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MatheMagicianPiMatheMagicianPi
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removed commented out code
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‎src/sage/dynamics/arithmetic_dynamics/dynamical_semigroup.py

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@@ -691,12 +691,6 @@ def _mul_(self, other_dynamical_semigroup):
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ValueError: left dynamical semigroup's domain must equal right dynamical semigroup's codomain
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"""
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# if isinstance(self, DynamicalSemigroup_projective) and \
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# not isinstance(other_dynamical_semigroup, DynamicalSemigroup_projective):
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# raise TypeError("can only multiply `DynamicalSemigroup_projective` objects")
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# if isinstance(self, DynamicalSemigroup_affine) and \
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# not isinstance(other_dynamical_semigroup, DynamicalSemigroup_affine):
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# raise TypeError("can only multiply `DynamicalSemigroup_projective` objects")
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if type(self) != type(other_dynamical_semigroup):
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raise TypeError("can only multiply dynamical semigroups with other dynamical semigroups of the same type")
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if self.domain() != other_dynamical_semigroup.codomain():
@@ -1035,175 +1029,6 @@ def dehomogenize(self, n):
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new_systems.append(new_system)
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return DynamicalSemigroup_affine(new_systems)
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# def _mul_(self, other_dynamical_semigroup):
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# r"""
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# Return a new :class:`DynamicalSemigroup_projective` that is the result of multiplying
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# this dynamical semigroup with another dynamical semigroup using the * operator.
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1043-
# Let `f` be a dynamical semigroup with generators `\{ f_1, f_2, \dots, f_m \}`
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# and `g` be a dynamical semigroup with generators `\{ g_1, g_2, \dots, g_n \}`.
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# The product `f * g` has generators
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# `\{ f_i(g_j) : 1 \leq i \leq m, 1 \leq j \leq n \} \cup \{ g_j(f_i) : 1 \leq i \leq m, 1 \leq j \leq n \}`.
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# INPUT:
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# - ``other_dynamical_semigroup`` -- a dynamical semigroup over projective space
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# OUTPUT: :class:`DynamicalSemigroup_projective`
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# EXAMPLES::
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# sage: P.<x,y> = ProjectiveSpace(QQ, 1)
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# sage: f1 = DynamicalSystem([x, y], P)
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# sage: f2 = DynamicalSystem([x^2, y^2], P)
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# sage: g1 = DynamicalSystem([x^3, y^3], P)
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# sage: g2 = DynamicalSystem([x^4, y^4], P)
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# sage: f = DynamicalSemigroup((f1, f2))
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# sage: g = DynamicalSemigroup((g1, g2))
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# sage: f*g
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# Dynamical semigroup over Projective Space of dimension 1 over Rational Field defined by 8 dynamical systems:
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# Dynamical System of Projective Space of dimension 1 over Rational Field
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# Defn: Defined on coordinates by sending (x : y) to
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# (x^3 : y^3)
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# Dynamical System of Projective Space of dimension 1 over Rational Field
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# Defn: Defined on coordinates by sending (x : y) to
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# (x^4 : y^4)
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# Dynamical System of Projective Space of dimension 1 over Rational Field
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# Defn: Defined on coordinates by sending (x : y) to
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# (x^6 : y^6)
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# Dynamical System of Projective Space of dimension 1 over Rational Field
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# Defn: Defined on coordinates by sending (x : y) to
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# (x^8 : y^8)
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# Dynamical System of Projective Space of dimension 1 over Rational Field
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# Defn: Defined on coordinates by sending (x : y) to
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# (x^3 : y^3)
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# Dynamical System of Projective Space of dimension 1 over Rational Field
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# Defn: Defined on coordinates by sending (x : y) to
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# (x^6 : y^6)
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# Dynamical System of Projective Space of dimension 1 over Rational Field
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# Defn: Defined on coordinates by sending (x : y) to
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# (x^4 : y^4)
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# Dynamical System of Projective Space of dimension 1 over Rational Field
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# Defn: Defined on coordinates by sending (x : y) to
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# (x^8 : y^8)
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# TESTS::
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1092-
# sage: P.<x,y> = ProjectiveSpace(QQ, 1)
1093-
# sage: f1 = DynamicalSystem([x, y], P)
1094-
# sage: f2 = DynamicalSystem([x^2, y^2], P)
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# sage: g1 = DynamicalSystem([x^3, y^3], P)
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# sage: g2 = DynamicalSystem([x^4, y^4], P)
1097-
# sage: f = DynamicalSemigroup((f1, f2))
1098-
# sage: g = DynamicalSemigroup((g1, g2))
1099-
# sage: f*g == g*f
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# True
