Attempting to use this on my matrix, I end up with the following results (D 
is my matrix):

D.apply_map(simplify_full)

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_61.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 
-*-\\n" + 
_support_.preparse_worksheet_cell(base64.b64decode("RC5hcHBseV9tYXAoc2ltcGxpZnlfZnVsbCk="),globals())+"\\n");
 
execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpKuOh6k/___code___.py", line 2, in <module>
    exec compile(u'D.apply_map(simplify_full)
  File "", line 1, in <module>
    
NameError: name 'simplify_full' is not defined

Then, trying this:
simplify_full(D)

I get:
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_60.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 
-*-\\n" + 
_support_.preparse_worksheet_cell(base64.b64decode("c2ltcGxpZnlfZnVsbChEKQ=="),globals())+"\\n");
 
execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpP_fTpm/___code___.py", line 2, in <module>
    exec compile(u'simplify_full(D)
  File "", line 1, in <module>
    
NameError: name 'simplify_full' is not defined

Using simplify in both methods gives me the unsimplified results mentioned 
in my first post.

I personally wish that sage simplify functions worked as follows:

simplify_rational and simplify_trig work as currently implemented.
simplify was renamed simplify_basic
Simplify was replaced with a new method/function that try/excepted the 
algorithms in simplify_full, simplify_trig, simplify_rational then 
simplify_basic, returning the first that succeeded. 
I understand the need to provide functions that control the level of detail 
used when simplifying complex problems. 
However I'd assume that most basic/mid-level users just want the 
expression/equation/object simplified with as little fiddly-ness as 
possible. Currently I tend to call simplify_full on most problems - I.e. 
simplify_full is my practical default rather than simplify.

Joal Heagney


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