Re: [sage-devel] Re: How to define a new ring class ? [We need a class representing genuine real field]
I would advocate that RLF is a very good approximation of what should
be RR. Perhaps one good direction to take is to try to make RLF
smarter and contains all constants from pi to cos(42^e).
Somehow, it already does (i.e. internally it keeps track of their
symbollic nature):
{{{
sage: b=RLF(cos(42^e))
sage: b
0.9578837974?
sage: b.eval(SR)
cos(42^e)
}}}
Maybe the issue is that there is no coercion between SR and RLF (there is
conversion from SR to RLF, and the .eval() method that can take elements
from RLF to SR, though).
--
You received this message because you are subscribed to the Google Groups
sage-devel group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-devel+unsubscr...@googlegroups.com.
To post to this group, send email to sage-devel@googlegroups.com.
Visit this group at http://groups.google.com/group/sage-devel.
For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: How to define a new ring class ? [We need a class representing genuine real field]
2014-03-14 10:45 UTC+01:00, mmarco mma...@unizar.es:
I would advocate that RLF is a very good approximation of what should
be RR. Perhaps one good direction to take is to try to make RLF
smarter and contains all constants from pi to cos(42^e).
Somehow, it already does (i.e. internally it keeps track of their
symbollic nature):
{{{
sage: b=RLF(cos(42^e))
sage: b
0.9578837974?
sage: b.eval(SR)
cos(42^e)
}}}
Maybe the issue is that there is no coercion between SR and RLF (there is
conversion from SR to RLF, and the .eval() method that can take elements
from RLF to SR, though).
This is half good, I am happy that RLF wraps symbolic constants. But,
first of all there can not be any reasonable coercion from SR to RLF
as SR is much bigger. Secondly, SR is not consistent with evaluation
sage: cos(1.).parent()
Real Field with 53 bits of precision
sage: cos(1).parent()
Symbolic Ring
I would prefer the second parent to be something like
RealSymbolicField or RealNumbers or whatever but not symbolic ring.
Thirdly, I would like to be able to compare real numbers built from
different sources :
- algebraic numbers (built from QQbar and NumberField)
- symbolic constants
- continued fractions
- binary expansions
- ...
But currently:
sage: R.X = QQ[]
sage: K.a = NumberField(X^4 - 5*X^2 + 5, embedding=1.17)
sage: RLF(a)
1.75570504584947?
sage: expr = 2 * cos(3*pi/10)
sage: RLF(expr)
1.17557050458946?
sage: RLF(a) == RLF(expr) # does not work in RLF
False
sage: bool(SR(a) == SR(expr)) # does not work in SR
False
Even if they are equal as real numbers. So what is broken : comparison
in SR? comparison in RLF?
Vincent
--
You received this message because you are subscribed to the Google Groups
sage-devel group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-devel+unsubscr...@googlegroups.com.
To post to this group, send email to sage-devel@googlegroups.com.
Visit this group at http://groups.google.com/group/sage-devel.
For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: How to define a new ring class ? [We need a class representing genuine real field]
This is half good, I am happy that RLF wraps symbolic constants. But, first of all there can not be any reasonable coercion from SR to RLF as SR is much bigger. Secondly, SR is not consistent with evaluation sage: cos(1.).parent() Real Field with 53 bits of precision sage: cos(1).parent() Symbolic Ring I don't see much problem: 1. is a floating point number, and hence an inexact element. So it makes sense to compute is cosine as an inexact number too. On the other hand, 1 is an exact element, so it makes sense to keep its cosine as an exact number. I would prefer the second parent to be something like RealSymbolicField or RealNumbers or whatever but not symbolic ring. Thirdly, I would like to be able to compare real numbers built from different sources : - algebraic numbers (built from QQbar and NumberField) - symbolic constants - continued fractions - binary expansions - ... But currently: sage: R.X = QQ[] sage: K.a = NumberField(X^4 - 5*X^2 + 5, embedding=1.17) sage: RLF(a) 1.75570504584947? sage: expr = 2 * cos(3*pi/10) sage: RLF(expr) 1.17557050458946? sage: RLF(a) == RLF(expr) # does not work in RLF False sage: bool(SR(a) == SR(expr)) # does not work in SR False Even if they are equal as real numbers. So what is broken : comparison in SR? comparison in RLF? IIRC it is not known if that problem is decidable or not. That is, in practice, comparison in SR or RLF will always be broken. It could be improved, but there will always be cases where the computer can not determine if two expressions are equal or not. