Re: [sage-support] Those cookies again...

2010-08-23 Thread Alex Ghitza
On Sat, 21 Aug 2010 19:12:49 -0700 (PDT), kcrisman  wrote:
> Sysadmin has found possible workaround of deleting history of the
> browser.  This is fine in a lab, but potentially very crippling for
> those of us who rely on auto-completion of often-visited sites.
> Sysadmin is also very unlikely to try 4.5.2 VMWare image after recent
> reports of it not being so hot, though I think those may have been
> exaggerated - and anyhow he has a lot to do with the start of classes.

I'd say the only way you will know whether 4.5.2 works for you is to try
it out.  The vmware image gets downloaded *a lot* (200 times in the
first 5 days), and as far as I know there were only two problems
reported with it:
* unable to access the notebook from the host machine on Windows
  (this works for me on Mac OS X, and I don't have a Windows machine to
  test on -- someone suggested a workaround on the list but we haven't
  heard the original poster confirm that it fixed his problem)
* request for having R installed with image support; I will look into
  this for 4.5.3, but if this is likely to be important to you, you can
  just install the ubuntu libraries in your copy of the virtual machine

So, I'm not saying that the 4.5.2 vmware image is perfect, but I'm not
convinced it's any worse than 4.3, and once again, you can find out
whether it works for you by trying it out.  Try it out on your computer
first and see if the cookies issue is fixed, and then see if your system
administrator is willing to give it a shot.


Best,
Alex




-- 
Alex Ghitza -- http://aghitza.org/
Lecturer in Mathematics -- The University of Melbourne -- Australia

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[sage-support] Re: tab on an iPad

2010-08-23 Thread Jason Grout

On 8/23/10 1:28 PM, A. Jorge Garcia wrote:

I had a problem with SAGE on my iPod Touch.  Everything worked fine
except for jMol when viewing 3D graphs. jMol requires jre and that is
not installed on Safari. Apparently this is a restriction on the iTouch,
there's no way to install jre for Safari on iTouch. I've seen it
installed on a MacBook Pro, however.

If you don't do 3D graphs, I think you're fine. I just don't know if the
iPad has the same restrictions as the iTouch



Does the iTouch or iPad support WebGL?

See 
https://cvs.khronos.org/svn/repos/registry/trunk/public/webgl/sdk/demos/webkit/SpinningBox.html 
for example.


Thanks,

Jason

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Re: [sage-support] tab on an iPad

2010-08-23 Thread A. Jorge Garcia
yup, I was just alluding to fact that if you use the default viewer 
you're
stuck.  As you say, you can use Tachyon but then you can't rotate the 
3D graphs!


BTW, I know it may sound strange, but I know all about Tachyon as 
that's how I
originally discovered SAGE.  At the time I was playing with 3D ray 
tracers like
Tachyon and povray.  I found a video demoing dSAGE running a povray 
plot and was
instantly hooked on SAGE.  I really should figure out how to distribute 
SAGE

jobs over a cluster

Thanx,
A. Jorge Garcia
http://shadowfaxrant.blogspot.com

--
Sent from my Verizon Wireless mobile phone

--Original Message--
From: kcrisman 
To: "sage-support" 
Date: Mon, Aug 23, 12:04 PM -0700
Subject: [sage-support] Re: tab on an iPad



On Aug 23, 2:28 pm, "A. Jorge Garcia"  wrote:

I had a problem with SAGE on my iPod Touch.  Everything worked fine
except for jMol when viewing 3D graphs.  jMol requires jre and that is
not installed on Safari.  Apparently this is a restriction on the
iTouch, there's no way to install jre for Safari on iTouch.  I've seen
it installed on a MacBook Pro, however.

If you don't do 3D graphs, I think you're fine.  I just don't know if
the iPad has the same restrictions as the iTouch



By the way, 3D graphs *will* work without Java, but you would need to
view them statically.

sage: var('y')
sage: plot3d(x^2 + y^2, (x,-2,2), (y,-2,2),viewer='tachyon')

This is unfortunately buried in the documentation, and not in
sage: plot3d?

