Re: [sage-support] Re: Set and real intervals

2010-12-10 Thread Laurent

>It seems like it would be relatively easy to implement a Sage class
>for real intervals that represents finite unions of open, closed, half
>open, and unbounded intervals and implements union() and
>intersection() methods.

I did it. I attach my piece of code. This is only python, but it is 
going to make the job.


Technically I define a class Interval that represent an interval (closed 
or open at each extremities). This class has the important 
__contrain__() method that tests if a number is contained in the interval.




Then class ContinuousSet that represent finite union and intersections 
of intervals. Its main attribute is a list of disjoint intervals. These 
intervals represent the set.


For the moment, I have working union() and __contain__() methods; the 
delicate part is to express the union of two lists of disjoints 
intervals as a new list of disjoint intervals. I'm working on 
intersections and I plan to be able to test inclusion.


doctest of the working methods are included in the code.

Up to writing better documentation and finishing the work, do one think 
that it can be included in some place in Sage ?



Have a good day
Laurent

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#! /usr/bin/python
# -*- coding: utf8 -*-

import doctest

def constructorContinuouSet(A):
	if type(A)==ContinuousSet:
		return A
	if type(A)==Interval:
		return ContinuousSet([A],[])

def EmptySet():
	return ContinuousSet([],[])

class Interval(object):
	"""
	Represent the real interval between a and b.

	By default, the interval is closed : [a,b]
	if low_open is false, the interval is lower opened
	if up_open is false, the interval is upper opened.

	Examples

	DEFINITION OF INTERVALS
	>>> I=Interval(0,2,low_open=False,up_open=True)
	>>> J=Interval(-2,-1)
	>>> K=Interval(1,3,low_open=False,up_open=True)
	>>> print I
	[0 , 2[
	>>> print J
	[-2 , -1]
	>>> print K
	[1 , 3[

	INTERSECTION
	>>> X = I.intersection(K)
	>>> print X 
	[1 , 2[
	>>> print 1 in X
	True
	>>> print 2 in X
	False

	FUSION
	The intervals I and J have no intersection, so the union is disjoint :
	>>> Y=I.fusion(J)
	>>> for a in Y:
	... print a
	[0 , 2[
	[-2 , -1]
	
	The intervals I and K have intersection, so the union is one interval:
	>>> Y=I.fusion(K)
	>>> for a in Y:
	... print a
	... 
	[0 , 3[

	UNION
	Asking the union of two intervals returns an object ContinuousSet
	>>> import math
	>>> I=Interval(1,4,low_open=False,up_open=False)
	>>> J=Interval(0,2,low_open=True,up_open=True)
	>>> M=Interval(7,8,low_open=True,up_open=False)
	>>> print I.union(J)
	]0 , 4]
	>>> print I.union(M)
	]7 , 8] U [1 , 4]
	>>> 7 in I.union(M)
	False
	>>> math.pi in I.union(M)
	True
	"""
	def __init__(self,a,b,low_open=False,up_open=False):
		self.low_bound=a
		self.up_bound=b
		self.low_open=low_open
		self.up_open=up_open
		def contains_oo(x):
			if x>a and xa and x<=b :
return True
			return False
		def contains_co(x):
			if x>=a and x=a and x<=b :
return True
			return False
		if self.low_open and self.up_open:
			self.contains=contains_oo
		elif self.low_open and not self.up_open:
			self.contains=contains_oc
		elif not self.low_open and self.up_open:
			self.contains=contains_co
		elif not self.low_open and not self.up_open:
			self.contains=contains_cc
	def intersection(self,A):
		if self.low_bound in A or self.up_bound in A or A.low_bound in self or A.up_bound in self :
			low_bound=self.low_bound
			up_bound=self.up_bound
			low_open=self.low_open
			up_open=self.up_open
			if A.low_bound>self.low_bound:
low_bound=A.low_bound
low_open=A.low_open
			if A.low_bound==self.low_bound:
low_open = self.low_bound and A.low_bound
			if A.up_bound>> I=Interval(1,4,low_open=False,up_open=False)
		>>> J=Interval(0,2,low_open=True,up_open=True)
		>>> K=Interval(3,5,low_open=False,up_open=True)
		>>> L=Interval(6,7,low_open=False,up_open=False)
		>>> X=I.fusion_with_list([J,K,L])
		>>> for a in X:
		... print a
		[6 , 7]
		]0 , 5[

