]> https://gitweb.dealii.org/ - dealii.git/log
dealii.git
8 years agofix test output 3185/head
Timo Heister [Tue, 4 Oct 2016 14:17:30 +0000 (10:17 -0400)]
fix test output

8 years agoindent
Timo Heister [Tue, 4 Oct 2016 14:17:15 +0000 (10:17 -0400)]
indent

8 years agochangelog entry
Timo Heister [Tue, 4 Oct 2016 14:09:26 +0000 (10:09 -0400)]
changelog entry

8 years agofix colorized hyper_cube_slit
Timo Heister [Tue, 4 Oct 2016 14:08:16 +0000 (10:08 -0400)]
fix colorized hyper_cube_slit

GridGenerator::hyper_cube_slit() was setting the wrong boundary ids when
colorize was set to true.

8 years agoMerge pull request #3173 from bangerth/updates-to-the-P1NC-element
Timo Heister [Tue, 4 Oct 2016 13:12:30 +0000 (09:12 -0400)]
Merge pull request #3173 from bangerth/updates-to-the-P1NC-element

Update the P1NC element implementation.

8 years agoUpdate the P1NC element implementation. 3173/head
Wolfgang Bangerth [Fri, 30 Sep 2016 22:25:44 +0000 (16:25 -0600)]
Update the P1NC element implementation.

Specifically, this updates the class documentation for language
and clarity. It also tightens up the code in a number of places.

8 years agoMerge pull request #3182 from bangerth/fix-tests
Timo Heister [Mon, 3 Oct 2016 21:43:42 +0000 (17:43 -0400)]
Merge pull request #3182 from bangerth/fix-tests

Correct ParameterHandler test outputs.

8 years agoCorrect test outputs. 3182/head
Wolfgang Bangerth [Mon, 3 Oct 2016 21:41:14 +0000 (15:41 -0600)]
Correct test outputs.

On my desktop, I have not installed numdiff yet, and these tests fail because
there are either differences in whitespace, or there is a trailing colon on
a line. Neither seem to bother numdiff, but they bother regular diff. Fix this
by checking in corrected versions of these output files.

8 years agoMerge pull request #3177 from bangerth/doc-update
David Wells [Mon, 3 Oct 2016 16:59:19 +0000 (12:59 -0400)]
Merge pull request #3177 from bangerth/doc-update

Fix formatting of doc text.

8 years agoMerge pull request #3178 from masterleinad/fix_style
Wolfgang Bangerth [Mon, 3 Oct 2016 16:28:15 +0000 (10:28 -0600)]
Merge pull request #3178 from masterleinad/fix_style

Fixup all the other ':: '

8 years agoMerge pull request #2753 from masterleinad/martin_extrapolate
Daniel Arndt [Mon, 3 Oct 2016 16:22:53 +0000 (18:22 +0200)]
Merge pull request #2753 from masterleinad/martin_extrapolate

FETools::extrapolate rebased

8 years agoFix related tests 2753/head
Daniel Arndt [Mon, 3 Oct 2016 13:21:35 +0000 (15:21 +0200)]
Fix related tests

8 years agoHide parallel implementation and use guards for vtk test output
Daniel Arndt [Wed, 28 Sep 2016 16:29:44 +0000 (18:29 +0200)]
Hide parallel implementation and use guards for vtk test output

8 years agoMake sure to receive messages from the correct round
Daniel Arndt [Tue, 27 Sep 2016 16:39:08 +0000 (18:39 +0200)]
Make sure to receive messages from the correct round

8 years agoAdd dealii comment blob and split extrapolate into an own file
Daniel Arndt [Tue, 27 Sep 2016 15:33:34 +0000 (17:33 +0200)]
Add dealii comment blob and split extrapolate into an own file

8 years agoEntry to changes.h
Daniel Arndt [Sat, 3 Sep 2016 09:02:43 +0000 (11:02 +0200)]
Entry to changes.h

8 years agoFix doxygen documentation
Daniel Arndt [Sat, 3 Sep 2016 08:56:03 +0000 (10:56 +0200)]
Fix doxygen documentation

8 years agoguard implementation by check for p4est
Daniel Arndt [Fri, 2 Sep 2016 21:35:21 +0000 (23:35 +0200)]
guard implementation by check for p4est

