Coerce actions¶
- class sage.structure.coerce_actions.ActOnAction[source]¶
- Bases: - GenericAction- Class for actions defined via the _act_on_ method. 
- class sage.structure.coerce_actions.ActedUponAction[source]¶
- Bases: - GenericAction- Class for actions defined via the _acted_upon_ method. 
- class sage.structure.coerce_actions.GenericAction[source]¶
- Bases: - Action- codomain()[source]¶
- Return 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 Issue #18157). - sage: M = MatrixSpace(ZZ, 2) # needs sage.modules sage: A = sage.structure.coerce_actions.ActedUponAction(M, Cusps, True) # needs sage.modular sage.modules sage: A.codomain() # needs sage.modular sage.modules Set P^1(QQ) of all cusps sage: # needs sage.groups 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 - >>> from sage.all import * >>> M = MatrixSpace(ZZ, Integer(2)) # needs sage.modules >>> A = sage.structure.coerce_actions.ActedUponAction(M, Cusps, True) # needs sage.modular sage.modules >>> A.codomain() # needs sage.modular sage.modules Set P^1(QQ) of all cusps >>> # needs sage.groups >>> S3 = SymmetricGroup(Integer(3)) >>> QQxyz = QQ['x,y,z'] >>> A = sage.structure.coerce_actions.ActOnAction(S3, QQxyz, False) >>> A.codomain() Multivariate Polynomial Ring in x, y, z over Rational Field 
 
- class sage.structure.coerce_actions.IntegerAction[source]¶
- Bases: - Action- 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[source]¶
- Bases: - IntegerAction- 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 - >>> from sage.all import * >>> from sage.structure.coerce_actions import IntegerMulAction >>> R = QQ['x']; (x,) = R._first_ngens(1) >>> act = IntegerMulAction(ZZ, R) >>> act(Integer(5), x) 5*x >>> act(Integer(0), x) 0 >>> act(-Integer(3), x-Integer(1)) -3*x + 3 
- class sage.structure.coerce_actions.IntegerPowAction[source]¶
- Bases: - IntegerAction- The right action - a ^ n = a * a * ... * awhere \(n\) is an integer.- The action is implemented using the - _pow_intmethod 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 - >>> from sage.all import * >>> from sage.structure.coerce_actions import IntegerPowAction >>> R = LaurentSeriesRing(QQ, names=('x',)); (x,) = R._first_ngens(1) >>> act = IntegerPowAction(ZZ, R) >>> act(x, Integer(5)) x^5 >>> act(x, -Integer(2)) x^-2 >>> act(x, int(Integer(5))) x^5 
- class sage.structure.coerce_actions.LeftModuleAction[source]¶
- Bases: - ModuleAction
- class sage.structure.coerce_actions.ModuleAction[source]¶
- Bases: - Action- Module action. - See also - This is an abstract class, one must actually instantiate a - LeftModuleActionor 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 - Sand- Gare 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 Issue #14249, the coercion model will pass these two elements to the- ModuleActionconstructor.- 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()[source]¶
- 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 Issue #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 - >>> from sage.all import * >>> from sage.structure.coerce_actions import LeftModuleAction >>> ZZxyz = ZZ['x,y,z'] >>> A = LeftModuleAction(QQ, ZZxyz) >>> A.codomain() Multivariate Polynomial Ring in x, y, z over Rational Field 
 - domain()[source]¶
- 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 Issue #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 - >>> from sage.all import * >>> from sage.structure.coerce_actions import LeftModuleAction >>> ZZxyz = ZZ['x,y,z'] >>> A = LeftModuleAction(QQ, ZZxyz) >>> A.domain() Multivariate Polynomial Ring in x, y, z over Integer Ring 
 
- class sage.structure.coerce_actions.RightModuleAction[source]¶
- Bases: - ModuleAction
- sage.structure.coerce_actions.detect_element_action(X, Y, X_on_left, X_el=None, Y_el=None)[source]¶
- 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 Issue #18157). - sage: from sage.structure.coerce_actions import detect_element_action sage: ZZx = ZZ['x'] sage: M = MatrixSpace(ZZ, 2) # needs sage.modules 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) # needs sage.modular sage.modules 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), # needs sage.modular sage.modules (None,) sage: detect_element_action(ZZ, QQ, True), (None,) - >>> from sage.all import * >>> from sage.structure.coerce_actions import detect_element_action >>> ZZx = ZZ['x'] >>> M = MatrixSpace(ZZ, Integer(2)) # needs sage.modules >>> detect_element_action(ZZx, ZZ, False) Left scalar multiplication by Integer Ring on Univariate Polynomial Ring in x over Integer Ring >>> detect_element_action(ZZx, QQ, True) Right scalar multiplication by Rational Field on Univariate Polynomial Ring in x over Integer Ring >>> detect_element_action(Cusps, M, False) # needs sage.modular sage.modules Left action by Full MatrixSpace of 2 by 2 dense matrices over Integer Ring on Set P^1(QQ) of all cusps >>> detect_element_action(Cusps, M, True), # needs sage.modular sage.modules (None,) >>> detect_element_action(ZZ, QQ, True), (None,)