- kcrisman

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[sage-support] Re: numerical evaluation

2010-08-23 Thread Jason Bandlow
Hi,

On 08/23/2010 03:42 PM, robin hankin wrote:
> I tried this:
> 
> roots = solve(x^3+10*x^2+11*x+8==0,x)

> 
> The best I can do is
> 
> N(roots[1].rhs())
> 
> but this is just one at a time.  How do I make N() operate on all of roots? 

You may like

for r in roots:
print N(r.rhs())

or

[N(r.rhs()) for r in roots]

Cheers,
Jason

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Re: [sage-support] numerical evaluation

2010-08-23 Thread Soroosh Yazdani
I'm not sure if this helps your situation or not, but if you are
interested in the roots of "f(x)=0", then using roots has a much more
predictable behaviour.
So for example:
sage: expr=(x^3+10*x^2+11*x+8)  
sage: expr.roots()

sage: expr.roots(ring=RR) 
[(-8.86042628425072, 1)]
sage: expr.roots(ring=CC)
[(-8.86042628425072, 1), (-0.569786857874640 - 0.760417012386730*I, 1),
(-0.569786857874640 + 0.760417012386730*I, 1)]

This way, you're giving just enough hint to SAGE to give you exactly
the answer you are looking for.

Soroosh

On Mon, 23 Aug 2010 20:42:39 +0100
robin hankin  wrote:

> Hi
> 
> thanks for your earlier answers.
> 
> I quite often do this:
> 
> sage:  solve(x^3 + 10*x^2+11*x+8==0,x)
> [snip]
> 
> Then I realize that the analytic solution is rather complicated.
> So  I want a numerical approximation.
> 
> I tried this:
> 
> roots = solve(x^3+10*x^2+11*x+8==0,x)
> sage: roots
> [x == -1/2*(1/3*sqrt(926) - 613/27)^(1/3)*(I*sqrt(3) + 1) -
> 1/18*(-67*I*sqrt(3) + 67)/(1/3*sqrt(926) - 613/27)^(1/3) - 10/3, x ==
> -1/2*(1/3*sqrt(926) - 613/27)^(1/3)*(-I*sqrt(3) + 1) -
> 1/18*(67*I*sqrt(3) + 67)/(1/3*sqrt(926) - 613/27)^(1/3) - 10/3, x ==
> (1/3*sqrt(926) - 613/27)^(1/3) + 67/9/(1/3*sqrt(926) - 613/27)^(1/3) -
> 10/3]
> sage: N(roots)
> 
> 
> but this returns an error ("too many values to unpack").
> 
> 
> The best I can do is
> 
> N(roots[1].rhs())
> 
> but this is just one at a time.  How do I make N() operate on all of
> roots? Or is there a much neater way of accomplishing the same thing?
> 
> cheers
> 
> rksh
> 
> 
> 
> 
> 



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[sage-support] Re: How can I make implicit_multiplication default?

2010-08-23 Thread Simon King
Hi Robert,

On 23 Aug., 18:08, Robert Bradshaw 
wrote:
> > ... And on the other hand, I can't see how life with Sage would be
> > any easier if automatic_names was the standard.
>
> Think about someone working through a series of calculus textbook
> exercises (mostly one-liners).

I didn't deny that there are situations where automatic_names is
handy, but I think it wouldn't be good as the default...

> Personally, I wouldn't every want it to
> be default,

... and see that we agree.

> This, and implicit multiplication, should be in the FAQ at least.

Certainly +1!

Cheers,
Simon

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[sage-support] numerical evaluation

2010-08-23 Thread robin hankin
Hi

thanks for your earlier answers.

I quite often do this:

sage:  solve(x^3 + 10*x^2+11*x+8==0,x)
[snip]

Then I realize that the analytic solution is rather complicated.
So  I want a numerical approximation.

