diff --git a/src/sage/manifolds/chart.py b/src/sage/manifolds/chart.py index 4c074b818cf..7e1610bacba 100644 --- a/src/sage/manifolds/chart.py +++ b/src/sage/manifolds/chart.py @@ -16,10 +16,10 @@ REFERENCES: -- Chap. 2 of [Lee11]_ J.M. Lee: *Introduction to Topological Manifolds*, +- Chap. 2 of [Lee11]_ \J.M. Lee: *Introduction to Topological Manifolds*, 2nd ed., Springer (New York) (2011) -- Chap. 1 of [Lee13]_ J.M. Lee : *Introduction to Smooth Manifolds*, +- Chap. 1 of [Lee13]_ \J.M. Lee : *Introduction to Smooth Manifolds*, 2nd ed., Springer (New York) (2013) """ diff --git a/src/sage/manifolds/coord_func.py b/src/sage/manifolds/coord_func.py index 8e54e201351..5bb47122a2d 100644 --- a/src/sage/manifolds/coord_func.py +++ b/src/sage/manifolds/coord_func.py @@ -27,11 +27,14 @@ class :class:`CoordFunction`. AUTHORS: - Eric Gourgoulhon, Michal Bejger (2013-2015) : initial version +- Travis Scrimshaw (2016) : make :class:`CoordFunction` inheritate from + :class:`~sage.structure.element.AlgebraElement` """ #***************************************************************************** # Copyright (C) 2015 Eric Gourgoulhon # Copyright (C) 2015 Michal Bejger +# Copyright (C) 2016 Travis Scrimshaw # # Distributed under the terms of the GNU General Public License (GPL) # as published by the Free Software Foundation; either version 2 of @@ -61,8 +64,7 @@ class CoordFunction(AlgebraElement): INPUT: - - ``chart`` -- :class:`~sage.manifolds.chart.Chart`; - the chart `(U, \varphi)` + - ``parent`` -- the algebra of coordinate functions on a given chart """ def __init__(self, parent): diff --git a/src/sage/manifolds/coord_func_symb.py b/src/sage/manifolds/coord_func_symb.py index ffc1e750ef8..551dda8db8b 100644 --- a/src/sage/manifolds/coord_func_symb.py +++ b/src/sage/manifolds/coord_func_symb.py @@ -24,11 +24,14 @@ AUTHORS: - Eric Gourgoulhon, Michal Bejger (2013-2015) : initial version +- Travis Scrimshaw (2016) : make coordinate functions elements of + :class:`CoordFunctionSymbRing`. """ #***************************************************************************** # Copyright (C) 2015 Eric Gourgoulhon # Copyright (C) 2015 Michal Bejger +# Copyright (C) 2016 Travis Scrimshaw # # Distributed under the terms of the GNU General Public License (GPL) # as published by the Free Software Foundation; either version 2 of @@ -41,7 +44,7 @@ from sage.structure.element import RingElement from sage.structure.parent import Parent from sage.structure.unique_representation import UniqueRepresentation -from sage.categories.algebras import Algebras +from sage.categories.commutative_algebras import CommutativeAlgebras from sage.manifolds.coord_func import CoordFunction, MultiCoordFunction from sage.manifolds.utilities import (ExpressionNice, simplify_chain_real, simplify_chain_generic) @@ -67,8 +70,8 @@ class CoordFunctionSymb(CoordFunction): INPUT: - - ``chart`` -- :class:`~sage.manifolds.chart.Chart`; - the chart `(U, \varphi)` + - ``parent`` -- the algebra of coordinate functions on the chart + `(U, \varphi)` - ``expression`` -- a symbolic expression representing `f(x^1, \ldots, x^n)`, where `(x^1, \ldots, x^n)` are the coordinates of the chart `(U, \varphi)` @@ -1624,6 +1627,23 @@ def collect_common_factors(self): class CoordFunctionSymbRing(Parent, UniqueRepresentation): """ Ring of all symbolic coordinate functions on a chart. + + INPUT: + + - ``chart`` -- a coordinate chart, as an instance of class + :class:`~sage.manifolds.chart.Chart` + + EXAMPLES:: + + sage: M = Manifold(2, 'M', structure='topological') + sage: X. = M.chart() + sage: FR = X.function_ring(); FR + Ring of coordinate functions on Chart (M, (x, y)) + sage: type(FR) + + sage: FR.category() + Category of commutative algebras over Symbolic Ring + """ def __init__(self, chart): """ @@ -1637,7 +1657,7 @@ def __init__(self, chart): sage: TestSuite(FR).run() """ self._chart = chart - Parent.__init__(self, base=SR, category=Algebras(SR)) + Parent.