sage.tensor: Canonicalize sym, antisym

[mkoeppe]

for #30229.

The new static method CompWithSym._canonicalize_sym_antisym brings sym and antisym into a canonical form as sorted tuples of sorted tuples, with trivial symmetries and antisymmetries dropped.

Using it also removes some code duplication.

CC: @egourgoulhon

Component: linear algebra

Author: Matthias Koeppe

Branch/Commit: 66009e7

Reviewer: Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/34451

[mkoeppe]

Author: Matthias Koeppe

[mkoeppe]

Branch: u/mkoeppe/sage_tensor__canonicalize_sym__antisym

[mkoeppe]

New commits:

3a65d2d	CompWithSym._canonicalize_sym_antisym: Factor out from __init__
07ab991	src/sage/tensor: Allow _sym, _antisym attributes to be tuples
3619b4c	src/sage/tensor, src/sage/manifolds: Sort _sym, _antisym, store as tuples of tuples
970c6c8	src/sage/tensor, src/sage/manifolds: Sort _sym, _antisym, store as tuples of tuples (fixup)
9f15e00	src/sage/tensor: Allow _sym, _antisym attributes to be tuples (fixup)

[mkoeppe]

Commit: 9f15e00

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1 +1,6 @@
-for #30229
+for #30229.
+
+The new static method `CompWithSym._canonicalize_sym_antisym` brings `sym` and `antisym` into a canonical form as sorted tuples of sorted tuples, with trivial symmetries and antisymmetries dropped.
+
+Using it also removes some code duplication.
+

[egourgoulhon]

comment:4

Thanks for introducing this and removing the code duplication!

It would useful to add INPUT and OUTPUT fields in the docstring of _canonicalize_sym_antisym.
Besides, I don't understand this change:

-                if len(isym) < 2:
-                    raise IndexError("at least two index positions must be " +
-                                     "provided to define a symmetry")
+                if len(isym) < 2:
+                    # Drop trivial symmetry
+                    continue

Shouldn't an error be raised if the input pretends to define a symmetry/antisymmetry with less than 2 index positions?

[mkoeppe]

comment:5

In this version of this code:

diff --git a/src/sage/tensor/modules/free_module_tensor.py b/src/sage/tensor/modules/free_module_tensor.py
index bbcc1ec..4d6d05c 100644
--- a/src/sage/tensor/modules/free_module_tensor.py
+++ b/src/sage/tensor/modules/free_module_tensor.py
@@ -309,41 +309,8 @@ class FreeModuleTensor(ModuleElementWithMutability):
                               # bases, with the bases as keys (initially empty)
 
         # Treatment of symmetry declarations:
-        self._sym = []
-        if sym is not None and sym != []:
-            if isinstance(sym[0], (int, Integer)):
-                # a single symmetry is provided as a tuple -> 1-item list:
-                sym = [tuple(sym)]
-            for isym in sym:
-                if len(isym) > 1:
-                    for i in isym:

... the trivial symmetries were dropped silently.

I suppose I can add a parameter trivial_symmetries='error' for the cases where you'd like to see the errors.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

d1a92e5	Merge tag '9.7.rc0' into t/34451/sage_tensor__canonicalize_sym__antisym
319ecfa	FiniteRankFreeModule.tensor: Use CompWithSym._canonicalize_sym_antisym
8e93626	CompWithSym._canonicalize_sym_antisym: Add documentation
564be35	FiniteRankFreeModule.tensor: Restore error when trivial symmetries are passed
ffea896	CompWithSym._canonicalize_sym_antisym: Code optimization

[sagetrac-git]

Changed commit from 9f15e00 to ffea896

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

fed09d5

CompWithSym._canonicalize_sym_antisym: Sort earlier to validate indices faster

[sagetrac-git]

Changed commit from ffea896 to fed09d5

[sagetrac-git]

Changed commit from fed09d5 to 421c660

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

421c660

src/sage/tensor/modules/finite_rank_free_module.py: Add doctest

[egourgoulhon]

comment:9

Replying to @mkoeppe:

In this version of this code:

... the trivial symmetries were dropped silently.

True...

I suppose I can add a parameter trivial_symmetries='error' for the cases where you'd like to see the errors.

I am wondering about what should be meant by trivial symmetry, especially for an antisymmetry: if only a single index position is provided, is there any meaning in stating that the components are antisymmetric with respect to this position?

---

New commits:

421c660

src/sage/tensor/modules/finite_rank_free_module.py: Add doctest

[sagetrac-git]

Changed commit from 421c660 to a1a3f36