I tried this:

roots = solve(x^3+10*x^2+11*x+8==0,x)
sage: roots
[x == -1/2*(1/3*sqrt(926) - 613/27)^(1/3)*(I*sqrt(3) + 1) -
1/18*(-67*I*sqrt(3) + 67)/(1/3*sqrt(926) - 613/27)^(1/3) - 10/3, x ==
-1/2*(1/3*sqrt(926) - 613/27)^(1/3)*(-I*sqrt(3) + 1) -
1/18*(67*I*sqrt(3) + 67)/(1/3*sqrt(926) - 613/27)^(1/3) - 10/3, x ==
(1/3*sqrt(926) - 613/27)^(1/3) + 67/9/(1/3*sqrt(926) - 613/27)^(1/3) -
10/3]
sage: N(roots)


but this returns an error ("too many values to unpack").


The best I can do is

N(roots[1].rhs())

but this is just one at a time.  How do I make N() operate on all of roots?
Or is there a much neater way of accomplishing the same thing?

cheers

rksh





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Uncertainty Analyst
hankin.ro...@gmail.com

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[sage-support] Re: tab on an iPad

2010-08-23 Thread kcrisman


On Aug 23, 2:28 pm, "A. Jorge Garcia"  wrote:
> I had a problem with SAGE on my iPod Touch.  Everything worked fine
> except for jMol when viewing 3D graphs.  jMol requires jre and that is
> not installed on Safari.  Apparently this is a restriction on the
> iTouch, there's no way to install jre for Safari on iTouch.  I've seen
> it installed on a MacBook Pro, however.
>
> If you don't do 3D graphs, I think you're fine.  I just don't know if
> the iPad has the same restrictions as the iTouch
>

By the way, 3D graphs *will* work without Java, but you would need to
view them statically.

sage: var('y')
sage: plot3d(x^2 + y^2, (x,-2,2), (y,-2,2),viewer='tachyon')

This is unfortunately buried in the documentation, and not in
sage: plot3d?

- kcrisman

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Re: [sage-support] tab on an iPad

2010-08-23 Thread A. Jorge Garcia
I had a problem with SAGE on my iPod Touch.  Everything worked fine 
except for jMol when viewing 3D graphs.  jMol requires jre and that is 
not installed on Safari.  Apparently this is a restriction on the 
iTouch, there's no way to install jre for Safari on iTouch.  I've seen 
it installed on a MacBook Pro, however.


If you don't do 3D graphs, I think you're fine.  I just don't know if 
the iPad has the same restrictions as the iTouch


HTH,
A. Jorge Garcia
http://shadowfaxrant.blogspot.com
http://www.youtube.com/calcpage2009

Teacher & Professor
Applied Mathematics, Physics & Computer Science
Baldwin Senior High School & Nassau Community College


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[sage-support] tab on an iPad

2010-08-23 Thread Ken Levasseur
Although I do most of my sage learning on a Mac, I've been playing around with 
using it on an iPad though http://www.sagenb.org/.   It works fine if I know 
what I want to type but I can't do completion, for example because there isn't 
a tab key (I think).  Anybody know of a workaround to that?

Ken Levasseur
UMass Lowell

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Re: [sage-support] Re: How can I make implicit_multiplication default?

