Skip to content
This repository has been archived by the owner on Jan 30, 2023. It is now read-only.

Commit

Permalink
Reviewer tweaks for #25457
Browse files Browse the repository at this point in the history
  • Loading branch information
@egourgoulhon
egourgoulhon committed Jun 18, 2018
1 parent 8ddc1b2 commit cae28a7
Show file tree
Hide file tree
Showing 2 changed files with 78 additions and 73 deletions.
12 changes: 7 additions & 5 deletions src/sage/manifolds/differentiable/manifold.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -3151,7 +3151,7 @@ def affine_connection(self, name, latex_name=None):
AffineConnection
return AffineConnection(self, name, latex_name)

def metric(self, name, signature=None, latex_name=None, dest_map=None, \
def metric(self, name, signature=None, latex_name=None, dest_map=None,
comp=None):
r"""
Define a pseudo-Riemannian metric on the manifold.
Expand All @@ -3177,6 +3177,8 @@ class :class:`~sage.manifolds.differentiable.diff_map.DiffMap`
representing the destination map `\Phi:\ U \rightarrow M`, where `U`
is the current manifold; if ``None``, the identity map is assumed
(case of a metric tensor field *on* `U`)
- ``comp`` -- (default: ``None``) components of the metric in the
manifold's default frame
OUTPUT:
Expand All @@ -3200,8 +3202,8 @@ class :class:`~sage.manifolds.differentiable.diff_map.DiffMap`
"""
vmodule = self.vector_field_module(dest_map)
return vmodule.metric(name, signature=signature, latex_name=latex_name,\
comp=comp)
return vmodule.metric(name, signature=signature, latex_name=latex_name,
comp=comp)

def riemannian_metric(self, name, latex_name=None, dest_map=None):
r"""
Expand Down Expand Up @@ -3346,8 +3348,8 @@ class :class:`~sage.manifolds.differentiable.diff_map.DiffMap`
index = 1
else:
signat = 2 - dim
index = dim -1
return vmodule.metric(name, signature=signat, latex_name=latex_name, \
index = dim - 1
return vmodule.metric(name, signature=signat, latex_name=latex_name,
comp=index)

def lorentz_metric(self, name, signature='positive', latex_name=None,
Expand Down
139 changes: 71 additions & 68 deletions src/sage/manifolds/differentiable/metric.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -10,6 +10,8 @@
- Eric Gourgoulhon, Michal Bejger (2013-2015) : initial version
- Pablo Angulo (2016): Schouten, Cotton and Cotton-York tensors
- Hans Fotsing Tetsing (2018): computation of metric signature and definition
of the components when declaring the metric
REFERENCES:
Expand All @@ -22,6 +24,7 @@
# Copyright (C) 2015 Eric Gourgoulhon <eric.gourgoulhon@obspm.fr>
# Copyright (C) 2015 Michal Bejger <bejger@camk.edu.pl>
# Copyright (C) 2016 Pablo Angulo <pang@cancamusa.net>
# Copyright (C) 2018 Hans Fotsing Tetsing <hans.fotsing@aims-cameroon.org>
#
# Distributed under the terms of the GNU General Public License (GPL)
# as published by the Free Software Foundation; either version 2 of
Expand All @@ -34,13 +37,7 @@
from sage.manifolds.differentiable.tensorfield import TensorField
from sage.manifolds.differentiable.tensorfield_paral import TensorFieldParal
from sage.matrix.matrix_space import MatrixSpace
from numpy import pi
from sage.symbolic.ring import SR
from sage.misc.latex import latex
from sage.symbolic.expression import Expression
from sage.tensor.modules.format_utilities import is_atomic, \
FormattedExpansion


class PseudoRiemannianMetric(TensorField):
r"""
Expand Down Expand Up @@ -1005,7 +1002,7 @@ def riemann(self, name=None, latex_name=None):
2-dimensional differentiable manifold S^2
sage: g.riemann()[:]
[[[[0, 0], [0, 0]], [[0, sin(th)^2], [-sin(th)^2, 0]]],
[[[0, (cos(th)^2 - 1)/sin(th)^2], [1, 0]], [[0, 0], [0, 0]]]]
[[[0, -1], [1, 0]], [[0, 0], [0, 0]]]]
In dimension 2, the Riemann tensor can be expressed entirely in terms of
the Ricci scalar `r`:
Expand Down Expand Up @@ -1901,31 +1898,31 @@ def hodge_star(self, pform):
resu.set_name(name=format_unop_txt('*', pform._name),
latex_name=format_unop_latex(r'\star ', pform._latex_name))
return resu


