几何函数图谱：Python 中几何函数理论的认证计算
Geometric Function Atlas: certified computing for geometric function theory in Python
- Indian Institute of Information Technology Kottayam（印度信息技术学院科塔亚姆分校）
- K. J. Somaiya College of Engineering, Mumbai（孟买K.J.索尼娅工程学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文介绍开源 Python 包 geometric-function-atlas，通过三十九个 Ma--Minda 生成元目录，提供几何函数理论极值问题的认证计算，包括精确系数、Fekete--Szegő 常数及三级证据验证，并附带可重放证书。
AI中文摘要：
我们描述了 geometric-function-atlas，这是我们用于几何函数理论尖锐极值问题的开源 Python 包。我们围绕三十九个 Ma--Minda 星形生成元的目录来组织它。从这个目录中，我们计算精确的 Taylor 系数、闭式 Fekete--Szegő 常数、Ma--Minda 极值函数的精确系数以及可容许性筛选。我们的验证器在三个证据级别上回答关于规范化多项式的成员资格问题：浮点网格筛选、在有理算术中决定的精确充分条件，以及在最差筛选点的认证区间包络。每个答案都指明我们获得该答案的级别。我们发布了一个带有校验和的人工制品快照，包含三百零六个系数证书和七百零二个有向包含半径。八个经过审查的半径通道携带证书，其证明链我们以符号方式重放，并且我们根据请求通过我们的精确 Schur 参数机制重新执行每个系数证书。我们通过一个版本化的信封发布所有结果，该信封记录方法、证据状态、假设和人工制品标识符。两个可选实验室将同样的纪律应用于密码学 S 盒指标和图像质量指标。我们介绍了我们的设计，将每个层级所确立的内容陈述为命题，跟踪一个从筛选到重放证书的半径通道，报告测量的计时，并将我们的包置于符号代数、严格数值和数学数据库软件之中。我们在 Python 包索引和此 https URL 下以 MIT 许可证发布 geometric-function-atlas。
英文摘要：
We describe geometric-function-atlas, our open-source Python package for the sharp extremal problems of geometric function theory. We organise it around a catalogue of thirty-nine Ma--Minda starlike generators. From this catalogue we compute exact Taylor coefficients, closed-form Fekete--Szegő constants, exact coefficients of the Ma--Minda extremal function, and admissibility screens. Our verifier answers membership questions for normalised polynomials at three levels of evidence: a floating-point grid screen, an exact sufficient condition decided in rational arithmetic, and a certified interval enclosure at the worst screened point. Every answer names the level at which we obtained it. We ship a checksummed artifact snapshot with three hundred and six coefficient certificates and seven hundred and two directed inclusion radii. Eight reviewed radius lanes carry certificates whose proof chains we replay symbolically, and we re-execute every coefficient certificate through our exact Schur-parameter machinery on request. We emit all results through one versioned envelope that records the method, the evidence status, the assumptions, and the artifact identifiers. Two optional laboratories apply the same discipline to cryptographic S-box metrics and to image-quality metrics. We present our design, state as propositions what each tier establishes, follow one radius lane from screen to replayed certificate, report measured timings, and place our package among symbolic-algebra, rigorous-numerics, and mathematical-database software. We release geometric-function-atlas under the MIT licence on the Python Package Index and at https://github.com/Prasanna28Devadiga/geometric-function-atlas.
