Make a symbolic mod function

[jasongrout]

A participant in the PREP program noticed that mod is not a symbolic function:

sage: mod(x,4)
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (4562, 0))

ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (4530, 0))

ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (842, 0))

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/home/grout/sage-4.5.2/devel/sage-main/sage/functions/<ipython console> in <module>()

/home/grout/sage/local/lib/python2.6/site-packages/sage/rings/finite_rings/integer_mod.so in sage.rings.finite_rings.integer_mod.Mod (sage/rings/finite_rings/integer_mod.c:2633)()

/home/grout/sage/local/lib/python2.6/site-packages/sage/rings/finite_rings/integer_mod.so in sage.rings.finite_rings.integer_mod.IntegerMod (sage/rings/finite_rings/integer_mod.c:2952)()

/home/grout/sage/local/lib/python2.6/site-packages/sage/rings/finite_rings/integer_mod.so in sage.rings.finite_rings.integer_mod.IntegerMod_int.__init__ (sage/rings/finite_rings/integer_mod.c:14249)()

/home/grout/sage/local/lib/python2.6/site-packages/sage/structure/parent.so in sage.structure.parent.Parent.__call__ (sage/structure/parent.c:6407)()

/home/grout/sage/local/lib/python2.6/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.NamedConvertMap._call_ (sage/structure/coerce_maps.c:4053)()

/home/grout/sage/local/lib/python2.6/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression._integer_ (sage/symbolic/expression.cpp:4026)()

TypeError: unable to convert x (=x) to an integer

Hopefully it should be easy to wrap mod in a symbolic function, something like:

sage: def eval_mod(self, x):
....:     if isinstance(x, (int, Integer)):
....:         return mod(x,5)
....:     return None
....:
sage: f=function('f', eval_func=eval_mod)
sage: f(x)
f(x)
sage: f(13)
3
sage: f(x^2+x+1)
f(x^2 + x + 1)
sage: f(x^2+x+1).subs(x=2)
2
sage: f(x^2+x+1).subs(x=3)
3
sage: f(x^2+x^3).subs(x=1)
2
sage: f(x^2+x^3).subs(x=2)
2
sage: f(x^2+x^3).subs(x=3)
1 

See also http://ask.sagemath.org/question/25037/declaring-variable-to-be-in-a-particular-fieldringgroup/

More discussions:
https://groups.google.com/forum/#!searchin/sage-devel/mod|sort:relevance/sage-devel/goNosLk_t9M/xYDgEdIsLYsJ
https://groups.google.com/forum/#!searchin/sage-devel/mod|sort:relevance/sage-devel/g7AdhAyQH-k/O1IGYbNRAQAJ

CC: @burcin @jdemeyer @rwst

Component: symbolics

Issue created by migration from https://trac.sagemath.org/ticket/9935

[jasongrout]

comment:1

Burcin, is there a nice example somewhere that we can just copy and modify to make a symbolic function? This sounds like it would be easy for a beginner to do if there was a good example almost like it somewhere.

[burcin]

comment:2

There are plenty of examples in the directory sage/functions/, just look for classes deriving from BuiltinFunction. You'll probably want to deprecate the parent keyword argument to mod(), so sage.functions.transcendental.Function_exp_integral might provide a good template.