#******************************************************************************

def _diag(self, n, m, k):
r"""
Return a list of `n` lists of length `m` each such that the first list
contains ``self`` at position `k+1`, the second list contains ``self`` at
Return a list of `n` lists of length `m` each such that the first list
contains ``self`` at position `k+1`, the second list contains ``self`` at
position `k+2`, and so on. The other positions of each list contain `0`.
INPUT:
- ``self`` -- an element
- ``n`` -- a non-negative integer, the number of sublists
- ``m`` -- a non-negative integer, the length of each sublist
- ``k`` -- a positive integer, `k+1` is the position of ``self`` in the
first list
- ``k`` -- a positive integer, `k+1` is the position of ``self`` in the
first list
EXAMPLES:
EXAMPLES::
sage: from sage.manifolds.differentiable.metric import _diag
sage: _diag(-2, 2, 4, 1)
[[0, -2, 0, 0], [0, 0, -2, 0]]
"""
"""
liste1 = []
for i in range(n):
liste2 = []
Expand Down Expand Up @@ -1973,12 +1970,12 @@ class PseudoRiemannianMetricParal(PseudoRiemannianMetric, TensorFieldParal):
- ``name`` -- name given to the metric
- ``latex_name`` -- (default: ``None``) LaTeX symbol to denote the metric;
if ``None``, it is formed from ``name``
- ``comp`` -- (default: ``None``) either the list of the lignes of the \
corresponding matrix of the metric in the default chart of the domain, \
or a non-negative integer `q` less than or egual to the dimension of the \
ambiant manifold and representing the index of the metric. In this last \
case, the standard pseudo-Euclidean metric of index `q` will be \
constructed. If ``None`` is given, the standard Euclidean metric will \
- ``comp`` -- (default: ``None``) either the list of the lines of the
corresponding matrix of the metric in the default chart of the domain,
or a non-negative integer `q` less than or egual to the dimension of the
ambiant manifold and representing the index of the metric. In this last
case, the standard pseudo-Euclidean metric of index `q` will be
constructed. If ``None`` is given, the standard Euclidean metric will
be constructed.
EXAMPLES:
Expand Down Expand Up @@ -2085,8 +2082,8 @@ def __init__(self, vector_field_module, name, latex_name=None, comp=None):
if index < 0:
index = -1*index
if index > ndim:
raise ValueError("The index must be less than the size of the \
metric")
raise ValueError("the index must be less than the size of "
+ "the metric")
liste = _diag(-1, index, ndim, 0)
liste.extend(_diag(1, ndim-index, ndim, index))
else:
Expand All @@ -2095,18 +2092,19 @@ def __init__(self, vector_field_module, name, latex_name=None, comp=None):
for elt in list(comp):
liste.append(list(elt))
if len(elt) != ndim:
raise ValueError("The metric must be squared")
raise ValueError("the metric must be squared")
for i in range(ndim):
for j in range(ndim):
if liste[i][j] != liste[j][i]:
raise ValueError("The metric must be squared")
raise ValueError("the metric must be squared")
except TypeError:
try:
for (j, elt) in enumerate(comp):
liste.extend(_diag(elt, 1, ndim, j))
except TypeError:
raise TypeError("The second argument must be an integer \
or an iterable or an iterable of iterables")
raise TypeError("the second argument must be an integer "
+ "or an iterable or an iterable of "
+ "iterables")
frame = chart.frame()
for i in range(ndim):
for j in range(ndim):
Expand Down Expand Up @@ -2134,7 +2132,7 @@ def _repr_(self):
'Lorentzian metric g on the 3-dimensional differentiable manifold M'
sage: g = M.metric('g', comp=[[-1,0,0],[0,-1,0],[0,0,-1]]);
sage: g._repr_()
'Pseudo-Riemannian metric g on the 3-dimensional differentiable manifold
'Pseudo-Riemannian metric g on the 3-dimensional differentiable manifold
M'
sage: g = M.metric('g', comp=[[0,0,0],[0,0,0],[0,0,0]]);
sage: g._repr_()
Expand All @@ -2152,7 +2150,7 @@ def _repr_(self):
description = "Pseudo-Riemannian metric "
description += self._name + " "
return self._final_repr(description)

def _new_instance(self):
r"""
Create an instance of the same class as ``self`` with the same.
Expand All @@ -2178,13 +2176,13 @@ def _new_instance(self):

def list_of_lines(self, chart=None):
r"""
Return the list of lines of the metric in a given chart, each line \
Return the list of lines of the metric in a given chart, each line
being given as a list.
INPUT:
- ``chart`` -- (default: ``None``) a chart on the manifold; if \
``None``, the default chart on the domain will be used.
- ``chart`` -- (default: ``None``) a chart on the manifold; if
``None``, the default chart on the domain will be used.
EXAMPLES:
Expand All @@ -2204,7 +2202,7 @@ def list_of_lines(self, chart=None):
sage: g = M.metric('g', comp=[[0,0,0],[0,0,0],[0,0,0]])
sage: g.list_of_lines()
[[0, 0, 0], [0, 0, 0], [0, 0, 0]]
"""
if chart == None:
chart = self.domain().default_chart()
Expand All @@ -2219,14 +2217,14 @@ def list_of_lines(self, chart=None):