8 years agoMake C++03 conforming
Daniel Arndt [Fri, 2 Sep 2016 15:36:13 +0000 (17:36 +0200)]
Make C++03 conforming

8 years agoAdd tests
Daniel Arndt [Fri, 2 Sep 2016 21:18:39 +0000 (23:18 +0200)]
Add tests

8 years agoFix implementation
Daniel Arndt [Fri, 2 Sep 2016 21:17:14 +0000 (23:17 +0200)]
Fix implementation

8 years agoRestructure fe_tools_interpolate.cc
Daniel Arndt [Fri, 2 Sep 2016 21:11:08 +0000 (23:11 +0200)]
Restructure fe_tools_interpolate.cc

8 years agomove p4est wrappers
Daniel Arndt [Fri, 2 Sep 2016 21:09:14 +0000 (23:09 +0200)]
move p4est wrappers

8 years agoFix some includes for rebasing
Daniel Arndt [Wed, 6 Jul 2016 16:13:21 +0000 (18:13 +0200)]
Fix some includes for rebasing

8 years agoFETools::extrapolate: add forward declaration
msteigemann [Thu, 18 Jun 2015 18:15:21 +0000 (20:15 +0200)]
FETools::extrapolate: add forward declaration

8 years agoFETools::extrapolate: Working on the extrapolate algorithm on distributed parallel...
msteigemann [Mon, 15 Jun 2015 13:59:08 +0000 (15:59 +0200)]
FETools::extrapolate: Working on the extrapolate algorithm on distributed parallel grids

8 years agoFixup all the other ':: ' 3178/head
Daniel Arndt [Mon, 3 Oct 2016 16:07:59 +0000 (18:07 +0200)]
Fixup all the other ':: '

8 years agoFix formatting of doc text. 3177/head
Wolfgang Bangerth [Mon, 3 Oct 2016 16:02:15 +0000 (10:02 -0600)]
Fix formatting of doc text.

8 years agoMerge pull request #3176 from bangerth/fix-style-issue
Bruno Turcksin [Mon, 3 Oct 2016 15:55:30 +0000 (11:55 -0400)]
Merge pull request #3176 from bangerth/fix-style-issue

Eliminate an unnecessary space.

8 years agoEliminate an unnecessary space. 3176/head
Wolfgang Bangerth [Mon, 3 Oct 2016 15:42:42 +0000 (09:42 -0600)]
Eliminate an unnecessary space.

8 years agoMerge pull request #3172 from bangerth/doc-update
Bruno Turcksin [Mon, 3 Oct 2016 13:07:29 +0000 (09:07 -0400)]
Merge pull request #3172 from bangerth/doc-update

Update the description of ConstraintMatrix::print().

8 years agoMerge pull request #3155 from Rombur/trapezoid
Bruno Turcksin [Mon, 3 Oct 2016 13:06:07 +0000 (09:06 -0400)]
Merge pull request #3155 from Rombur/trapezoid

Add GridGenerator for a general quadrilateral/general hexahedron.

8 years agoAdd GridGenerator for a general cell. 3155/head
Bruno Turcksin [Thu, 22 Sep 2016 21:39:05 +0000 (17:39 -0400)]
Add GridGenerator for a general cell.

8 years agoMerge pull request #3170 from kronbichler/documentation_fe_evaluation
Bruno Turcksin [Mon, 3 Oct 2016 12:22:59 +0000 (08:22 -0400)]
Merge pull request #3170 from kronbichler/documentation_fe_evaluation

Augment documentation

8 years agoMerge pull request #3174 from JaeryunYim/master
Wolfgang Bangerth [Sun, 2 Oct 2016 23:40:36 +0000 (17:40 -0600)]
Merge pull request #3174 from JaeryunYim/master

Add a description of the addition of FE_P1NC

8 years agoMerge pull request #3119 from kronbichler/master
Timo Heister [Sun, 2 Oct 2016 21:12:01 +0000 (17:12 -0400)]
Merge pull request #3119 from kronbichler/master

Restrict the complete defect at once to the coarse level.

8 years agoMerge pull request #3175 from luca-heltai/manifold-fix-2
Martin Kronbichler [Sun, 2 Oct 2016 17:42:38 +0000 (19:42 +0200)]
Merge pull request #3175 from luca-heltai/manifold-fix-2

Fix #3165

8 years agoAdd a description of the addition of the class FE_P1NC. 3174/head
Jaeryun Yim [Sun, 2 Oct 2016 17:05:30 +0000 (02:05 +0900)]
Add a description of the addition of the class FE_P1NC.