2010-08-23 Thread Robert Bradshaw
On Mon, Aug 23, 2010 at 9:08 AM, Robert Bradshaw
 wrote:
> On Mon, Aug 23, 2010 at 6:54 AM, Simon King  wrote:
>> Hi Robin,
>>
>> On 23 Aug., 13:43, robin hankin  wrote:
>>> Re automatic_names(): why isn't this the default?
>>>
>>> Now I know it exists, I think I'll probably use it all the time.
>>>
>>> Who uses sage without this option?
>>
>> I find automatic_names horrible, to say the least! In my opinion, such
>> thing should *never ever* be standard!
>>
>> 1. If you write a little program on the command line and it does
>> something, but simply it doesn't do the right thing or you get strange
>> error messages about missing attributes -- it would be very hard to
>> find out that you forgot to define some object X, so that Sage worked
>> in the wrong assumption that X is a symbolic variable. I strongly
>> prefer to get a clear error message, namely "NameError: Name 'X' is
>> not defined" or so.
>>
>> 2. "Explicit is better than implicit" is a quite common credo. I think
>> it is unsafe to rely on implicit assumptions of the type of an object.
>>
>> 3. I hardly ever work with symbolic variables. So, I really don't see
>> the point why "X" should default to a symbolic variable.
>>
>> 4. My impression is that for quite many people a symbolic variable is
>> the first thing that comes to mind when computing in a CAS - and it
>> takes them a long while until they find that for their particular
>> problem a different class (like a polynomial) works much better.
>> Making a symbolic variable the default, I am afraid that one would
>> support the wrong belief that symbolic variables are good for
>> *everything*.
>>
>>
>> So, it is not so much that programs would break. But debugging would
>> be more difficult, and it would teach the people the wrong lesson,
>> IMHO. And on the other hand, I can't see how life with Sage would be
>> any easier if automatic_names was the standard.
>
> Think about someone working through a series of calculus textbook
> exercises (mostly one-liners). Personally, I wouldn't every want it to
> be default, but can see how some people could really find it useful
> (especially as we're aiming to be a viable alternative to the Ma's.
> Also, note that Python itself has implicit variable declaration (as
> opposed to, say, C, etc.) which has its pros and cons (though I like
> it).
>
> This, and implicit multiplication, should be in the FAQ at least.

One more thing--I find it really handy when I'm pasting in expressions
form elsewhere, e.g. a paper or something. However, rather than enable
the options in the preparser and changing the language, I do


sage: SR("x^2 + 2x - 5y")
x^2 + 2*x - 5*y

This string-level implicit multiplication/variable binding for
polynomial rings too:

sage: R = QQ['x']
sage: R("3x^5 - 2x")
3*x^5 - 2*x

- Robert

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Re: [sage-support] Re: How can I make implicit_multiplication default?

2010-08-23 Thread Robert Bradshaw
On Mon, Aug 23, 2010 at 6:54 AM, Simon King  wrote:
> Hi Robin,
>
> On 23 Aug., 13:43, robin hankin  wrote:
>> Re automatic_names(): why isn't this the default?
>>
>> Now I know it exists, I think I'll probably use it all the time.
>>
>> Who uses sage without this option?
>
> I find automatic_names horrible, to say the least! In my opinion, such
> thing should *never ever* be standard!
>
> 1. If you write a little program on the command line and it does
> something, but simply it doesn't do the right thing or you get strange
> error messages about missing attributes -- it would be very hard to
> find out that you forgot to define some object X, so that Sage worked
> in the wrong assumption that X is a symbolic variable. I strongly
> prefer to get a clear error message, namely "NameError: Name 'X' is
> not defined" or so.
>
> 2. "Explicit is better than implicit" is a quite common credo. I think
> it is unsafe to rely on implicit assumptions of the type of an object.
>
> 3. I hardly ever work with symbolic variables. So, I really don't see
> the point why "X" should default to a symbolic variable.
>
> 4. My impression is that for quite many people a symbolic variable is
> the first thing that comes to mind when computing in a CAS - and it
> takes them a long while until they find that for their particular
> problem a different class (like a polynomial) works much better.
> Making a symbolic variable the default, I am afraid that one would
> support the wrong belief that symbolic variables are good for
> *everything*.
>
>
> So, it is not so much that programs would break. But debugging would
> be more difficult, and it would teach the people the wrong lesson,
> IMHO. And on the other hand, I can't see how life with Sage would be
> any easier if automatic_names was the standard.

Think about someone working through a series of calculus textbook
exercises (mostly one-liners). Personally, I wouldn't every want it to
be default, but can see how some people could really find it useful
(especially as we're aiming to be a viable alternative to the Ma's.
Also, note that Python itself has implicit variable declaration (as
opposed to, say, C, etc.) which has its pros and cons (though I like
it).

This, and implicit multiplication, should be in the FAQ at least.

- Robert

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[sage-support] Re: Those cookies again...

2010-08-23 Thread kcrisman
Wow, I really didn't expect to open this discussion with that post.