def matrix(self, chart=None):
r"""
Return the correnponding matrix of the metric in the given chart. The \
difference with ``g[:]`` is that the components of the matrix retuned \
here are instances of Symbolic Ring and not chart functions.
Return the correnponding matrix of the metric in the given chart. The
difference with ``g[:]`` is that the components of the matrix retuned
here are instances of Symbolic Ring and not chart functions.
INPUT:
- ``chart`` -- (default: ``None``) a chart on the domain. if ``None``, \
the default chart on the domain will be used.
- ``chart`` -- (default: ``None``) a chart on the domain; if ``None``,
the default chart on the domain will be used
EXAMPLES:
Expand Down Expand Up @@ -2254,7 +2252,7 @@ def matrix(self, chart=None):
[0 0 0]
[0 0 0]
[0 0 0]
"""
mat0 = self.list_of_lines(chart)
mat1 = []
Expand All @@ -2263,19 +2261,20 @@ def matrix(self, chart=None):
for elt in L:
mat2.append(elt.expr())
mat1.append(mat2)
mat1 = MatrixSpace(SR, self._ambient_domain.dimension(), self._ambient_domain.dimension())(mat1)
return mat1
mat1 = MatrixSpace(SR, self._ambient_domain.dimension(),
self._ambient_domain.dimension())(mat1)
return mat1

def sign(self):
r"""
This method works well only when the index of the metric is constant.
OUTPUT:
- ``[n_-, n_+, n_0]`` -- being ``n_-`` (resp. ``n_+``, n_0``) the \
number of negative terms (resp. positive terms, null terms) in any \
diagonal writing of the metric components
- ``[n_-, n_+, n_0]`` -- being ``n_-`` (resp. ``n_+``, n_0``) the
number of negative terms (resp. positive terms, null terms) in any
diagonal writing of the metric components
EXAMPLES:
Expand All @@ -2297,7 +2296,7 @@ def sign(self):
[0, 0, 3]
"""
mat = self.matrix().jordan_form()
index, sign, sing = 0, 0, 0
index, sign, sing = 0, 0, 0
for i in range(self.domain().dimension()):
if mat[i, i].is_zero():
sing += 1
Expand All @@ -2306,16 +2305,18 @@ def sign(self):
else:
sign += 1
return [index, sign, sing]

def index(self):
r"""
Return the index of the metric. This method works well only when the \
index of the metric is constant.
Return the index of the metric, i.e. the number of negative terms in
any diagonal writing of the metric components.
This method works well only when the index of the metric is constant.
OUTPUT:
- ``index`` -- the number of negative terms in any diagonal writing of \
the metric components
- ``index`` -- the number of negative terms in any diagonal writing of
the metric components
EXAMPLES:
Expand All @@ -2335,23 +2336,24 @@ def index(self):
sage: g = M.metric('g', comp=[[0,0,0],[0,0,0],[0,0,0]])
sage: g.index()
0
"""
return self.sign()[0]

def signature(self):
r"""
This method works well only when the index of the metric is constant.
OUTPUT:
- `n_+-n_-` -- being `n_+` the number of positive terms and `n_-` the \
number of negative terms in any diagonal writing of the metric components
- `n_+-n_-` -- being `n_+` the number of positive terms and `n_-` the
number of negative terms in any diagonal writing of the metric
components
EXAMPLES:
Index on a 3-dimensional manifold::
Signature on a 3-dimensional manifold::
sage: M = Manifold(3, 'M')
sage: X.<t,x,y> = M.chart()
Expand All @@ -2367,19 +2369,21 @@ def signature(self):
sage: g = M.metric('g', comp=[[0,0,0],[0,0,0],[0,0,0]])
sage: g.signature()
0
"""
return self.sign()[1]-self.sign()[0]

def kernel_dimension(self):
r"""
Return the dimension of the kernel of the metric. This method works \
well only when the dimension of the kernel is constant.
Return the dimension of the kernel of the metric.
This method works well only when the dimension of the kernel is
constant.
OUTPUT:
- the number of null terms in any diagonal writing of the
metric components
- the number of null terms in any diagonal writing of the metric
components
EXAMPLES:
Expand All @@ -2399,10 +2403,9 @@ def kernel_dimension(self):
sage: g = M.metric('g', comp=[[0,0,0],[0,0,0],[0,0,0]])
sage: g.kernel_dimension()
3
"""
return self.sign()[2]


def _init_derived(self):
r"""
Expand Down

0 comments on commit cae28a7

Please sign in to comment.