8 years agoFixed bug in SphericalManifold for 3D case. 3175/head
Luca Heltai [Sat, 1 Oct 2016 16:42:30 +0000 (18:42 +0200)]
Fixed bug in SphericalManifold for 3D case.

When R>>1 and C != Point<spacedim>(), SphericalManifold
computed directions by subtracting the center twice.

8 years agoMerge pull request #3171 from bangerth/reimplement-2d-grid-orientation-fixes
Timo Heister [Sat, 1 Oct 2016 20:32:42 +0000 (16:32 -0400)]
Merge pull request #3171 from bangerth/reimplement-2d-grid-orientation-fixes

Apply the fixes requested by @tjhei in #3166.

8 years agoAugment documentation of FEEvaluation 3170/head
Martin Kronbichler [Fri, 30 Sep 2016 14:56:35 +0000 (16:56 +0200)]
Augment documentation of FEEvaluation

8 years agoMerge pull request #2851 from JaeryunYim/master
Wolfgang Bangerth [Fri, 30 Sep 2016 21:42:40 +0000 (15:42 -0600)]
Merge pull request #2851 from JaeryunYim/master

P1 nonconforming finite element on quads : FE_P1NC

8 years agoMerge pull request #3115 from davydden/feature/fe_enriched
Wolfgang Bangerth [Fri, 30 Sep 2016 21:12:26 +0000 (15:12 -0600)]
Merge pull request #3115 from davydden/feature/fe_enriched

FE_Enriched

8 years agoMerge pull request #3122 from drwells/parameterhandler-exceptions
Wolfgang Bangerth [Fri, 30 Sep 2016 21:11:01 +0000 (15:11 -0600)]
Merge pull request #3122 from drwells/parameterhandler-exceptions

Parameterhandler exceptions

8 years agoUpdate the description of ConstraintMatrix::print(). 3172/head
Wolfgang Bangerth [Fri, 30 Sep 2016 19:08:37 +0000 (13:08 -0600)]
Update the description of ConstraintMatrix::print().

8 years agoMerge pull request #3168 from masterleinad/remove_manifold_warning
David Wells [Fri, 30 Sep 2016 18:16:29 +0000 (14:16 -0400)]
Merge pull request #3168 from masterleinad/remove_manifold_warning

Remove warning about hidden function

8 years agoApply the fixes requested by @tjhei in #3166. 3171/head
Wolfgang Bangerth [Fri, 30 Sep 2016 18:11:37 +0000 (13:11 -0500)]
Apply the fixes requested by @tjhei in #3166.

8 years agoMerge pull request #3166 from bangerth/reimplement-2d-grid-reorientation
Daniel Arndt [Fri, 30 Sep 2016 17:29:41 +0000 (19:29 +0200)]
Merge pull request #3166 from bangerth/reimplement-2d-grid-reorientation

Reimplement 2d grid reorientation

8 years agoMerge pull request #3169 from kronbichler/fix_trilinos_vector_mpi
Daniel Arndt [Fri, 30 Sep 2016 17:28:26 +0000 (19:28 +0200)]
Merge pull request #3169 from kronbichler/fix_trilinos_vector_mpi

Make compile without MPI

8 years agoMake compile without MPI 3169/head
Martin Kronbichler [Fri, 30 Sep 2016 14:55:29 +0000 (16:55 +0200)]
Make compile without MPI

8 years agoRemove warning about hidden function 3168/head
Daniel Arndt [Fri, 30 Sep 2016 14:16:27 +0000 (16:16 +0200)]
Remove warning about hidden function

8 years agoremove an empty line 2851/head
Jaeryun Yim [Fri, 30 Sep 2016 13:37:00 +0000 (22:37 +0900)]
remove an empty line

8 years agoMinor edits on the description.
Jaeryun Yim [Fri, 30 Sep 2016 13:28:58 +0000 (22:28 +0900)]
Minor edits on the description.

8 years agoEdit indents.
Jaeryun Yim [Fri, 30 Sep 2016 12:45:55 +0000 (21:45 +0900)]
Edit indents.

