Hi Dan,

first of all: thanks for looking at the patch!

> Unless someone has a better idea, or objects, maybe the patch should
> just update the test result
> in hopf_algebras_with_basis so that the test passes.

I wait until tomorrow if someone has some idea, otherwise I will just
update the test.

> This function is only called once in all of sage, namely at the
> end of dict_linear_combination. Would it be a good idea to inline
> the code here to save the overhead of the function call?

It is called at the end of dict_linear_combination and as well at the
end of dict_addition. That's why I chose to make it an extra method.
Do you recommend to put it back into those places to save the function
call overhead (isn't this nanosecs)?

> Similar code is inlined in the _from_dict method of
> CombinatorialFreeModule. There the code is optional depending
> on a parameter remove_zeros.

At this position, calling the method would result in another iteration
through dict.iteritems(), compare l. 1534 and l. 22. This might take a
while in big cases, thus I didn't use the method in this place.

> In some cases _from_dict is called on data that is direct
> output of dict_linear_combination. This happens
> in the _neg_ and _sub_ methods of CombinatorialFreeModule.
> In those cases the zero removal is done twice. I am not
> I think one could safely pass remove_zeros=False to _from_dict in
> these two
> places and maybe other places in the code. But I am not
> necessarily recommending this.

That's right, I gonna look for places where it is save to set
remove_zeros=False.

In general, an element in CombinatorialFreeModule should never have
zero entries, but I do not know, if this is ensured everywhere. That's
why I added remove_zeros also in places where it might not be
necessary, see e.g. l. 437.

Thanks again, I will upload the changes tomorrow, Christian

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