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: How to define a new ring class ? [We need a class representing genuine real field]
2014-03-14 14:24 UTC+01:00, mmarco mma...@unizar.es: This is half good, I am happy that RLF wraps symbolic constants. But, first of all there can not be any reasonable coercion from SR to RLF as SR is much bigger. Secondly, SR is not consistent with evaluation sage: cos(1.).parent() Real Field with 53 bits of precision sage: cos(1).parent() Symbolic Ring I don't see much problem: 1. is a floating point number, and hence an inexact element. So it makes sense to compute is cosine as an inexact number too. On the other hand, 1 is an exact element, so it makes sense to keep its cosine as an exact number. I agree with you but it is a real number not any symbolic expression. If you read my previous post 1.2 * pi behaves badly because it should be coerced into RR and not kept into SR (coercion should be from more precision to less precision). This is the reason why I do not want to keep symbolic constants into the symbolic ring. Am I wrong ? I would prefer the second parent to be something like RealSymbolicField or RealNumbers or whatever but not symbolic ring. Thirdly, I would like to be able to compare real numbers built from different sources : - algebraic numbers (built from QQbar and NumberField) - symbolic constants - continued fractions - binary expansions - ... But currently: sage: R.X = QQ[] sage: K.a = NumberField(X^4 - 5*X^2 + 5, embedding=1.17) sage: RLF(a) 1.75570504584947? sage: expr = 2 * cos(3*pi/10) sage: RLF(expr) 1.17557050458946? sage: RLF(a) == RLF(expr) # does not work in RLF False sage: bool(SR(a) == SR(expr)) # does not work in SR False Even if they are equal as real numbers. So what is broken : comparison in SR? comparison in RLF? IIRC it is not known if that problem is decidable or not. That is, in practice, comparison in SR or RLF will always be broken. It could be improved, but there will always be cases where the computer can not determine if two expressions are equal or not. Any number cos(rational x pi) is algebraic and equality of algebraic numbers is decidable. Moreover, it is not because something is undecidable that Sage should return a wrong answer. In that case, it would be good to have a third party in comparison (either returning Unknown or raising exception). -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: How to define a new ring class ? [We need a class representing genuine real field]
Any number cos(rational x pi) is algebraic and equality of algebraic numbers is decidable. Moreover, it is not because something is undecidable that Sage should return a wrong answer. In that case, it would be good to have a third party in comparison (either returning Unknown or raising exception). Yes, in this particular case, you are right (and in fact, you can check for equality of those two elements if you convert them to AA), but in general, determining if a real number given by a symbollic expression involving e,pi, rationals, roots, logarithms... is zero or not is not doable. So, no matter how you implement this new field of real numbers, it will have broken comparison. But maybe you are right about the Unknown answer. Although it might cause some other problems: you cannot know if you can take the inverse, or the logarithm of a real numbers. We could have then something like the NaN problem: an unknown thing that contaminates everything it touches. I don't really think we can find a good solution. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: How to define a new ring class ?