8 years agoEdit the functions related with face & subface data.
Jaeryun Yim [Fri, 30 Sep 2016 12:42:49 +0000 (21:42 +0900)]
Edit the functions related with face & subface data.
- Add get_face_data(), get_subface_data()
- Fix fill_fe_face_values(), fill_fe_subface_values()

8 years agoEdits for the Hessian.
Jaeryun Yim [Fri, 30 Sep 2016 10:19:18 +0000 (19:19 +0900)]
Edits for the Hessian.

8 years agoMerge pull request #3167 from bangerth/fix-typo
Martin Kronbichler [Fri, 30 Sep 2016 08:31:01 +0000 (10:31 +0200)]
Merge pull request #3167 from bangerth/fix-typo

Fix a typo.

8 years agoEdit the codes for the tests.
Jaeryun Yim [Fri, 30 Sep 2016 07:21:09 +0000 (16:21 +0900)]
Edit the codes for the tests.
- remove the macros: '#define PRECISION'
- edit spacings

8 years agoFix a typo. 3167/head
Wolfgang Bangerth [Thu, 29 Sep 2016 22:16:16 +0000 (17:16 -0500)]
Fix a typo.

8 years agoEdit indents.
Jaeryun Yim [Fri, 30 Sep 2016 02:27:19 +0000 (11:27 +0900)]
Edit indents.

8 years agoMake the algorithm backward compatible by replicating a previous (harmless) bug. 3166/head
Wolfgang Bangerth [Thu, 29 Sep 2016 17:35:17 +0000 (12:35 -0500)]
Make the algorithm backward compatible by replicating a previous (harmless) bug.

8 years agoReimplement the 2d implementation of edge orientation.
Wolfgang Bangerth [Wed, 1 Jul 2015 16:09:26 +0000 (11:09 -0500)]
Reimplement the 2d implementation of edge orientation.

The old implementation, written in 2003 by Mike Anderson, is quite concise
and of high quality. But it is not extensively documented, and is
unnecessarily hard to read because it uses different conventions for names
etc than we use in the rest of the library.

This reimplementation uses standard conventions, and it uses the language and
symbols of a paper about to be submitted that concisely describes the algorithms
and data structures used in this algorithm. As an additional benefit,
it uses the standard vertex ordering of cells rather than the
old-style ordering used in the existing algorithm.

Following the algorithm without understanding the graph theoretical context
of the problem may be difficult, but because it uses the same symbols as in
the paper, should be easy enough if you have the paper.

8 years agoRemove the spaces before semicolons.
Jaeryun Yim [Thu, 29 Sep 2016 17:11:07 +0000 (02:11 +0900)]
Remove the spaces before semicolons.

8 years agoEdits.
Jaeryun Yim [Thu, 29 Sep 2016 16:58:35 +0000 (01:58 +0900)]
Edits.

- remove FE_P1NC::get_nonzero_component().
- declare class InternalData.
- compute Hessians in get_data().

8 years agoMake read_input print error messages again. 3122/head
David Wells [Fri, 23 Sep 2016 22:26:11 +0000 (18:26 -0400)]
Make read_input print error messages again.

This commit partially restores the old behavior of read_input: this
function now prints out the exception message and returns
false. Previously this function printed all parsing error messages.

Some tests expected (see 79e0a380fb) read_input to raise a specific
exception message: those were fixed by calling parse_input instead.

8 years agoRemove the parts for a graphical issue already resolved.
Jaeryun Yim [Wed, 28 Sep 2016 16:22:39 +0000 (01:22 +0900)]
Remove the parts for a graphical issue already resolved.

8 years agoUse parse_input, not read_input, in tutorials.
David Wells [Sat, 17 Sep 2016 17:21:02 +0000 (13:21 -0400)]
Use parse_input, not read_input, in tutorials.

read_input is now deprecated in favor of parse_input, which raises
exceptions.

8 years agoMention ParameterHandler exceptions in changes.h.
David Wells [Fri, 16 Sep 2016 00:02:29 +0000 (20:02 -0400)]
Mention ParameterHandler exceptions in changes.h.

The last few commits change the behavior in an incompatible way by
raising exceptions on invalid input instead of using a return code.

8 years agoClarify error handling with PathSearch/read_input.
David Wells [Fri, 16 Sep 2016 00:02:23 +0000 (20:02 -0400)]
Clarify error handling with PathSearch/read_input.

