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structure/detect element action #37918

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structure/detect element action #37918

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dc98444
fix bug and documentation typo in detect_element_action
mantepse May 1, 2024
f9124c5
fix PoincareBirkhoffWittBasis.Element._act_on_
mantepse May 2, 2024
2f381d9
Merge branch 'develop' into structure/detect_element_action
mantepse May 10, 2024
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18 changes: 9 additions & 9 deletions src/sage/algebras/lie_algebras/poincare_birkhoff_witt.py
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Original file line number Diff line number Diff line change
Expand Up @@ -609,24 +609,24 @@ def _act_on_(self, x, self_on_left):
return ret
cm = get_coercion_model()
L = self.parent()._g
if self_on_left:
if cm.discover_action(L, x.parent(), mul):
ret = x.parent().zero()
X = x.parent()
action = X.get_action(L, self_on_left=not self_on_left)
if action:
assert action.actor() is L
ret = X.zero()
if self_on_left:
for mon, coeff in self._monomial_coefficients.items():
term = coeff * x
for k, exp in reversed(mon._sorted_items()):
for _ in range(exp):
term = L.monomial(k) * term
ret += term
return ret
else:
if cm.discover_action(x.parent(), L, mul):
ret = x.parent().zero()
else:
for mon, coeff in self._monomial_coefficients.items():
term = coeff * x
term = x * coeff
for k, exp in reversed(mon._sorted_items()):
for _ in range(exp):
term = term * L.monomial(k)
ret += term
return ret
return ret
return None
35 changes: 26 additions & 9 deletions src/sage/structure/coerce_actions.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -159,7 +159,7 @@ cdef class ActedUponAction(GenericAction):

def detect_element_action(Parent X, Y, bint X_on_left, X_el=None, Y_el=None):
r"""
Return an action of X on Y as defined by elements of X, if any.
Return an action of Y on X as defined by elements of X, if any.

EXAMPLES:

Expand Down Expand Up @@ -197,6 +197,23 @@ def detect_element_action(Parent X, Y, bint X_on_left, X_el=None, Y_el=None):
Traceback (most recent call last):
...
RuntimeError: an_element() for <__main__.MyParent object at ...> returned None

Check that we have a right action of the symmetric group on the
polynomial ring, but not a left action::

sage: S3 = SymmetricGroup(3)
sage: R.<x,y,z> = QQ[]
sage: detect_element_action(R, S3, True)
Right action by Symmetric group of order 3! as a permutation group on
Multivariate Polynomial Ring in x, y, z over Rational Field
sage: detect_element_action(R, S3, False)

Also, we don't have an action of the polynomial ring on the
symmetric group::

sage: detect_element_action(S3, R, True)
sage: detect_element_action(S3, R, False)

"""
cdef Element x

Expand Down Expand Up @@ -224,15 +241,15 @@ def detect_element_action(Parent X, Y, bint X_on_left, X_el=None, Y_el=None):
except CoercionException as msg:
_record_exception()

# element x defining _act_on_
try:
if x._act_on_(y, X_on_left) is not None:
return ActOnAction(X, Y, X_on_left, False)
Comment on lines -229 to -230
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@mantepse mantepse May 3, 2024 •
edited
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I 'traced' (using print)

sage: cm = get_coercion_model()
sage: c = cm.get_action(ZZ, list, operator.mul)

and it is line 230 that returns

Left action by Integer Ring on <class 'list'>

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Yea, I think we are just being too strict with making sure Y is a parent. We need to allow that to not be a Parent, and maybe need to catch an error (or fix some other code). Not 100% sure at this point.

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I think, to be of any help I would need to know precisely what detect_element_action is supposed to be doing. And, I guess, that's part of the problem, right?

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Indeed, we are kind of guessing at its purpose based on its code, its doc, and how it is used. Unfortunately there doesn’t seem to be any consistency with these three. @nbruin Do you have any recollections, thoughts, or opinions on this?

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I'm not sure which three routines are in play here. I don't think we can have an action of integers on a list, if that's what you're aiming for. Lists are way to coarse a "parent" to determine actions for. There may also be the problem that non-parents probably fail to have the right slots/attributes to properly participate in the coercion system. And there's the conflict that 3*[1,2,3] and [1,2,3]*3 already means "repeated concatenation" in python.

There was recently a discussion on action discovery concerning int vs. Integer where Parent participating in actions also came up: https://groups.google.com/g/sage-devel/c/RvmljIs7wBI/
and in a different form in this relatively recent PR: #37369
(which in the end did end up with a patch so that action discovery for int on ZZ-modules should also work!)

except CoercionException:
_record_exception()

# element x defining _acted_upon_
if isinstance(Y, Parent):
# element y defining _act_on_
try:
if y._act_on_(x, not X_on_left) is not None:
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If we follow the docstring as defined by elements of X, this looks wrong. Indeed, in the old code, we were only looking at methods of x.

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I don't quite think it is saying that it defined by the methods of x (the action is defined by x using the method of y is how I read this), but you can read it that way. Although I don't think the docstring is accurate in this regard either.

return ActOnAction(Y, X, not X_on_left, False)
except CoercionException:
_record_exception()

# element x defining _acted_upon_
try:
if x._acted_upon_(y, X_on_left) is not None:
return ActedUponAction(Y, X, not X_on_left, False)
Expand Down
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