__init__(self, base=SR, category=CommutativeAlgebras(SR)) def _repr_(self): """ @@ -1709,6 +1729,14 @@ def from_base_ring(self, r): - ``r`` -- an element of ``self.base_ring()`` EXAMPLES:: + + sage: M = Manifold(2, 'M', structure='topological') + sage: X. = M.chart() + sage: FR = X.function_ring() + sage: f = FR.from_base_ring(x*y) + sage: f.display() + (x, y) |--> x*y + """ return self.element_class(self, r) @@ -1721,12 +1749,14 @@ def is_integral_domain(self): sage: M = Manifold(2, 'M', structure='topological') sage: X. = M.chart() sage: FR = X.function_ring() + sage: FR.is_integral_domain() + False sage: FR.is_field() False """ return False - is_commutative = is_field = is_integral_domain + is_field = is_integral_domain Element = CoordFunctionSymb diff --git a/src/sage/manifolds/manifold.py b/src/sage/manifolds/manifold.py index 81c4e1baaf2..c5cbcc4ceac 100644 --- a/src/sage/manifolds/manifold.py +++ b/src/sage/manifolds/manifold.py @@ -349,7 +349,7 @@ are set, then the function returns a copy of the options dictionary. The ``options`` to manifolds can be accessed as the method - :obj:`TopologicalManifolds.global_options`. + :obj:`Manifold.global_options`. """, end_doc=r""" EXAMPLES:: diff --git a/src/sage/manifolds/point.py b/src/sage/manifolds/point.py index 8fdb6d4d576..29599425e41 100644 --- a/src/sage/manifolds/point.py +++ b/src/sage/manifolds/point.py @@ -14,9 +14,9 @@ REFERENCES: -- [Lee11]_ J.M. Lee : *Introduction to Topological Manifolds*, 2nd ed., +- [Lee11]_ \J.M. Lee : *Introduction to Topological Manifolds*, 2nd ed., Springer (New York) (2011) -- [Lee13]_ J.M. Lee : *Introduction to Smooth Manifolds*, 2nd ed., +- [Lee13]_ \J.M. Lee : *Introduction to Smooth Manifolds*, 2nd ed., Springer (New York, 2013) EXAMPLES: diff --git a/src/sage/manifolds/scalarfield.py b/src/sage/manifolds/scalarfield.py index a7845716f64..cb6737359d8 100644 --- a/src/sage/manifolds/scalarfield.py +++ b/src/sage/manifolds/scalarfield.py @@ -14,19 +14,21 @@ AUTHORS: - Eric Gourgoulhon, Michal Bejger (2013-2015): initial version +- Travis Scrimshaw (2016): review tweaks REFERENCES: -- [Lee11]_ : *Introduction to Topological Manifolds*, 2nd ed., Springer (New - York) (2011) -- [KN63]_ : *Foundations of Differential Geometry*, vol. 1, - Interscience Publishers (New York) (1963) +- [Lee11]_ \J.M. Lee : *Introduction to Topological Manifolds*, 2nd ed., + Springer (New York) (2011) +- [KN63]_ \S. Kobayashi & K. Nomizu : *Foundations of Differential Geometry*, + vol. 1, Interscience Publishers (New York) (1963) """ #****************************************************************************** # Copyright (C) 2015 Eric Gourgoulhon # Copyright (C) 2015 Michal Bejger +# Copyright (C) 2016 Travis Scrimshaw # # Distributed under the terms of the GNU General Public License (GPL) # as published by the Free Software Foundation; either version 2 of diff --git a/src/sage/manifolds/scalarfield_algebra.py b/src/sage/manifolds/scalarfield_algebra.py index 5231cbb8058..d0a8e1692df 100644 --- a/src/sage/manifolds/scalarfield_algebra.py +++ b/src/sage/manifolds/scalarfield_algebra.py @@ -11,19 +11,21 @@ AUTHORS: - Eric Gourgoulhon, Michal Bejger (2014-2015): initial version +- Travis Scrimshaw (2016): review tweaks REFERENCES: -- [Lee11]_ : *Introduction to Topological Manifolds*, 2nd ed., Springer (New - York) (2011) -- [KN63]_ : *Foundations of Differential Geometry*, vol. 1, - Interscience Publishers (New York) (1963) +- [Lee11]_ \J.M. Lee : *Introduction to Topological Manifolds*, 2nd ed., + Springer (New York) (2011) +- [KN63]_ \S. Kobayashi & K. Nomizu : *Foundations of Differential Geometry*, + vol. 1, Interscience Publishers (New York) (1963) """ #****************************************************************************** # Copyright (C) 2015 Eric Gourgoulhon # Copyright (C) 2015 Michal Bejger +# Copyright (C) 2016 Travis Scrimshaw # # Distributed under the terms of the GNU General Public License (GPL) # as published by the Free Software Foundation; either version 2 of diff --git a/src/sage/manifolds/utilities.py b/src/sage/manifolds/utilities.py index ed4b99cbe8d..59f4e754894 100644 --- a/src/sage/manifolds/utilities.py +++ b/src/sage/manifolds/utilities.py @@ -8,6 +8,7 @@ - Michal Bejger (2015) : class :class:`ExpressionNice` - Eric Gourgoulhon (2015) : simplification functions +- Travis Scrimshaw (2016): review tweaks """ @@ -15,6 +16,7 @@ # # Copyright (C) 2015 Michal Bejger # Copyright (C) 2015 Eric Gourgoulhon +# Copyright (C) 2016 Travis Scrimshaw # # Distributed under the terms of the GNU General Public License (GPL) # as published by the Free Software Foundation; either version 2 of