The trouble was that I wanted common code for both additive and
multiplicative groups, which I can -- almost-- implement. Your way,
we have one type of element derived from some MultiplicativeElement
class and another from an Additive one, with a lot of duplicated code.
But I'll look at your code and see if it can help what I was trying to do.
John
2008/8/29 Robert Bradshaw <[EMAIL PROTECTED]>:
>
> On Aug 29, 2008, at 2:24 AM, Nils Skoruppa wrote:
>
>> On 28 Aug., 15:20, "John Cremona" <[EMAIL PROTECTED]> wrote:
>>> Thanks for your comments, David. I am having some success:
>>>
>>> The one thing I cannot get to work in the additive case is (for
>>> example) 2*g where g is a group element. I have tried all possible
>>> combinations of __lmul__, _lmul_, __rmul__, _rmul_, but although I
>>> have this ok:
>>>
>>> sage: a,b=A.gens()
>>> sage: b._lmul_(20)
>>> 2*b
>>> sage: 2*b
>>>
>>> inputting 20*b gives an error:
>>> TypeError Traceback (most recent
>>> call last)
>>
>>>>> John
>>
>> Hi John,
>>
>> I have a class which derives from AdditiveGroupElement and whose
>> parent derives from AbelianGroup. Concerning multiplication I did not
>> implement more than __mul__() with two underscores ( and no _lmul_,
>> _rmul_, mil_impl-c ... and the like). It seems to work OK:
>>
>> sage: A.<a,b,c> = FiniteQuadraticModule ('3^3')
>> sage: 5*a
>> 2*a
>> sage: b*7
>> b
>> sage: -a +
>> 2*c
>> 2*a + 2*c
>>
>> I cannot explain why this works, but if you want to have a look:
>> http://hg.countnumber.de/fqm-devel/file/98bb736f0c07/cn_group/
>> finite_quadratic_module.sage
>> (and then line 2132 class
>> FiniteQuadraticModuleElement(AdditiveGroupElement).
>
> Here is what should be implemented (and I just tried it out and it
> does for me with the latest Sage). Most of the coercion model focus
> has been considered in the context of Rings, but groups are fine too.
> Let me know if this doesn't work for you.
>
>
> from sage.groups.group import AbelianGroup
> from sage.structure.element import AdditiveGroupElement
>
> class MyAbelianGroup(AbelianGroup):
> def __call__(self, n):
> return MyAdditiveGroupElement(self, n)
>
> class MyAdditiveGroupElement(AdditiveGroupElement):
> def __init__(self, parent, n):
> AdditiveGroupElement.__init__(self, parent)
> self.n = n
> def __repr__(self):
> return "My(%s)" % self.n
> def _add_(left, right):
> # Guaranteed left and right have the same parent.
> return MyAdditiveGroupElement(left.parent(), left.n + right.n)
> def _rmul_(self, a):
> # Guaranteed a is in the basering (probably ZZ)
> return MyAdditiveGroupElement(self.parent(), self.n * a)
> def _lmul_(self, a):
> # Guaranteed a is in the basering (probably ZZ)
> return self._rmul_(a) # should this be a default?
>
>
> sage: G = MyAbelianGroup()
> sage: G.base_ring()
> Integer Ring
> sage: G(3) + G(9)
> My(12)
> sage: 7*G(3)
> My(21)
> sage: G(2)*5
> My(10)
> sage: sum([G(2), G(3), G(7)])
> My(12)
> sage: G(55) * int(4)
> My(220)
>
>
> One thing that mystifies me is that I though repeated doubling was
> supposed to be provided by default if neither _rmul_ nor _lmul_ were
> provided. I'll have to look at this, but it's orthogonal to what you
> are trying to do.
>
> - Robert
>
>
> >
>
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