I've done much work in this area over the years, and find myself using Sage as my preferred system [http://www.sagemath.org/]. It is extremely efficient and has a natural language for schemes and other algebraic structures. Others I have used and enjoy are OpenAxiom and Magma. I tend to avoid MathCad and Mathematica, as they tend to have a lot if overhead in their parsers and provide a lot of bloat related to their interfaces unrelated to getting your calculations resolved.
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多年来我在这个领域做了很多工作，并发现自己使用 Sage 作为我的首选系统 [http://www.sagemath.org/]。它非常高效，并且具有用于方案和其他代数结构的自然语言。我使用过并喜欢的其他工具是 OpenAxiom 和 Magma。我倾向于避免使用 MathCad 和 Mathematica，因为它们的解析器往往会产生大量开销，并且会提供大量与其接口相关的臃肿内容，而这些接口与解决计算无关。
支持仿射方案的示例可以在 http://www.sagemath.org/doc/reference/sage/schemes/generic/affine_space.html?highlight=affine#sage.schemes.generic.affine_space
I've done much work in this area over the years, and find myself using Sage as my preferred system [http://www.sagemath.org/]. It is extremely efficient and has a natural language for schemes and other algebraic structures. Others I have used and enjoy are OpenAxiom and Magma. I tend to avoid MathCad and Mathematica, as they tend to have a lot if overhead in their parsers and provide a lot of bloat related to their interfaces unrelated to getting your calculations resolved.
An example of the support for affine schemes can be seen at http://www.sagemath.org/doc/reference/sage/schemes/generic/affine_space.html?highlight=affine#sage.schemes.generic.affine_space