Symbolic cmp

[vbraun]

In the symbolic ring, cmp implements the print comparison which is probably not what you envisioned:

sage: cmp(1, sqrt(2))     # mathematically correct, uses rich comparison
-1
sage: cmp(SR(1), sqrt(2)) # unexpectedly, you get the print sort order
1
sage: cmp(log(8), 3*log(2))
-1

Everybody who coerces to same parents internally before comparing trips over this, for example the real lazy field:

sage: RLF(1) < RLF(sqrt(2))
False

This also makes RealSet unusable with symbolics:

sage: RealSet((0, pi),[pi, pi],(pi,4))
[pi, 4)
sage: RealSet((0, pi),[0, pi],(pi,4))
[pi, 4)
sage: RealSet((0, pi),[0, 3.5],(pi,4))
(pi, 4)

CC: @videlec @mezzarobba @jpflori

Component: symbolics

Author: Volker Braun, Ralf Stephan

Branch/Commit: 07f12cd

Reviewer: Ralf Stephan, Volker Braun

Issue created by migration from https://trac.sagemath.org/ticket/16397

[vbraun]

Description changed:

--- 
+++ 
@@ -1 +1,8 @@
+In the symbolic ring, cmp implements the print comparison which is probably not what you envisioned:
 
+```
+sage: cmp(1, sqrt(2))     # mathematically correct, uses rich comparison
+-1
+sage: cmp(SR(1), sqrt(2)) # unexpectedly, you get the print sort order
+1
+```

[vbraun]

Description changed:

--- 
+++ 
@@ -6,3 +6,10 @@
 sage: cmp(SR(1), sqrt(2)) # unexpectedly, you get the print sort order
 1
 ```
+Everybody who coerces to same parents internally before comparing trips over this, for example the real lazy field:
+
+```
+sage: RLF(1) < RLF(sqrt(2))
+False
+```
+

[burcin]

comment:3

I can see how that might be surprising. :)

IIRC, that was a conscious decision to expose the print order from Pynac to !Python/Sage to be used for sorting lists, etc. where symbolic expressions occur. I guess many places in the code call cmp() instead of using the comparison operators.

We would need to get rid of this design for Python 3 compatibility anyway. Shall we remove support for cmp() and change all places where lists are returned from symbolics to explicitly call the print order?

[vbraun]

comment:4

Yes, thats what I'm thinking as well. I'll write a print_order function and see if I can get rid of all cmp calls...

[vbraun]

Branch: u/vbraun/symbolic_cmp

[videlec]

Commit: 62be17e

[videlec]

New commits:

62be17e

print_sorted and math_sorted utility functions

[rwst]

Changed branch from u/vbraun/symbolic_cmp to u/rws/symbolic_cmp

[rwst]

comment:9

Trying to push this ticket a bit. I also found this cmp call:

 File "matrix_integer_dense.pyx", line 604, in sage.matrix.matrix_integer_dense.Matrix_integer_dense.__richcmp__ (build/cythonized/sage/matrix/matrix_integer_dense.c:9503)
  File "element.pyx", line 873, in sage.structure.element.Element._richcmp (build/cythonized/sage/structure/element.c:8891)
  File "element.pyx", line 855, in sage.structure.element.Element._richcmp_ (build/cythonized/sage/structure/element.c:8615)
  File "element.pyx", line 902, in sage.structure.element.Element._richcmp (build/cythonized/sage/structure/element.c:9316)
  File "element.pyx", line 949, in sage.structure.element.Element._richcmp_c_impl (build/cythonized/sage/structure/element.c:9645)
  File "matrix_dense.pyx", line 126, in sage.matrix.matrix_dense.Matrix_dense._cmp_c_impl (build/cythonized/sage/matrix/matrix_dense.c:3092)
  File "expression.pyx", line 3066, in sage.symbolic.expression.Expression.__cmp__ (build/cythonized/sage/symbolic/expression.cpp:16865)

Do I understand it right that this should call math_sorted instead of cmp?

---

New commits:

215cff4	Merge branch 'develop' into t/16397/symbolic_cmp
af5f800	16397: use print_sorted() in two further places; fix doctest