> I expect Sage upgrades will slip further down your system admin's priority 
> list
> if they are causing him problems.

Though he's actually quite Sage-friendly, and sounds like he'll do
it.  The only issue was

> > I am really hesitant
> > to use this in class when I can't even make it work on my own computer
> > properly.
>
> I don't blame you.

Though again, I am personally quite likely to just find a way about
it, since I've invested so much in Sage.

> === From Peter Jeremy ===
> I am very concerned at this "release it now, we'll make it work later" 
> mentality.
> ===
> The only possible way Sage might get less buggy, is for more people with 
> similar
> views to me, make them known to William. *Perhaps*, if he realises people like
> you are reluctant to use Sage for classes because of the bug rates, he might 
> do
> something to address the quality control issues.
>

Well, in general it seems to me that most Sage bugs come from things/
functionality that didn't exist before, and once they exist people
want to start using them.  But unlike a commercial system, the only
realistic way we have to look for these bugs is for people to use the
system.  I just don't see how else to do it; I don't think most Sage
developers necessarily use the latest bleeding-edge release for day-to-
day stuff.  For instance, I have a modified R optional package
installed on one of my Sage installs, and since getting that to play
nice on every new Sage would be tedious and boring, I just keep
sage-4.4.4 on my laptop for research only. Similarly for classroom use
- one usually uses the same server all semester, so there isn't
opportunity to see *new* bugs.

> ===
> in a suitably complex system there is a certain irreducible number of errors.
> Any attempt to fix observed errors tends to result in the introduction of 
> other
> errors
> ===

I think that while there are certainly some bugs that really don't
satisfy this, there are plenty of bugfixes that introduce new errors
in Sage - it is easily that complex.  However, these usually result as
a result of uncovering some hitherto non-existent (or possibly non-
wrapped) functionality which turns out to have bugs, which will only
be uncovered by "real" users.

So actually, I find the release early and often mantra to be helpful,
because it helps make it better; finding edge cases is much less
likely to happen without a full-time team of dedicated staff
otherwise.  I think that even some randomized test suite is not so
likely to find things unless it starts just entering random valid Sage
commands, even ones that don't make sense to a "real" user.

And I don't think there is a lack of attention to fixing bugs; every
release is a bug-fix release.  It is also a new-functionality release
- which yes, introduces bugs, but not ones that would have even been
visible before.

- kcrisman

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[sage-support] Re: Those cookies again...

2010-08-23 Thread Simon King
PS:

On 23 Aug., 12:55, Simon King  wrote:
> ...
> My impression is that the Sage development process is quite far from
> that way of thinking.

... or perhaps it is not so much the way of thinking?
I would expect that Python has a lot more person power than Sage. How
many people do release management for Python?

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[sage-support] Re: How can I make implicit_multiplication default?

2010-08-23 Thread Simon King
Hi Robin,

On 23 Aug., 13:43, robin hankin  wrote:
> Re automatic_names(): why isn't this the default?
>
> Now I know it exists, I think I'll probably use it all the time.
>
> Who uses sage without this option?

I find automatic_names horrible, to say the least! In my opinion, such
thing should *never ever* be standard!

1. If you write a little program on the command line and it does
something, but simply it doesn't do the right thing or you get strange
error messages about missing attributes -- it would be very hard to
find out that you forgot to define some object X, so that Sage worked
in the wrong assumption that X is a symbolic variable. I strongly
prefer to get a clear error message, namely "NameError: Name 'X' is
not defined" or so.

2. "Explicit is better than implicit" is a quite common credo. I think
it is unsafe to rely on implicit assumptions of the type of an object.

3. I hardly ever work with symbolic variables. So, I really don't see
the point why "X" should default to a symbolic variable.

4. My impression is that for quite many people a symbolic variable is
the first thing that comes to mind when computing in a CAS - and it
takes them a long while until they find that for their particular
problem a different class (like a polynomial) works much better.
Making a symbolic variable the default, I am afraid that one would
support the wrong belief that symbolic variables are good for
*everything*.


