Here's something better. Now unless I made a mistake, the floor and
ceiling functions
return a minimal interval that contains the *image* of the interval
under the floor and ceiling maps. This is sensible, given how most
functions on intervals work. It's a reasonable compromise until there
are integer intervals, which should definitely be implemented soon.
William
On 5/11/07, Michel <[EMAIL PROTECTED]> wrote:
>
> Thanks!
>
> I am sorry however but I think this implementation is morally wrong. I
> think floor and ceil should
> throw a ValueError
> when their value is not uniquely determined, i.e. when the interval
> contains an integer.
> After all the point of an IntervalField is to have results which are
> guaranteed to be correct.
>
> Michel
>
> On May 11, 5:14 pm, "William Stein" <[EMAIL PROTECTED]> wrote:
> > On 5/11/07, Michel <[EMAIL PROTECTED]> wrote:
> >
> >
> >
> > > I get the following strange behaviour on sage-2.5:
> >
> > > sage: R=RealIntervalField(100)
> > > sage: floor(R(10))
> >
> > > Sage just hangs. ^C twice gets the prompt back.
> >
> > > Michel
> >
> > > PS. It would seem more logical to me if floor and ceil were actually
> > > methods. An element
> > > of a RealIntervalField could have a _floor_ method which the global
> > > floor function
> > > could call if present.
> >
> > floor just tried to call the floor method if it is there, then tries other
> > methods if there is no floor method. It fails in this case since it has
> > no way of computing the floor, since nobody implemented it yet for
> > intervals,
> > for some reason. Anyway, I've implemented it just now.
> >
> > [4408.txt]# HG changeset patch
> > # User William Stein <[EMAIL PROTECTED]>
> > # Date 1178896400 25200
> > # Node ID 04c23de44a4eb595683d52f864df42d24ee0b43d
> > # Parent e90e3396991d07bf491cf671066dd46787606049
> > added floor and ceil for mpfi intervals
> >
> > diff -r e90e3396991d -r 04c23de44a4e sage/rings/real_mpfi.pyx
> > --- a/sage/rings/real_mpfi.pyx Thu May 10 23:19:15 2007 -0700
> > +++ b/sage/rings/real_mpfi.pyx Fri May 11 08:13:20 2007 -0700
> > @@ -1390,46 +1390,58 @@ cdef class RealIntervalFieldElement(sage
> > # mpfr_round(x.value, self.value)
> > # return x
> >
> > -# def floor(self):
> > -# """
> > -# Returns the floor of this number
> > -
> > -# EXAMPLES:
> > -# sage: R = RealIntervalField()
> > -# sage: (2.99).floor()
> > -# 2
> > -# sage: (2.00).floor()
> > -# 2
> > -# sage: floor(RR(-5/2))
> > -# -3
> > -# """
> > -# cdef RealIntervalFieldElement x
> > -# x = self._new()
> > -# mpfr_floor(x.value, self.value)
> > -# return x.integer_part()
> > -
> > -# def ceil(self):
> > -# """
> > -# Returns the ceiling of this number
> > -
> > -# OUTPUT:
> > -# integer
> > -
> > -# EXAMPLES:
> > -# sage: (2.99).ceil()
> > -# 3
> > -# sage: (2.00).ceil()
> > -# 2
> > -# sage: (2.01).ceil()
> > -# 3
> > -# """
> > -# cdef RealIntervalFieldElement x
> > -# x = self._new()
> > -# mpfr_ceil(x.value, self.value)
> > -# return x.integer_part()
> > -
> > -# def ceiling(self):
> > -# return self.ceil()
> > + def floor(self):
> > + """
> > + Returns the floor of this number
> > +
> > + EXAMPLES:
> > + sage: R = RealIntervalField()
> > + sage: (2.99).floor()
> > + 2
> > + sage: (2.00).floor()
> > + 2
> > + sage: floor(RR(-5/2))
> > + -3
> > + sage: R = RealIntervalField(100)
> > + sage: a = R(9.5, 11.3); a
> > + [9.5000000000000000000000000000000 ..
> > 11.300000000000000710542735760101]
> > + sage: floor(a)
> > + 9
> > + sage: a.floor()
> > + 9
> > + sage: ceil(a)
> > + 12
> > + sage: a.ceil()
> > + 12
> > + """
> > + return self.lower().floor()
> > +
> > + def ceil(self):
> > + """
> > + Returns the ceiling of this number
> > +
> > + OUTPUT:
> > + integer
> > +
> > + EXAMPLES:
> > + sage: (2.99).ceil()
> > + 3
> > + sage: (2.00).ceil()
> > + 2
> > + sage: (2.01).ceil()
> > + 3
> > + sage: R = RealIntervalField(30)
> > + sage: a = R(-9.5, -11.3); a
> > + [-11.300000012 .. -9.5000000000]
> > + sage: a.floor()
> > + -12
> > + sage: a.ceil()
> > + -9
> > + """
> > + return self.upper().ceil()
> > +
> > + def ceiling(self):
> > + return self.ceil()
> >
> > # def trunc(self):
> > # """
>
>
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://www.williamstein.org
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# HG changeset patch
# User William Stein <[EMAIL PROTECTED]>
# Date 1178898666 25200
# Node ID c6f86ef0019f1d8c26a21c08442c5ad130710201
# Parent 95b4bd205a125109be441683a7099087887103aa
make a "moral" improvement to real mpfi floor and ceiling.
diff -r 95b4bd205a12 -r c6f86ef0019f sage/rings/real_mpfi.pyx
--- a/sage/rings/real_mpfi.pyx Fri May 11 08:16:38 2007 -0700
+++ b/sage/rings/real_mpfi.pyx Fri May 11 08:51:06 2007 -0700
@@ -1406,15 +1406,15 @@ cdef class RealIntervalFieldElement(sage
sage: a = R(9.5, 11.3); a
[9.5000000000000000000000000000000 ..
11.300000000000000710542735760101]
sage: floor(a)
- 9
+ [9.0000000000000000000000000000000 ..
11.000000000000000000000000000000]
sage: a.floor()
- 9
+ [9.0000000000000000000000000000000 ..
11.000000000000000000000000000000]
sage: ceil(a)
- 12
+ [10.000000000000000000000000000000 ..
12.000000000000000000000000000000]
sage: a.ceil()
- 12
- """
- return self.lower().floor()
+ [10.000000000000000000000000000000 ..
12.000000000000000000000000000000]
+ """
+ return self.parent()(self.lower().floor(), self.upper().floor())
def ceil(self):
"""
@@ -1434,11 +1434,13 @@ cdef class RealIntervalFieldElement(sage
sage: a = R(-9.5, -11.3); a
[-11.300000012 .. -9.5000000000]
sage: a.floor()
- -12
+ [-12.000000000 .. -10.000000000]
sage: a.ceil()
- -9
- """
- return self.upper().ceil()
+ [-11.000000000 .. -9.0000000000]
+ sage: ceil(a)
+ [-11.000000000 .. -9.0000000000]
+ """
+ return self.parent()(self.lower().ceil(), self.upper().ceil())
def ceiling(self):
return self.ceil()
