Fractional part function {x}

[rwst]

This symbolic function will also be needed by the periodic piecewise function enhancement (#21215). It is in Sympy too.

https://en.wikipedia.org/wiki/Fractional_part

Component: symbolics

Author: Ralf Stephan

Branch/Commit: 141a784

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/21232

[rwst]

Branch: u/rws/fractional_part_function__x_

[rwst]

Commit: 3fcaf85

[rwst]

New commits:

3fcaf85

21232: Fractional part function {x}

[rwst]

Author: Ralf Stephan

[mkoeppe]

comment:3

+            if isinstance(x, (int, long)):
+                return x - Integer(x)

Probably can just return Integer(0)

+    def _print_latex_(self, x):
+        r"""
+        EXAMPLES::
+
+            sage: latex(frac(x))
+            \left\{ x \right\}
+        """
+        return r"\left\{ %s \right\}"%latex(x)

I use this braces notation myself, but I can imagine that it's not universally used, and some people may prefer \mathop{\mathrm{frac}}(x). Perhaps a global option?

[mkoeppe]

Reviewer: Matthias Koeppe

[mkoeppe]

comment:5

+            elif isinstance(x, (float, complex)):
+                return x - Integer(int(math.floor(x)))

Also, going through int seems dangerous here

[mkoeppe]

comment:7

Replying to @mkoeppe:

+            elif isinstance(x, (float, complex)):
+                return x - Integer(int(math.floor(x)))

Also, going through int seems dangerous here

I retract this comment. I didn't realize int() makes Python bignums.

[sagetrac-git]

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

141a784

21232: change LaTeX, return shortcut

[sagetrac-git]

Changed commit from 3fcaf85 to 141a784

[mkoeppe]

comment:10

Looks good to me.

For full symbolic functionality (which I never use), I guess one would need to tie this in with the simplification and assumptions machinery, so that things like this behave better:

sage: simplify(frac(frac(x)))
frac(frac(x))
sage: simplify(frac(floor(x)))
frac(floor(x))
sage: assume(x, 'integer')
sage: simplify(frac(x))
frac(x)

Perhaps on a follow-up ticket?

[vbraun]

Changed branch from u/rws/fractional_part_function__x_ to 141a784