This commit keeps the same control flow if one tries to use this
function to write out default values to a file but gets rid of the
std::cerr messages (like the recent changes to read_input).

8 years agoUse exceptions in ParameterHandler::read_input.
David Wells [Thu, 15 Sep 2016 23:12:03 +0000 (19:12 -0400)]
Use exceptions in ParameterHandler::read_input.

8 years agoUse exceptions when reading XML parameter files.
David Wells [Thu, 15 Sep 2016 23:05:33 +0000 (19:05 -0400)]
Use exceptions when reading XML parameter files.

8 years agoFix two XML files.
David Wells [Thu, 15 Sep 2016 23:45:57 +0000 (19:45 -0400)]
Fix two XML files.

8 years agoFix tests to not use absolute paths.
David Wells [Sat, 24 Sep 2016 13:15:18 +0000 (09:15 -0400)]
Fix tests to not use absolute paths.

8 years agoUse exceptions in ParameterHandler::scan_line.
David Wells [Thu, 15 Sep 2016 12:19:47 +0000 (08:19 -0400)]
Use exceptions in ParameterHandler::scan_line.

This commit overhauls the private function ParameterHandler::scan_line
to no longer use a boolean error code to mark failure; instead the
function will raise one of four new exceptions to precisely indicate
what went wrong.

This change broke a large number of ParameterHandler tests that handled
parsing failures: I modified those to print the exception messages to
deallog.

8 years agoadd FE_Enriched finite element 3115/head
Denis Davydov [Wed, 28 Sep 2016 09:52:07 +0000 (11:52 +0200)]
add FE_Enriched finite element

8 years agoMerge pull request #3163 from bangerth/parallelize-compute_number_cache-3
Daniel Arndt [Wed, 28 Sep 2016 13:19:31 +0000 (15:19 +0200)]
Merge pull request #3163 from bangerth/parallelize-compute_number_cache-3

In compute_number_cache(), only compute n_levels if necessary.

8 years agoIn compute_number_cache(), only compute n_levels if necessary. 3163/head
Wolfgang Bangerth [Tue, 27 Sep 2016 18:42:58 +0000 (13:42 -0500)]
In compute_number_cache(), only compute n_levels if necessary.

Also, only populate the number_cache.n_(lines|quads|hexes)_level arrays if they are
actually used.

8 years agoMerge pull request #3162 from bangerth/parallelize-compute_number_cache-2
Wolfgang Bangerth [Wed, 28 Sep 2016 12:14:52 +0000 (06:14 -0600)]
Merge pull request #3162 from bangerth/parallelize-compute_number_cache-2

Merge two loops in a number of related places.

8 years agoAdd changelog 3119/head
Martin Kronbichler [Fri, 16 Sep 2016 10:56:46 +0000 (12:56 +0200)]
Add changelog

8 years agoWork on comments. Fix and test W and F cycles.
Martin Kronbichler [Fri, 16 Sep 2016 10:09:50 +0000 (12:09 +0200)]
Work on comments. Fix and test W and F cycles.

8 years agoRestrict the complete defect at once to the coarse level.
Martin Kronbichler [Thu, 15 Sep 2016 12:54:40 +0000 (14:54 +0200)]
Restrict the complete defect at once to the coarse level.

8 years agoMerge two loops in a number of related places. 3162/head
Wolfgang Bangerth [Tue, 27 Sep 2016 04:57:41 +0000 (23:57 -0500)]
Merge two loops in a number of related places.

8 years agoMerge pull request #3161 from bangerth/doc-update-47
David Wells [Wed, 28 Sep 2016 00:15:35 +0000 (20:15 -0400)]
Merge pull request #3161 from bangerth/doc-update-47

Convert a comment from old-style vertex numbering to the way we currently do it.

8 years agoMerge pull request #3159 from bangerth/parallelize-compute_number_cache
David Wells [Wed, 28 Sep 2016 00:13:13 +0000 (20:13 -0400)]
Merge pull request #3159 from bangerth/parallelize-compute_number_cache

Parallelize the operation of compute_number_cache().

8 years agoConvert a comment from old-style vertex numbering to the way we currently do it. 3161/head
Wolfgang Bangerth [Tue, 27 Sep 2016 23:32:27 +0000 (18:32 -0500)]
Convert a comment from old-style vertex numbering to the way we currently do it.

