The sage coercion model guarantees that when x.__add__(y) is called
(well, technically x._add_ or x._add_c_impl), the argument y is of
the same type and parent as x. For example
sage: R.<x> = ZZ[]
sage: x+1/2
x + 1/2
sage: parent(x)
Univariate Polynomial Ring in x over Integer Ring
sage: parent(1/2)
Rational Field
sage: parent(x+1/2)
Univariate Polynomial Ring in x over Rational Field
In your case, someone could type
sage: g = CompleteGraph(5)
sage: g+1 # will call g.__add__(1)
???
which you have to deal with. Typically, just throw an error if it's
not a graph. But what about graph + digraph? Digraph + digraph? Etc.
Should graph + x be a new graph with a new (unconnected) vertex 'x'?
- Robert
On Sep 25, 2007, at 4:59 PM, Hamptonio wrote:
> Thanks, now I understand what to do. However, I don't understand your
> comment about "...the SAGE coercion model". What is an example of
> that - the sage integers?
>
> -M. Hampton
>
> On Sep 25, 12:10 pm, "Mike Hansen" <[EMAIL PROTECTED]> wrote:
>> Since I don't think that graphs and polytopes fall under the SAGE
>> coercion model, overloading operators is pretty straightforward. You
>> just need to define the __add__ method in your class. x + y will
>> call
>> x.__add__(y).
>>
>> sage: class Foo:
>> ....: def __add__(self, y):
>> ....: return 42
>> ....:
>> sage: a = Foo()
>> sage: b = Foo()
>> sage: a + b
>> 42
>> sage: b + a
>> 42
>>
>> Note that you'll want to do some type-checking so that y is what you
>> actually think it should be.
>>
>> --Mike
>>
>> On 9/25/07, Hamptonio <[EMAIL PROTECTED]> wrote:
>>
>>
>>
>>> I would appreciate any tips on how to extend the + operator in this
>>> way, since I would like to implement Minkowski sums of polytopes and
>>> this is natural notation for that.
>>> Marshall
>>
>>> On Sep 25, 10:37 am, "Mike Hansen" <[EMAIL PROTECTED]> wrote:
>>>> In SAGE, '+' is used for union of sets. For example,
>>
>>>> sage: a = Set([1,2])
>>>> sage: b = Set([2,3])
>>>> sage: a+b
>>>> {1, 2, 3}
>>
>>>> Since currently, + is not defined for graphs, it'd be a natural
>>>> choice.
>>
>>>> --Mike
>>
>>>> On 9/25/07, Jason Grout <[EMAIL PROTECTED]> wrote:
>>
>>>>> I'm thinking more about how to make the Graph class easy to
>>>>> use. One
>>>>> thing that crops up is that the operations that combine graphs
>>>>> only
>>>>> combine two graphs at a time (e.g., g.union(h), where g and h
>>>>> are graphs).
>>
>>>>> Is there a way to define an infix operator that would allow one
>>>>> to say:
>>
>>>>> g union h union i union j union k?
>>
>>>>> I could do it with something like:
>>
>>>>> reduce(lambda x,y: x.union(y), [g,h,i,j,k])
>>
>>>>> But that doesn't seem as clear as the infix things above.
>>
>>>>> For reference, Mathematica allows an operator in backticks to
>>>>> be applied
>>>>> to its surrounding arguments, so the equivalent operation above
>>>>> would be:
>>
>>>>> g `union` h `union` i `union` j `union` k
>>
>>>>> And of course, you can set whether the operator is left-
>>>>> associative or
>>>>> right-associative.
>>
>>>>> Of course, one solution is to use a for loop:
>>
>>>>> newgraph=Graph()
>>>>> for graph in [g,h,i,j,k]:
>>>>> newgraph.union(graph)
>>
>>>>> But that seems a lot clunkier than the infix expression above.
>>
>>>>> I guess another solution is to return the new graph from the
>>>>> union, so
>>>>> that you could do:
>>
>>>>> g.union(h).union(i).union(j)
>>
>>>>> Thoughts?
>>
>>>>> -Jason
>
>
>
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