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1102-
# ::
1103-
1104-
# sage: P.<x,y> = ProjectiveSpace(QQ, 1)
1105-
# sage: Q.<z,w> = ProjectiveSpace(QQ, 1)
1106-
# sage: f1 = DynamicalSystem([x, y], P)
1107-
# sage: f2 = DynamicalSystem([x^2, y^2], P)
1108-
# sage: g1 = DynamicalSystem([z^3, w^3], Q)
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# sage: g2 = DynamicalSystem([z^4, w^4], Q)
1110-
# sage: f = DynamicalSemigroup((f1, f2))
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# sage: g = DynamicalSemigroup((g1, g2))
1112-
# sage: f*g == g*f
1113-
# True
1114-
1115-
# ::
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1117-
# sage: P.<x,y> = ProjectiveSpace(QQ, 1)
1118-
# sage: f1 = DynamicalSystem([x, y], P)
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# sage: f2 = DynamicalSystem([x^2, y^2], P)
1120-
# sage: g1 = DynamicalSystem([x^3, y^3], P)
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# sage: g2 = DynamicalSystem([x^4, y^4], P)
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# sage: h1 = DynamicalSystem([x^5, y^5], P)
1123-
# sage: h2 = DynamicalSystem([x^6, y^6], P)
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# sage: f = DynamicalSemigroup((f1, f2))
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# sage: g = DynamicalSemigroup((g1, g2))
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# sage: h = DynamicalSemigroup((h1, h2))
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# sage: f*(g*h) == (f*g)*h
1128-
# True
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1130-
# ::
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1132-
# sage: P.<x,y> = ProjectiveSpace(QQ, 1)
1133-
# sage: Q.<z,w> = ProjectiveSpace(QQ, 1)
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# sage: R.<u,v> = ProjectiveSpace(QQ, 1)
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# sage: f1 = DynamicalSystem([x, y], P)
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# sage: f2 = DynamicalSystem([x^2, y^2], P)
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# sage: g1 = DynamicalSystem([z^3, z^3], Q)
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# sage: g2 = DynamicalSystem([z^4, w^4], Q)
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# sage: h1 = DynamicalSystem([u^5, v^5], R)
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# sage: h2 = DynamicalSystem([u^6, v^6], R)
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# sage: f = DynamicalSemigroup((f1, f2))
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# sage: g = DynamicalSemigroup((g1, g2))
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# sage: h = DynamicalSemigroup((h1, h2))
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# sage: f*(g*h) == (f*g)*h
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# True
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# ::
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# sage: P.<x,y> = ProjectiveSpace(QQ, 1)
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# sage: A.<z> = AffineSpace(QQ, 1)
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# sage: f1 = DynamicalSystem([x, y], P)
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# sage: f2 = DynamicalSystem([x^2, y^2], P)
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# sage: g1 = DynamicalSystem(z^3, A)
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# sage: g2 = DynamicalSystem(z^4, A)
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# sage: f = DynamicalSemigroup((f1, f2))
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# sage: g = DynamicalSemigroup((g1, g2))
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# sage: f*g
1158-
# Traceback (most recent call last):
1159-
# ...
1160-
# TypeError: can only multiply `DynamicalSemigroup_projective` objects
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1162-
# ::
1163-
1164-
# sage: P.<x,y> = ProjectiveSpace(QQ, 1)
1165-
# sage: Q.<u, v, w> = ProjectiveSpace(QQ, 2)
1166-
# sage: f1 = DynamicalSystem([x, y], P)
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# sage: f2 = DynamicalSystem([x^2, y^2], P)
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# sage: g1 = DynamicalSystem([u^3, v^3, w^3], Q)
1169-
# sage: g2 = DynamicalSystem([u^4, v^4, w^4], Q)
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# sage: f = DynamicalSemigroup((f1, f2))
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# sage: g = DynamicalSemigroup((g1, g2))
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# sage: f*g
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# Traceback (most recent call last):
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# ...
1175-
# ValueError: cannot multiply dynamical semigroups of different dimensions
1176-
# """
1177-
# if isinstance(self, DynamicalSemigroup_projective) and \
1178-
# not isinstance(other_dynamical_semigroup, DynamicalSemigroup_projective):
1179-
# raise TypeError("can only multiply `DynamicalSemigroup_projective` objects")
1180-
# if isinstance(self, DynamicalSemigroup_affine) and \
1181-
# not isinstance(other_dynamical_semigroup, DynamicalSemigroup_affine):
1182-
# raise TypeError("can only multiply `DynamicalSemigroup_projective` objects")
1183-
# if self.domain() != other_dynamical_semigroup.codomain():
1184-
# raise ValueError("left dynamical semigroup's domain must equal right dynamical semigroup's codomain")
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# composite_systems = []
1186-
# my_polys = self.defining_polynomials()
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# other_polys = other_dynamical_semigroup.defining_polynomials()
1188-
# for my_poly in my_polys:
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# for other_poly in other_polys:
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# composite_poly = []
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# for coordinate_poly in my_poly:
1192-
# composite_poly.append(coordinate_poly(other_poly))
1193-
# composite_system = DynamicalSystem_projective(composite_poly)
1194-
# composite_systems.append(composite_system)
1195-
# for other_poly in other_polys:
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# for my_poly in my_polys:
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# composite_poly = []
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# for coordinate_poly in other_poly:
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# composite_poly.append(coordinate_poly(my_poly))
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# composite_system = DynamicalSystem_projective(composite_poly)
1201-
# composite_systems.append(composite_system)
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# for f in self.defining_systems():
1203-
# for g in other_dynamical_semigroup.defining_systems():
1204-
# composite_systems.append(f*g)
1205-
# return DynamicalSemigroup_projective(composite_systems)
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class DynamicalSemigroup_projective_field(DynamicalSemigroup_projective):
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pass
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