I do not agree with Miguel: it makes sense to have a Parent modeling the set of all real numbers (even if it has no element). And the natural name for it would be RR. Now, concerning concrete computation, what you can do is either : - use floating points (ie approximate operations +, x, -, / and exact equality) - use computable numbers (ie exact operations but approximate equality) - deal with a nice subsets of RR (such as algebraic numbers, finite transcendantal extensions, ...) where you can deal with exact operations and exact equality. - mix of the one above It is bad that only QQ, QQbar and SR can handle arbitrary precision real number. It would make more sense to have pi, e, cos(3/4), ... in a ring of exact reals. It deviates from the initial subject but it is always good to say that real numbers should not be in SR and that RR is misnamed ! Vincent 2014-03-12 21:29 UTC+01:00, mmarco mma...@unizar.es: Since the ring you want will be an algebra over the reals, the best fit for base ring would be the reals. Now, since it is impossible to represent the real field in practice, there are different possible solutions in sage: RR if you don't care about the lack of exactness QQ or some extension (like AA) if you want exactness but don't mind the lack of transcendentals SR if you want to allow arbitrary expressions, with the problem of speed and maybe the lack of a unique form for each element. I don't think that you can do much better than that to work with the reals. In practice, since in every computation there will only be a finite number of symbols involved, it can be done in something like AA(t1,t2,...,tn) (a trascendental extension of the algebraic reals) or QQ[a](t1,t2,...,tn) with a in AA. But working in those rings can be extremely slow, and you would need in advance which numbers would appear, which are algebraic and which trascendental and so on. So i wouldn't advise it. El miércoles, 12 de marzo de 2014 20:37:00 UTC+1, Eric Gourgoulhon escribió: Thanks for your answer and suggestions. Best wishes, Eric. Le mercredi 12 mars 2014 17:55:46 UTC+1, Nils Bruin a écrit : On Wednesday, March 12, 2014 6:41:07 AM UTC-7, Eric Gourgoulhon wrote: The issue here is that CommutativeRing.__init__ requires the argument base_ring and in the present context, I don't know what to put here: the ring C^oo(N) does not depend upon any other ring. Shall I put self, i.e. write CommutativeRing.__init__(self, self) ? Every ring ultimately has ZZ as a base, by virtue of being an additive group. You could use that. On the other hand, if you expect the thing to be finitely generated over its base then perhaps the ring should be its own base (I don't think that's a formal requirement, given that `ZZ[['x']].base_ring()==ZZ`). This does happen in Sage elsewhere: sage: ZZ.base_ring() Integer Ring sage: QQ.base_ring() Rational Field sage: GF(3).base_ring() Finite Field of size 3 On the other hand, if you find it's doable to avoid specifying a base, perhaps that's the better way to go. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: How to define a new ring class ? [We need a class representing genuine real field]
Salut Thierry, I did not see your post before posting mine ! I mostly agreed but I would love to have something better. There are two kinds of approximation that one can have when dealing with computations : - approximate operations +, -, x, / (that allows for example to deal with a finite subset) - approximate equality The term exact in Sage (as in RR.is_exact()) currently refers to the first kind. Now if you deal with computable numbers, or large enough subset of the reals, then you can not guarantee equality (and this is the case for example with SR that can answer False to A == B even if it is True). I know that there are other issue with SR, but it was just to claim that the set of reals that it handle is somewhat too large to ensure exact equality. A first step in having sane reals would be to refined this notion of exactness. This implies to declare convention about the answer of A == B. I think that this should be the mathematical answer (True, False) or an exception that can be either of the kind raise NotAbleToSolveTheProblem or return Unkown (from sage.misc.unknown). Now, concerning implementation, I see at least there levels of fields - subrings with exact computations and identity problem solvable, ie algebraic numbers, algebraic reals with exponentials, ... - subrings with approximate computations (and identity problem solvable), ie floating points - subrings with exact computations and identity problem unsolvable, like the RSF and CSF that you propose. And it defintely makes sense to have a parent RR with no dedicated class of element. Best Vincent -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: How to define a new ring class ?
