Coerce actions¶

class sage.structure.coerce_actions.ActOnAction

Class for actions defined via the _act_on_ method.

class sage.structure.coerce_actions.ActedUponAction

Class for actions defined via the _acted_upon_ method.

class sage.structure.coerce_actions.GenericAction
codomain()

Returns the “codomain” of this action, i.e. the Parent in which the result elements live. Typically, this should be the same as the acted upon set.

EXAMPLES:

Note that coerce actions should only be used inside of the coercion model. For this test, we need to strongly reference the domains, for otherwise they could be garbage collected, giving rise to random errors (see trac ticket #18157).

sage: M = MatrixSpace(ZZ,2)
sage: A = sage.structure.coerce_actions.ActedUponAction(M, Cusps, True)
sage: A.codomain()
Set P^1(QQ) of all cusps

sage: S3 = SymmetricGroup(3)
sage: QQxyz = QQ['x,y,z']
sage: A = sage.structure.coerce_actions.ActOnAction(S3, QQxyz, False)
sage: A.codomain()
Multivariate Polynomial Ring in x, y, z over Rational Field
class sage.structure.coerce_actions.IntegerAction

Abstract base class representing some action by integers on something. Here, “integer” is defined loosely in the “duck typing” sense.

INPUT:

• Z – a type or parent representing integers

For the other arguments, see Action.

Note

This class is used internally in Sage’s coercion model. Outside of the coercion model, special precautions are needed to prevent domains of the action from being garbage collected.

class sage.structure.coerce_actions.IntegerMulAction

Implement the action $$n \cdot a = a + a + ... + a$$ via repeated doubling.

Both addition and negation must be defined on the set $$M$$.

INPUT:

• Z – a type or parent representing integers
• M – a ZZ-module
• m – (optional) an element of M

EXAMPLES:

sage: from sage.structure.coerce_actions import IntegerMulAction
sage: R.<x> = QQ['x']
sage: act = IntegerMulAction(ZZ, R)
sage: act(5, x)
5*x
sage: act(0, x)
0
sage: act(-3, x-1)
-3*x + 3
class sage.structure.coerce_actions.IntegerPowAction

The right action a ^ n = a * a * ... * a where $$n$$ is an integer.

The action is implemented using the _pow_int method on elements.

INPUT:

• Z – a type or parent representing integers
• M – a parent whose elements implement _pow_int
• m – (optional) an element of M

EXAMPLES:

sage: from sage.structure.coerce_actions import IntegerPowAction
sage: R.<x> = LaurentSeriesRing(QQ)
sage: act = IntegerPowAction(ZZ, R)
sage: act(x, 5)
x^5
sage: act(x, -2)
x^-2
sage: act(x, int(5))
x^5
class sage.structure.coerce_actions.LeftModuleAction
class sage.structure.coerce_actions.ModuleAction

Module action.

This is an abstract class, one must actually instantiate a LeftModuleAction or a RightModuleAction.

INPUT:

• G – the actor, an instance of Parent.
• S – the object that is acted upon.
• g – optional, an element of G.
• a – optional, an element of S.
• check – if True (default), then there will be no consistency tests performed on sample elements.

NOTE:

By default, the sample elements of S and G are obtained from an_element(), which relies on the implementation of an _an_element_() method. This is not always available. But usually, the action is only needed when one already has two elements. Hence, by trac ticket #14249, the coercion model will pass these two elements to the ModuleAction constructor.

The actual action is implemented by the _rmul_ or _lmul_ function on its elements. We must, however, be very particular about what we feed into these functions, because they operate under the assumption that the inputs lie exactly in the base ring and may segfault otherwise. Thus we handle all possible base extensions manually here.

codomain()

The codomain of self, which may or may not be equal to the domain.

EXAMPLES:

Note that coerce actions should only be used inside of the coercion model. For this test, we need to strongly reference the domains, for otherwise they could be garbage collected, giving rise to random errors (see trac ticket #18157).

sage: from sage.structure.coerce_actions import LeftModuleAction
sage: ZZxyz = ZZ['x,y,z']
sage: A = LeftModuleAction(QQ, ZZxyz)
sage: A.codomain()
Multivariate Polynomial Ring in x, y, z over Rational Field
domain()

The domain of self, which is the module that is being acted on.

EXAMPLES:

Note that coerce actions should only be used inside of the coercion model. For this test, we need to strongly reference the domains, for otherwise they could be garbage collected, giving rise to random errors (see trac ticket #18157).

sage: from sage.structure.coerce_actions import LeftModuleAction
sage: ZZxyz = ZZ['x,y,z']
sage: A = LeftModuleAction(QQ, ZZxyz)
sage: A.domain()
Multivariate Polynomial Ring in x, y, z over Integer Ring
class sage.structure.coerce_actions.PyScalarAction
class sage.structure.coerce_actions.RightModuleAction
sage.structure.coerce_actions.detect_element_action(X, Y, X_on_left, X_el=None, Y_el=None)

Return an action of X on Y as defined by elements of X, if any.

EXAMPLES:

Note that coerce actions should only be used inside of the coercion model. For this test, we need to strongly reference the domains, for otherwise they could be garbage collected, giving rise to random errors (see trac ticket #18157).

sage: from sage.structure.coerce_actions import detect_element_action
sage: ZZx = ZZ['x']
sage: M = MatrixSpace(ZZ,2)
sage: detect_element_action(ZZx, ZZ, False)
Left scalar multiplication by Integer Ring on Univariate Polynomial Ring in x over Integer Ring
sage: detect_element_action(ZZx, QQ, True)
Right scalar multiplication by Rational Field on Univariate Polynomial Ring in x over Integer Ring
sage: detect_element_action(Cusps, M, False)
Left action by Full MatrixSpace of 2 by 2 dense matrices over Integer Ring on Set P^1(QQ) of all cusps
sage: detect_element_action(Cusps, M, True),
(None,)
sage: detect_element_action(ZZ, QQ, True),
(None,)