系数功能慢 [英] Coefficient function is slow

问题描述

请考虑:

Clear[x]
expr = Sum[x^i, {i, 15}]^30;

CoefficientList[expr, x]; // Timing
Coefficient[Expand@expr, x, 234]; // Timing
Coefficient[expr, x, 234]; // Timing

{0.047, Null}

{0.047, Null}

{4.93, Null}

帮助状态:

不管是否以扩展形式显式给出expr，

Coefficient都可以工作.

Coefficient works whether or not expr is explicitly given in expanded form.

为什么在最后一种情况下Coefficient需要这么慢?

Is there a reason why Coefficient needs to be so slow in the last case?

推荐答案

Coefficient除非绝对必要，否则不会扩展.这确实可以避免内存爆炸.我相信从版本3开始就采用这种方式(我想我是在1995年左右开始研究它的.)

Coefficient will not expand unless it deems it absolutely necessary to do so. This does indeed avoid memory explosions. I believe it has been this way since version 3 (I think I was working on it around 1995 or so).

也可以更快地避免扩展.这是一个简单的例子.

It can also be faster to avoid expansion. Here is a simple example.

In[28]:= expr = Sum[x^i + y^j + z^k, {i, 15}, {j, 10}, {k, 20}]^20;

In[29]:= Coefficient[expr, x, 234]; // Timing

Out[29]= {0.81, Null}

但是下一个似乎挂在版本8中，并且在开发Mathematica(更改了Expand的地方)中至少花费了半分钟.

But this next appears to hang in version 8, and takes at least a half minute in the development Mathematica (where Expand was changed).

Coefficient[Expand[expr], x, 234]; // Timing

可能应该添加一些试探法来寻找不会爆炸的单变量.不过，这似乎不是一个高优先级的项目.

Possibly some heuristics should be added to look for univariates that will not explode. Does not seem like a high priority item though.

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