The problem is that you cannot know if a certain expression involving pi, e and cos(3/4) is zero or not (well, you can determine that it is not zero, if a numerical approximation is not, but a zero numerical aproximation doesn't imply the expression to be zero). That means that, for instance, you don't know if you can take its inverse. If you assume that they are transcendental (that is, that such expressions are not zero), you are working on AA(t1,t2.t3) with t1=pi, t2=e, t3=cos(3/4). So maybe the right approach would be to implement arbitrary extensions of QQ (that is, QQ(t1,t2...tn)[a], with a algebraic over QQ(t1,t2,...,tn)) providing methods to compute numerical aproximations for t1,t2...tn And also make it dynamically, so that new symbols can be added on the fly. That way we have best of both worlds: algebraic exactness plus the ability to get numerical aproximations. That is, a real would be something that lives in an extension of QQ, with a method to get numerical aproximations, and such that all those numerical aproximations have no imaginary part Would that make sense? El jueves, 13 de marzo de 2014 09:17:34 UTC+1, vdelecroix escribió: I do not agree with Miguel: it makes sense to have a Parent modeling the set of all real numbers (even if it has no element). And the natural name for it would be RR. Now, concerning concrete computation, what you can do is either : - use floating points (ie approximate operations +, x, -, / and exact equality) - use computable numbers (ie exact operations but approximate equality) - deal with a nice subsets of RR (such as algebraic numbers, finite transcendantal extensions, ...) where you can deal with exact operations and exact equality. - mix of the one above It is bad that only QQ, QQbar and SR can handle arbitrary precision real number. It would make more sense to have pi, e, cos(3/4), ... in a ring of exact reals. It deviates from the initial subject but it is always good to say that real numbers should not be in SR and that RR is misnamed ! Vincent 2014-03-12 21:29 UTC+01:00, mmarco mma...@unizar.es javascript:: Since the ring you want will be an algebra over the reals, the best fit for base ring would be the reals. Now, since it is impossible to represent the real field in practice, there are different possible solutions in sage: RR if you don't care about the lack of exactness QQ or some extension (like AA) if you want exactness but don't mind the lack of transcendentals SR if you want to allow arbitrary expressions, with the problem of speed and maybe the lack of a unique form for each element. I don't think that you can do much better than that to work with the reals. In practice, since in every computation there will only be a finite number of symbols involved, it can be done in something like AA(t1,t2,...,tn) (a trascendental extension of the algebraic reals) or QQ[a](t1,t2,...,tn) with a in AA. But working in those rings can be extremely slow, and you would need in advance which numbers would appear, which are algebraic and which trascendental and so on. So i wouldn't advise it. El miércoles, 12 de marzo de 2014 20:37:00 UTC+1, Eric Gourgoulhon escribió: Thanks for your answer and suggestions. Best wishes, Eric. Le mercredi 12 mars 2014 17:55:46 UTC+1, Nils Bruin a écrit : On Wednesday, March 12, 2014 6:41:07 AM UTC-7, Eric Gourgoulhon wrote: The issue here is that CommutativeRing.__init__ requires the argument base_ring and in the present context, I don't know what to put here: the ring C^oo(N) does not depend upon any other ring. Shall I put self, i.e. write CommutativeRing.__init__(self, self) ? Every ring ultimately has ZZ as a base, by virtue of being an additive group. You could use that. On the other hand, if you expect the thing to be finitely generated over its base then perhaps the ring should be its own base (I don't think that's a formal requirement, given that `ZZ[['x']].base_ring()==ZZ`). This does happen in Sage elsewhere: sage: ZZ.base_ring() Integer Ring sage: QQ.base_ring() Rational Field sage: GF(3).base_ring() Finite Field of size 3 On the other hand, if you find it's doable to avoid specifying a base, perhaps that's the better way to go. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+...@googlegroups.com javascript:. To post to this group, send email to sage-...@googlegroups.comjavascript:. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the
Re: [sage-devel] Re: How to define a new ring class ? [We need a class representing genuine real field]
On Wednesday, March 12, 2014 8:45:57 PM UTC-4, Thierry (sage-googlesucks@xxx) wrote: - create RSF (for real symbolic field) to isolate pi and sqrt(2) from cos(x) in the symbolic ring. Thats essentially what RLF does. - re-create RR as an overlay field over the different representations Its a basic fact that you can't represent a generic real number on a computer. You can argue that one should default to a lazy evaluation and not pick a favorite, but that also means that it'll be useless in practice. You can't safely effectively do floating-point computations without picking a particular representation first. Trying to pretend otherwise is just kidding yourself. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: How to define a new ring class ? [We need a class representing genuine real field]
2014-03-13 21:32 UTC+01:00, Volker Braun vbraun.n...@gmail.com: On Wednesday, March 12, 2014 8:45:57 PM UTC-4, Thierry (sage-googlesucks@xxx) wrote: - create RSF (for real symbolic field) to isolate pi and sqrt(2) from cos(x) in the symbolic ring. Thats essentially what RLF does. Nope, pi belongs to SR and not to RLF and there is a huge difference: sage: RLF(pi) * 1.2 # fine, coercion into RR 3.76991118430775 sage: pi * 1.2# what the f*** ? 1.20*pi The claim was to put all symbolic constants into RLF or CLF or a better ring in order to avoid many problems like this one sage: pi_approx = RR(pi) sage: bool(pi == SR(pi_approx)) True and many, many, many others. - re-create RR as an overlay field over the different representations Its a basic fact that you can't represent a generic real number on a computer. You can argue that one should default to a lazy evaluation and not pick a favorite, but that also means that it'll be useless in practice. You can't safely effectively do floating-point computations without picking a particular representation first. Trying to pretend otherwise is just kidding yourself. Of course, and it was not the argument advanced to redefine RR. Let say that RR is the set of real numbers. Even if there is no way to define general operations or comparisons on its elements, we can still ask * if some element belongs to it (in particular NaN and Infinity do not) * what is its structure as a topological space * what is its cardinality * a random element I would advocate that RLF is a very good approximation of what should be RR. Perhaps one good direction to take is to try to make RLF smarter and contains all constants from pi to cos(42^e). Vincent -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: How to define a new ring class ? [We need a class representing genuine real field]
On Thu, Mar 13, 2014 at 01:32:10PM -0700, Volker Braun wrote:
On Wednesday, March 12, 2014 8:45:57 PM UTC-4, Thierry
(sage-googlesucks@xxx) wrote:
- create RSF (for real symbolic field) to isolate pi and sqrt(2) from
cos(x) in the symbolic ring.
