计算代数几何
Computational algebraic geometry
Hal Schenck · 初版 2003 年
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探讨代数与几何之间的相互作用。涵盖：homological algebra、algebraic combinatorics 与 algebraic topology，以及 algebraic geometry。
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Computational algebraic geometry
Hal Schenck · 初版 2003 年
探讨代数与几何之间的相互作用。涵盖：homological algebra、algebraic combinatorics 与 algebraic topology，以及 algebraic geometry。
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……好）。如果你做的是那种硬核图形编程，或者编写机器人的空间推理程序，代数几何（algebraic geometry）可能会带来回报——不过，代数几何的入门门槛可不低。（一个例外可能是 Hal Schenck 写的《Computational Algebraic Geometry》这本书）。至于数论是否能“带来回报”：1）数论中的许多证明在本质上都是算法化的；2）计算机处理整数比处理伪实数（psuedo-reals）容易得多……
…well). If you do crazy graphics programming, or if you program robots' spatial reasoning, algebraic geometry might pay off - though, AG doesn't have as easy an entry. (One exception might be via the book Computational Algebraic Geometry by Hal Schenck). As far as number theory "paying off": 1) Many proofs in number theory are algorithmic in nature; 2) Computers understand integers with greater facility than they do the psuedo-reals…
……两个：https://faculty.math.illinois.edu/Macaulay2/Book/Computation... https://faculty.math.illinois.edu/Macaulay2/Book/Computation... 更多内容可以看《Computations in algebraic geometry with Macaulay 2》这本书，网上有免费版。另外也可以参考 Schenck 的《Computational Algebraic Geometry》。编辑补充：另外，在这方面 topos theory 绝对不是正路。亲自动手去死磕代数曲线（algebraic curves）才是。比如参考 Griffiths 的《Introduction to Algebraic Curves》。
…two: https://faculty.math.illinois.edu/Macaulay2/Book/Computation... https://faculty.math.illinois.edu/Macaulay2/Book/Computation... There's more in the book "Computations in algebraic geometry with Macaulay 2," which is free online. See also Schenck's "Computational Algebraic Geometry." edit: Also, topos theory is definitely not the way to go here. Getting your hands dirty with algebraic curves is. See e.g. Griffiths' Introduction to Algebraic Curves.