulation skill using Trotter-Suzuki decomposition

Skill for statistical power analysis and sample size calculation

Apply propensity score methods, instrumental variables, difference-in-differences, and regression discontinuity designs for causal identification

A comprehensive mathematics tutor covering arithmetic through calculus, adapted to multiple national curricula worldwide. This skill transforms the AI agent into a patient, adaptive math teacher that

Fetch current, hourly, and daily weather forecasts and display required attribution using WeatherKit. Use when integrating weather data, showing forecasts, handling weather alerts, displaying Apple Weather attribution, or querying historical weather statistics in iOS apps.

Search Mathlib for lemmas by type signature pattern using Loogle.

使用 GLM 库实现 Vector3TransformNormal 和 Vector3TransformCoord 函数，模拟 DirectXMath 的行为，并使用 const T& 模板参数以支持多种向量类型。

基于历史数据利用统计分析方法预测下一组数字，严格遵守前5位(1-35)和后2位(1-12)的范围限制，输出简洁的预测结果。

提供使用R^2指标评估线性回归、支持向量回归(SVR)和随机森林模型的代码，并演示如何使用网格搜索和交叉验证进行参数调优。

针对数学除法或方程问题，使用竖式格式进行计算，并提供详细的步骤分析和说明。

实现一个使用位置编码将像素坐标映射到像素值的PyTorch MLP网络，专门用于拟合灰度图像。支持任意分辨率输出、模型保存加载及设备管理。

用于计算给定数据集的平均数、标准差以及两组数据间的P值。当用户要求“无需过程”或“只需结果”时，仅输出最终数值。

Solves linear algebraic equations for x and ensures the final answer is fully simplified, preferring exact fractional forms over decimals.

Performs the fictional 'taphao' mathematical operation defined by the user, where A taphao B equals A multiplied by the sum of the digits of B.

Provides answers to statistics questions in both English and Chinese.

Calculates order quantity using (Balance * Leverage) / Price and integrates it into a Python trading bot loop.

Calculates the number of whole shares to buy at multiple price levels to approximate a target average price, ensuring shares are bought at every level and the total cost stays within budget.

Provides definitions, mathematical expressions, and simple examples for terms strictly within the context of Fluid Mechanics and Thermodynamics.

Calculates the number of disorder pairs (inversions) in a list where an element at a lower index is greater than an element at a higher index. Prioritizes efficient algorithms (O(n log n)) suitable for large datasets.

Creates a Python program with a `factorial` function that calculates the factorial of an integer and returns a string showing the calculation steps (e.g., '4x3x2x1 = 24'). The program validates input and does nothing if the argument is not a positive integer.

Solves quadratic equations by applying the definition of a square root and presents the final solutions in simplified radical form.

Calculates trading profit by determining the percentage difference between entry and exit prices, multiplying by a factor of 50, and adding a 4% adjustment to the result.

Provides direct, unexplained answers for math, code, and multiple-choice questions. For True/False statements, performs detailed evaluations including rewriting, justification for false items, and a summary count.

Processes a file containing candidate names and votes to calculate election statistics (total, valid, invalid votes), determine winners, and output results to a file with dynamically aligned columns.

Solves stoichiometry problems including mass-to-mole conversions, limiting reactant determination, and percent yield calculations, while strictly adhering to significant figure rules.

Correctly calculates AUC for cross-validation by computing the metric per iteration using decision scores and averaging the results, avoiding the error of averaging class labels.