Thats essentially what RLF does.
RLF loses some symbolic (resp. algebraic) information compared to SR:
sage: a = sqrt(2)
sage: a^2
2
sage: b = RLF(a)
sage: b^2
2.000?
sage: b^2 == 2
False
- re-create RR as an overlay field over the different representations
Its a basic fact that you can't represent a generic real number on a
computer. You can argue that one should default to a lazy evaluation and
not pick a favorite, but that also means that it'll be useless in practice.
You can't safely effectively do floating-point computations without
picking a particular representation first. Trying to pretend otherwise is
just kidding yourself.
This is not about floating-point arithmetic nor evaluation, but about a
common parent with some semantics in it.
Not all binary infinite words can be represented by a computer (with the
same countability argument), still Sage proposes a
Words('01', finite=False) parent.
Ciao,
Thierry
--
You received this message because you are subscribed to the Google Groups
sage-devel group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-devel+unsubscr...@googlegroups.com.
To post to this group, send email to sage-devel@googlegroups.com.
Visit this group at http://groups.google.com/group/sage-devel.
For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: How to define a new ring class ? [We need a class representing genuine real field]
On Thu, Mar 13, 2014 at 10:08:05PM +0100, Vincent Delecroix wrote: [...] I would advocate that RLF is a very good approximation of what should be RR. Perhaps one good direction to take is to try to make RLF smarter and contains all constants from pi to cos(42^e). A generalisation of RLF could be real computable numbers (the set of numbers whose digits can be enumerated by a Turing machine). It seems that some usable implementations do exist already. I am not sure one representation should be selected above another. Even if this representation is the most expressive (contains a lot of elements), it is not able to decide equality, while e.g. AA is. Ciao, Thierry -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: How to define a new ring class ? [We need a class representing genuine real field]
On Thursday, March 13, 2014 5:10:53 PM UTC-4, Thierry (sage-googlesucks@xxx) wrote: This is not about floating-point arithmetic nor evaluation, but about a common parent with some semantics in it. Its fine to strive for generality, but I don't think its a good idea to have something particularly prominent in the namespace for which you can't / don't want to create elements. Also, we can't replace RR without breaking lots of existing code or slowing it down to a crawl, so that possibility is pretty much out. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
[sage-devel] Re: How to define a new ring class ?
On Wednesday, March 12, 2014 6:41:07 AM UTC-7, Eric Gourgoulhon wrote: The issue here is that CommutativeRing.__init__ requires the argument base_ring and in the present context, I don't know what to put here: the ring C^oo(N) does not depend upon any other ring. Shall I put self, i.e. write CommutativeRing.__init__(self, self) ? Every ring ultimately has ZZ as a base, by virtue of being an additive group. You could use that. On the other hand, if you expect the thing to be finitely generated over its base then perhaps the ring should be its own base (I don't think that's a formal requirement, given that `ZZ[['x']].base_ring()==ZZ`). This does happen in Sage elsewhere: sage: ZZ.base_ring() Integer Ring sage: QQ.base_ring() Rational Field sage: GF(3).base_ring() Finite Field of size 3 On the other hand, if you find it's doable to avoid specifying a base, perhaps that's the better way to go. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
[sage-devel] Re: How to define a new ring class ?
