On Apr 7, 2010, at 9:29 AM, Kenneth A. Ribet wrote:
Hello All,
I asked myself how I could use sage to compute the standard
deviation of a grade distribution for one of my courses. Rooting
around, I found that I can compute for example
sage: vector(RDF,[1,2,2,1]).standard_deviation()
and get the answer 0.57735026919. However, if I try the same
command with "RDF" replaced by "RR," I get anAttributeError. My
first question is: What's going on here; how come RDF and RR are so
different in this context? Their respective descriptions look very
similar --
Because no one's yet taken the time to unify the interfaces yet (the
two different "rings" use different implementations under the hood--
the one for RDF is optimized as a double* whereas the one for RR is
just the generic one). It would probably make sense to put a
standard_deviation method higher up the inheritance tree.
To be clear, I consider this a bug (fortunately easy to fix) and a
ticket should be filed.
"An approximation to the field of real numbers using double
precision floating point numbers. Answers derived from calculations
in this approximation may differ from what they would be if those
calculations were performed in the true field of real numbers. This
is due to the rounding errors inherent to finite precision
calculations."
"An approximation to the field of real numbers using floating point
numbers with any specified precision. Answers derived from
calculations in this approximation may differ from what they would
be if those calculations were performed in the true field of real
numbers. This is due to the rounding errors inherent to finite
precision calculations."
If I had found some documentation about the standard deviation
command, I would probably have have found the answer to my first
question. This leads to my second question: Why I don't I see
information about standard_deviation when I type
"standard_deviation?" at the command line?
Sage has an object-oriented design, which is to say that functions are
attached to objects rather than all dumped into the global session.
This allows stuff like
sage: v = vector(RDF, [1,2,2,1])
sage: v.norm()
3.16227766017
sage: I = NumberField(x^3-x+1, 'a').ideal(2)
sage: I.norm()
8
where doing v.norm? and I.norm? can give good contextual information
given the wide variety of objects and paradigms that Sage supports
(and it makes tab completion work much smoother too). I could see a
case for standard_deviation being a top-level function though, like we
do for many other basic operations. (Typically f(X) calls X.f()).
- Robert
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