The comment dates back to a time when we numbered vertices in quadrilaterals in counter-clockwise
sense. Fix this. While there, also re-wrap the comments.

8 years agoNumber continuation lines with their first line.
David Wells [Thu, 15 Sep 2016 12:16:32 +0000 (08:16 -0400)]
Number continuation lines with their first line.

Since a continuation line in a parameter file consists of several lines
concatenated by trailing '\'s, use the first line number when printing
error messages to make things a bit clearer.

8 years agoChange: get_linear_shape -> get_linear_shape_coefficients.
Jaeryun Yim [Tue, 27 Sep 2016 17:16:46 +0000 (02:16 +0900)]
Change: get_linear_shape -> get_linear_shape_coefficients.

8 years agoAdd changelog entry. 3159/head
Wolfgang Bangerth [Tue, 27 Sep 2016 14:32:25 +0000 (09:32 -0500)]
Add changelog entry.

8 years agoEdit comments for the description.
Jaeryun Yim [Tue, 27 Sep 2016 13:44:04 +0000 (22:44 +0900)]
Edit comments for the description.

8 years agoMerge pull request #3148 from luca-heltai/fix-spherical-manifold
Martin Kronbichler [Tue, 27 Sep 2016 07:53:02 +0000 (09:53 +0200)]
Merge pull request #3148 from luca-heltai/fix-spherical-manifold

Implemented Praveen fix.

8 years agoMerge pull request #3158 from bangerth/cleanup-changelog
Martin Kronbichler [Tue, 27 Sep 2016 07:50:54 +0000 (09:50 +0200)]
Merge pull request #3158 from bangerth/cleanup-changelog

Re-sort the changelog.

8 years agoParallelize the operation of compute_number_cache().
Wolfgang Bangerth [Mon, 26 Sep 2016 21:49:55 +0000 (16:49 -0500)]
Parallelize the operation of compute_number_cache().

For these functions, the 3d version calls the 2d version which itself calls the
1d version. These operations can all run concurrently. All three include two
loops each over all cells/quads/lines, so there should be plenty to do to
amortize parallel execution.

The only tricky part is that the quad and hex functions accessed a variable
that was first set by the 1d function (number_cache.n_lines). This may now
no longer be available in time for the 2d/3d functions, and so they
need to compute this information themselves. This is cheap, fortunately.

8 years agoMerge pull request #3157 from bangerth/doc-update-46
David Wells [Mon, 26 Sep 2016 20:54:09 +0000 (16:54 -0400)]
Merge pull request #3157 from bangerth/doc-update-46

Update some comments for Triangulation::compute_number_cache().

8 years agoMove some changes from 'general changes' to 'specific improvements'. 3158/head
Wolfgang Bangerth [Mon, 26 Sep 2016 20:38:33 +0000 (14:38 -0600)]
Move some changes from 'general changes' to 'specific improvements'.

8 years agoMove some changes from 'incompatible changes' to 'specific improvements'.
Wolfgang Bangerth [Mon, 26 Sep 2016 20:30:24 +0000 (14:30 -0600)]
Move some changes from 'incompatible changes' to 'specific improvements'.

8 years agoClarify comments for compute_number_cache(). 3157/head
Wolfgang Bangerth [Mon, 26 Sep 2016 19:40:51 +0000 (14:40 -0500)]
Clarify comments for compute_number_cache().

8 years agoReindent comments.
Wolfgang Bangerth [Mon, 26 Sep 2016 19:38:48 +0000 (14:38 -0500)]
Reindent comments.

8 years agoMerge pull request #3156 from bangerth/fix-typo
David Wells [Sat, 24 Sep 2016 04:03:54 +0000 (00:03 -0400)]
Merge pull request #3156 from bangerth/fix-typo

Fix a typo.

8 years agoFix a typo. 3156/head
Wolfgang Bangerth [Fri, 23 Sep 2016 22:44:00 +0000 (16:44 -0600)]
Fix a typo.

8 years agoMerge pull request #3152 from bangerth/doc-update-77
Daniel Arndt [Fri, 23 Sep 2016 15:23:00 +0000 (17:23 +0200)]
Merge pull request #3152 from bangerth/doc-update-77

Use latex formulas to describe tensor invariants.


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