		The result does not depend on the order of the list:
		>>> X=I.fusion_with_list([L,K,J])
		>>> for a in X:
		... print a
		[6 , 7]
		]0 , 5[
	
		"""
		new_list=[]
		happend_fusion=False
		for I in intervals_list:
			a = self.fusion(I)
			if len(a)==1:
if happend_fusion == False:
	new_guy=a[0]
	happend_fusion=True
else :
	new_list.append(a[0])
			if len(a)==2:
new_list.append(I)
		if happend_fusion :
			return new_guy.fusion_with_list(new_list)
		else :
			new_list.append(self)
			return tuple(new_list)
	def union(self,A):
		return constructorContinuouSet(self).union(constructorContinuouSet(A))
	def copy(self):
		"""
		Return a copy of the interval which is a new object.

		>>> I=Interval(1,4,low_open=False,up_open=False)
		>>> X=I.copy()
		>>> I.low_open=T

[sage-support] Re: Set and real intervals

2010-12-09 Thread BFJ
I was going to suggest this too, but the RIF behaves differently than
you might naively expect "intervals" of real number to behave. For
example, "union" means convex hull:

sage: a = RIF(0,1)
sage: b = RIF(2,3)
sage: a.union(b).endpoints()
(0.000, 3.00)

Also, it seems from the documentation that RIF intervals are only
designed to represent closed intervals { x : a <= x <= b }

It seems like it would be relatively easy to implement a Sage class
for real intervals that represents finite unions of open, closed, half
open, and unbounded intervals and implements union() and
intersection() methods.

-Benjamin Jones


On Dec 9, 8:21 pm, Marshall Hampton  wrote:
> I think you want the RealIntervalField.  For exampe:
>
> sage: a = RIF(0,1)
> sage: b = RIF(.5,pi)
> sage: a.overlaps(b)
> True
>
> see:http://www.sagemath.org/doc/reference/sage/rings/real_mpfi.html
>
> -M. Hampton
>
> On Dec 9, 8:16 am, Laurent Claessens  wrote:
>
>
>
>
>
>
>
> >   Hi
>
> > I would like to work with sets that are real intervals or combinations
> > of them : mainly intersection and union.
> > Example :
> > [0,1] intersection with [0.5 , pi]
>
> > Using the Sage Reference Manual 4.1.1, I was able to do that :
>
> > sage:A=Set(RealField())
> > sage: sqrt(2) in A
> > True
>
> > So it is possible to consider parts of R as sets. How can I build an
> > interval ?
>
> > Have a good day
> > Laurent Claessens
>
> > PS : I send this message by email on December, 4. Since I did not even
> > saw my message appearing, I decided to repost it from the GoogleGroup
> > online interface. I'm wrong in doing that ?

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[sage-support] Re: Set and real intervals

2010-12-09 Thread Marshall Hampton
I think you want the RealIntervalField.  For exampe:

sage: a = RIF(0,1)
sage: b = RIF(.5,pi)
sage: a.overlaps(b)
True

see:
http://www.sagemath.org/doc/reference/sage/rings/real_mpfi.html

-M. Hampton

On Dec 9, 8:16 am, Laurent Claessens  wrote:
>   Hi
>
> I would like to work with sets that are real intervals or combinations
> of them : mainly intersection and union.
> Example :
> [0,1] intersection with [0.5 , pi]
>
> Using the Sage Reference Manual 4.1.1, I was able to do that :
>
> sage:A=Set(RealField())
> sage: sqrt(2) in A
> True
>
> So it is possible to consider parts of R as sets. How can I build an
> interval ?
>
> Have a good day
> Laurent Claessens
>
> PS : I send this message by email on December, 4. Since I did not even
> saw my message appearing, I decided to repost it from the GoogleGroup
> online interface. I'm wrong in doing that ?

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