cleanup variable factories

[videlec]

Various parents need to create variable names (the polynomial rings, free algebras, groups, the symbolic ring, etc). We fusion all of them.

1. the following will now raise TypeError

sage: R.<a,b> = PolynomialRing(QQ, ('a', 'b'))
sage: A.<x,y,z> = FreeAlgebra(QQ, 'x,y,z')

(see the "polynomial ring" thread)

2. The many versions are normalize_names are fused in sage.misc.variables.normalize_names

3. Deprecations:

   • the var_array argument in PolynomialRing
   • the methods normalize_names, _certify_name of CategoryObject

4. Problems with injection of reserved names

sage: a = SR.var('or')   # this should work
Traceback (most recent call last):
...
ValueError: The name "or" is not a valid Python identifier.
sage: QQ['or'].inject_variables()   # this should not
Defining or

note: should take care of '_', 'True', 'False', 'None' and builtins (see the "reserved name for variables" thread)

As a sided effect, we got some speedup in polynomial ring creation!

See also:

• "polynomial ring (bis)" thread about the allowed form for creation of PolynomialRing, FreeAlgebra, etc

CC: @mforets

Component: algebra

Author: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/18390

[videlec]

Description changed:

--- 
+++ 
@@ -1 +1,14 @@
-Creation of polynomial ring is very slow. In this ticket we do some cleanup that significatively increase the creation.
+The `PolynomialRing` factory is written in a very complicated way and is slightly different to `FreeAlgebra`. In this ticket, we normalize the inputs of all factories involving variables. 
+
+Some changes are noticeable
+
+1. the following will now raise `TypeError`
+
+```
+sage: R.<a,b> = PolynomialRing(QQ, ('a', 'b'))
+sage: A.<x,y,z> = FreeAlgebra(QQ, 'x,y,z')
+```
+
+2. The `var_array` argument in `PolynomialRing` is deprecated
+
+As a sided effect, we got some speedup in polynomial ring creation!

[videlec]

Description changed:

--- 
+++ 
@@ -9,6 +9,10 @@
 sage: A.<x,y,z> = FreeAlgebra(QQ, 'x,y,z')
 ```
 
-2. The `var_array` argument in `PolynomialRing` is deprecated
+2. The many versions are `normalize_names` are fused in `sage.misc.variables.normalize_names`
+
+3. Deprecations:
+   - the `var_array` argument in `PolynomialRing`
+   - the methods `normalize_names`, `_certify_name` of `CategoryObject`
 
 As a sided effect, we got some speedup in polynomial ring creation!

[videlec]

Description changed:

--- 
+++ 
@@ -1,6 +1,4 @@
-The `PolynomialRing` factory is written in a very complicated way and is slightly different to `FreeAlgebra`. In this ticket, we normalize the inputs of all factories involving variables. 
-
-Some changes are noticeable
+Various parents need to create variable names (the polynomial rings, free algebras, groups, the symbolic ring, etc). We fusion all of them.
 
 1. the following will now raise `TypeError`
 
@@ -8,6 +6,7 @@
 sage: R.<a,b> = PolynomialRing(QQ, ('a', 'b'))
 sage: A.<x,y,z> = FreeAlgebra(QQ, 'x,y,z')
 ```
+  (see [the "polynomial ring" thread](https://groups.google.com/forum/#!topic/sage-devel/DRT84Yj73Nc))
 
 2. The many versions are `normalize_names` are fused in `sage.misc.variables.normalize_names`
 
@@ -15,4 +14,19 @@
    - the `var_array` argument in `PolynomialRing`
    - the methods `normalize_names`, `_certify_name` of `CategoryObject`
 
+4. Problems with injection of reserved names
+
+```
+sage: a = SR.var('or')   # this should work
+Traceback (most recent call last):
+...
+ValueError: The name "or" is not a valid Python identifier.
+sage: QQ['or'].inject_variables()   # this should not
+Defining or
+```
+ note: should take care of '_', 'True', 'False', 'None' and builtins (see [the "reserved name for variables" thread](https://groups.google.com/forum/#!topic/sage-devel/5BAtCZnQj6o))
+
 As a sided effect, we got some speedup in polynomial ring creation!
+
+See also:
+- ["polynomial ring (bis)" thread](https://groups.google.com/forum/#!topic/sage-devel/Z7rXiKaMbOk) about the allowed form for creation of `PolynomialRing`, `FreeAlgebra`, etc