#19282: Operators expander in categories
-------------------------------------+-------------------------------------
Reporter: elixyre | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.9
Component: categories | Resolution:
Keywords: | Merged in:
Authors: Jean-Baptiste | Reviewers:
Priez | Work issues:
Report Upstream: N/A | Commit:
Branch: | 8e35b830e77028d25e2614aadc9d0708a1872fca
public/hopf_algebras/categories/misc| Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Changes (by zabrocki):
* type: PLEASE CHANGE => enhancement
Old description:
> In Sage, mathematical structures as dendrifom algebras, algebras with
> internal product, ''etc'' involve to implement operators in several
> class. For example, if I wish define a new amazing operator `foo` in the
> category `CategoryOfSomeWonderfulStructures`, I have to do that:
>
> {{{#!python
> class CategoryOfSomeWonderfulStructures(Category):
>
> def super_categories(self):
> return [...]
>
> class ParentMethods:
>
> def foo(self, I):
> '''
> My amazing unary operator with definition
> '''
>
> class ElementMethods:
>
> def foo(self):
> '''
> My amazing unary operator applied
> '''
> return self.parent().foo(self)
>
> class WithRealizations(WithRealizationsCategory):
> class ParentMethods:
>
> def foo(self, I):
> return self.a_realization().foo(I)
>
> class Realizations(RealizationsCategory):
> class ParentMethods:
>
> def foo_by_coercion(self, I):
> ... looking for the good realizations which knows
> how to do
>
> class WithBasis(CategoryWithAxiom_over_base_ring):
> class ParentMethods:
>
> @abstract_method
> def foo_on_basis(self, i):
> pass
>
> def foo_by_linearity(self, I):
> return self.linear_combination(...)
> }}}
>
> I propose to provide two methods (one for unary operator and one other
> for binary operator) such that the implementation could be resume to
>
> {{{#!python
> class CategoryOfSomeWonderfulStructures(Category):
>
> def super_categories(self):
> return [...]
>
> class ParentMethods:
>
> def foo(self, I):
> '''
> My amazing unary operator with definition
> '''
>
> expand_unary_operator(CategoryOfSomeWonderfulStructures,
> CategoryOfSomeWonderfulStructures.ParentMethods.foo)
> }}}
New description:
In Sage, mathematical structures as dendrifom algebras, algebras with
internal product, scalar products, ''etc'' involve to implement operators
in several class. For example, if I wish define a new amazing operator
`foo` in the category `CategoryOfSomeWonderfulStructures`, I have to do:
{{{#!python
class CategoryOfSomeWonderfulStructures(Category):
def super_categories(self):
return [...]
class ParentMethods:
def foo(self, I):
'''
My amazing unary operator with definition
'''
class ElementMethods:
def foo(self):
'''
My amazing unary operator applied
'''
return self.parent().foo(self)
class WithRealizations(WithRealizationsCategory):
class ParentMethods:
def foo(self, I):
return self.a_realization().foo(I)
class Realizations(RealizationsCategory):
class ParentMethods:
def foo_by_coercion(self, I):
look for a good realization which knows how to
foo
class WithBasis(CategoryWithAxiom_over_base_ring):
class ParentMethods:
@abstract_method
def foo_on_basis(self, i):
pass
def foo_by_linearity(self, I):
return self.linear_combination(...)
}}}
I propose to provide two methods (one for unary operator and one other for
binary operator) such that the implementation could be simplified to
{{{#!python
class CategoryOfSomeWonderfulStructures(Category):
def super_categories(self):
return [...]
class ParentMethods:
def foo(self, I):
'''
My amazing unary operator with definition
'''
expand_unary_operator(CategoryOfSomeWonderfulStructures,
CategoryOfSomeWonderfulStructures.ParentMethods.foo)
}}}
--
Comment:
A number of previously implemented Hopf algebras could be greatly
simplified with this code. In QSym alone the methods: `internal_product`,
`skew_by`, `duality_pairing`, `degree_negation`, `counit`, and probably a
few others follow this pattern.
--
Ticket URL: <http://trac.sagemath.org/ticket/19282#comment:2>
Sage <http://www.sagemath.org>
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