Re: More on Vincent's comments on text
On 2013-02-18 21:51:53 +0000, John Pryce wrote:
> On 31 Jan 2013, at 17:13, Vincent Lefevre wrote:
> > §8.8.7: With the rule given on NaI, code ending with something like
> > (e.g. for piecewise functions):
> > y = convexHull(u_du,v_dv)
> > dy = dx
> > or
> > y_dy = convexHullDec(u_du,v_dv)
> > may be wrong if NaI can occur in intermediate results! There should
> > be a note with some warning. I suspect problems may occur in practice
> > with parameterized intervals (a function may become nowhere defined
> > for some values of the parameter). This is a problem with specific
> > rules for NaI: here a NaI can be produced by evaluating a function
> > that is never defined, but having such an operation on intervals is
> > not necessarily a user error.
> I sort of see what you mean but would like a specific example. Would
> this, which might happen in CAD, give an example?
> Write an interval extension of f(t), defined to be the closest
> distance of the point (t,0) on the x-axis, to the disk
> D: x^2 + (y-b)^2 <= r^2,
> where b>=0, r>0 are given parameters. Then for r>b there is an
> interval round t=0 in which f(t)=0; for r=b this shrinks to the
> single point [0,0]; for r<b there is no such interval.
Yes. Now, if ill can only be produced by constructors in the set-based
flavor, this may no longer be a problem. However the user would still
need to write special code to express something like: the set of reals
x such that a <= x and x <= b (where one may have b < a) in order to
avoid a NaI to be produced.
> > §8.8.9, Example (i): Replace "2½" by "2+½"? I don't know whether "2½"
> > is a common notation. However it may be ambiguous.
>
> It's the usual British notation. E.g. Wikipedia:
> > Mixed numbers
> > A mixed numeral (often called a mixed number, also called a mixed
> > fraction) is the sum of a non-zero integer and a proper fraction.
> > This sum is implied without the use of any visible operator such
> > as "+". For example, in referring to two entire cakes and three
> > quarters of another cake, the whole and fractional parts of the
> > number are written next to each other:
I've also seen that in very old French math books, but never in text
from the 20th or 21th century. So, I was wondering. But even if it
sometimes used in practice, I'm still wondering whether this notation
is allowed in international standards. There may be restrictions to
improve understanding by users from different countries or to avoid
ambiguity. For instance, http://en.wikipedia.org/wiki/ISO_31-0#Numbers
says:
Numbers consisting of long sequences of digits can be made more
readable by separating them into groups, preferably groups of three,
separated by a small space. For this reason, ISO 31-0 specifies that
such groups of digits should never be separated by a comma or point,
as these are reserved for use as the decimal sign.
There's nothing about the "mixed number" notation, though I don't have
the text of the standard.
> > §8.8.11: Since decorations trv, emp, ill and dac are mentioned,
> > I suppose that compressed arithmetic is specified only for the
> > set-based flavor (and the common one). This should be said.
> It's part of the set-based chapter. Need more be said?
OK, I forgot about that.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
100% accessible validated (X)HTML - Blog: <http://www.vinc17.net/blog/>
Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)