> The question, now, is why the coercion system is invoked at all: I'm doing
> arithmetic within my own ring. The culprit, I guess, is the expression
> 1/self in element.pyx.
>
> Does a ring keep track of its own multiplicative identity element?
>
A: yes, it does. If I replace, in element.pyx line 1927,
return 1/self
by
return self._parent.one_element() / self
then my code runs in half the time. How do I check if this impacts other
parts of Sage?
Unrelated: the __invert__ method of the MultiplicativeGroupElement class
(again in element.pyx) calls "self.is_one()" but the class does not
implement that method. Example (obtained from digging in the source code):
sage: s = EtaGroupElement(EtaGroup(8), {1:24, 2:-24})
sage: s^(-1)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
...
AttributeError: 'EtaGroupElement' object has no attribute 'is_one'
Cheers,
Stefan.
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