性能问题：用 Mathematica 中的多个假设求解不等式
我需要在给定几个假设（也是不等式）的情况下证明不等式（或找到反例）。不幸的是，要证明的不等式是一个相当长且复杂的表达式。大约有 15 个变量，FullSimplify 的输出可以填满几张 A4 页。对于变量较少的示例，FindInstance 有助于查找反例，或者如果不等式成立则给出 {} 的结果。我还尝试以这种方式使用Reduce：
Reduce[
Implies[
assumtion1 && assumtion2,
inequality
],
Reals
]
对于简单的示例，如果不等式成立，则输出“True”。但就我而言，经过几个小时的运行时间后，Mathematica 需要 5-6 GB RAM（和交换），因此我不得不中止该进程。
我可以使用 Mathematica 做些什么来提高性能吗？
I need to prove an inequality (or find a counter example) given several assumptions (also inequalities). Unfortunately the inequality to prove is a quite long and complicated expression. There are about 15 variables and FullSimplify's output fills several A4 pages. For examples with less variables, FindInstance helps to find a counterexample or gives a result of {} if the inequality is true. I also tried to use Reduce in that way:
Reduce[
Implies[
assumtion1 && assumtion2,
inequality
],
Reals
]
For simple examples this outputs "True", if the inequality holds. But in my case, after several hours of running time Mathematica needed 5-6 GB of RAM (and swap) so I had to abort the process.
Is there anything that I could do with Mathematica to improve the performance?
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您将在此处找到一篇关于 Mma CAD 算法的非常好的论文a>
Mma 使用的圆柱代数分解 (CAD)，在变量数量上以双指数行为进行缩放。
较新的方法在量词交替的数量上是双指数的。
我认为仅使用 Mma 内部引擎将不会有好运，但您可以根据问题的对称性（如果有）自行推出
You will find a very nice paper on Mma CAD algorithms here
The cylindrical algebraic decomposition (CAD), which Mma uses, scales with a double exponential behavior on the number of variables.
Newer methods are double exponential in the number of quantifier alternations.
I think you'll have no luck using only the Mma internal engine, but you may roll your own based in the symmetries of your problem (if any)