Thanks for your answer and suggestions. Best wishes, Eric. Le mercredi 12 mars 2014 17:55:46 UTC+1, Nils Bruin a écrit : On Wednesday, March 12, 2014 6:41:07 AM UTC-7, Eric Gourgoulhon wrote: The issue here is that CommutativeRing.__init__ requires the argument base_ring and in the present context, I don't know what to put here: the ring C^oo(N) does not depend upon any other ring. Shall I put self, i.e. write CommutativeRing.__init__(self, self) ? Every ring ultimately has ZZ as a base, by virtue of being an additive group. You could use that. On the other hand, if you expect the thing to be finitely generated over its base then perhaps the ring should be its own base (I don't think that's a formal requirement, given that `ZZ[['x']].base_ring()==ZZ`). This does happen in Sage elsewhere: sage: ZZ.base_ring() Integer Ring sage: QQ.base_ring() Rational Field sage: GF(3).base_ring() Finite Field of size 3 On the other hand, if you find it's doable to avoid specifying a base, perhaps that's the better way to go. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
[sage-devel] Re: How to define a new ring class ?
Since the ring you want will be an algebra over the reals, the best fit for base ring would be the reals. Now, since it is impossible to represent the real field in practice, there are different possible solutions in sage: RR if you don't care about the lack of exactness QQ or some extension (like AA) if you want exactness but don't mind the lack of transcendentals SR if you want to allow arbitrary expressions, with the problem of speed and maybe the lack of a unique form for each element. I don't think that you can do much better than that to work with the reals. In practice, since in every computation there will only be a finite number of symbols involved, it can be done in something like AA(t1,t2,...,tn) (a trascendental extension of the algebraic reals) or QQ[a](t1,t2,...,tn) with a in AA. But working in those rings can be extremely slow, and you would need in advance which numbers would appear, which are algebraic and which trascendental and so on. So i wouldn't advise it. El miércoles, 12 de marzo de 2014 20:37:00 UTC+1, Eric Gourgoulhon escribió: Thanks for your answer and suggestions. Best wishes, Eric. Le mercredi 12 mars 2014 17:55:46 UTC+1, Nils Bruin a écrit : On Wednesday, March 12, 2014 6:41:07 AM UTC-7, Eric Gourgoulhon wrote: The issue here is that CommutativeRing.__init__ requires the argument base_ring and in the present context, I don't know what to put here: the ring C^oo(N) does not depend upon any other ring. Shall I put self, i.e. write CommutativeRing.__init__(self, self) ? Every ring ultimately has ZZ as a base, by virtue of being an additive group. You could use that. On the other hand, if you expect the thing to be finitely generated over its base then perhaps the ring should be its own base (I don't think that's a formal requirement, given that `ZZ[['x']].base_ring()==ZZ`). This does happen in Sage elsewhere: sage: ZZ.base_ring() Integer Ring sage: QQ.base_ring() Rational Field sage: GF(3).base_ring() Finite Field of size 3 On the other hand, if you find it's doable to avoid specifying a base, perhaps that's the better way to go. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: How to define a new ring class ? [We need a class representing genuine real field]
Hi, On Wed, Mar 12, 2014 at 01:29:47PM -0700, mmarco wrote: RR if you don't care about the lack of exactness QQ or some extension (like AA) if you want exactness but don't mind the lack of transcendentals SR if you want to allow arbitrary expressions, with the problem of speed and maybe the lack of a unique form for each element. I don't think that you can do much better than that to work with the reals. One could imagine the following improvement (which i would love, at least to make things easier to learn and teach): - rename RR as RFF (for real floating field), so that this representation is not preferred than the others (especially RDF which is faster and allows using more libraries, with the same 53 bits of precision). The current name RR suggests it is the right default choice. - create RSF (for real symbolic field) to isolate pi and sqrt(2) from cos(x) in the symbolic ring. - re-create RR as an overlay field over the different representations (numeric (RFF, RDF, RIF), algebraic, symbolic) of the genuine real field in Sage. Perhaps could the experience of the community with the category framework help in the design of such a meta-representation. Idem with CFF, CSF, CC for complex numbers. Ciao, Thierry -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