So, it is not so much that programs would break. But debugging would
be more difficult, and it would teach the people the wrong lesson,
IMHO. And on the other hand, I can't see how life with Sage would be
any easier if automatic_names was the standard.

Cheers,
Simon

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Re: [sage-support] Re: How can I make implicit_multiplication default?

2010-08-23 Thread robin hankin
Hello

thanks for this.  I liked the preparser manpage that Simon pointed me to.

Re automatic_names(): why isn't this the default?

Now I know it exists, I think I'll probably use it all the time.

Who uses sage without this option?

Or, more precisely, can anyone give me an example of a way
of working with sage that this option will break?  I'm hoping
to understand why you expert sage users chose the default
as you did.

best wishes


Robin



On Mon, Aug 23, 2010 at 12:07 PM, Simon King  wrote:
> Hi Robin,
>
> On 23 Aug., 12:58, robin hankin  wrote:
>> But, if I didn't know it existed, how could I possibly have found it?
>> (give me a pointer to a FAQ!)
>
> I just tried to find it in the FAQ, but without success.
>
> Anyway. If you know  that it is called implicit_multiplication then
> you can do
>  sage: implicit_multiplication?
> to see the documentation, or consult the manual, e.g., at
> http://www.sagemath.org/doc/reference/sage/misc/preparser.html#sage.misc.preparser.implicit_multiplication
>
> Of course, the manuals can also be searched.
>
> Cheers,
> Simon
>
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Robin Hankin
Uncertainty Analyst
hankin.ro...@gmail.com

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[sage-support] Re: How can I make implicit_multiplication default?

2010-08-23 Thread Simon King
Hi Robin,

On 23 Aug., 12:58, robin hankin  wrote:
> But, if I didn't know it existed, how could I possibly have found it?
> (give me a pointer to a FAQ!)

I just tried to find it in the FAQ, but without success.

Anyway. If you know  that it is called implicit_multiplication then
you can do
  sage: implicit_multiplication?
to see the documentation, or consult the manual, e.g., at
http://www.sagemath.org/doc/reference/sage/misc/preparser.html#sage.misc.preparser.implicit_multiplication

Of course, the manuals can also be searched.

Cheers,
Simon

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Re: [sage-support] Re: How can I make implicit_multiplication default?

2010-08-23 Thread robin hankin
Hello everybody


>> > implicit_multiplication is very time-saving, and a much more natural way
>> > to write things. I'd love it to be default.


Wow, implicit_multiplication(True) is *exactly* what I have been looking for.
I have tried it just now, and it is brill.

OK, my question:  Now that I know implicit_multiplication() exists,
I can search for it and get documentation about it.

But, if I didn't know it existed, how could I possibly have found it?
(give me a pointer to a FAQ!)

best wishes

rksh


-- 
Robin Hankin
Uncertainty Analyst
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[sage-support] Re: Those cookies again...

2010-08-23 Thread Simon King
Hi All!

Shouldn't this discussion better go to sage-devel?

On 22 Aug., 22:01, "Dr. David Kirkby"  wrote:
> ...
> http://www.python.org/dev/peps/pep-0006/

Quoting from this source:
"In general, only the N-1 release will be under active maintenance at
any time. That is, during Python 2.4's development, Python 2.3
gets
bugfix releases."

I see that simultaneously, there is work on Python 2.6.6 final (to
appear tomorrow) and Python 3.2 alpha2 (to appear September 5th).

My impression is that the Sage development process is quite far from
that way of thinking.

First of all, is there in Sage the concept of "maintenance" of a
previous version? Usually, if people hit a problem with, say,
sage-4.4, then they are told that they use a bronze age version and
should upgrade to the *latest* version sage-4.5.2. According to the
above quote, one would rather say "upgrade to bugfix release
sage-4.4.3".

So, in a way, only one Sage version is actively maintained at a time,
namely always the latest version.

If I remember correctly, there recently was a thread (sage-devel?)
about the role of milestones in the Sage trac. My impression is that
people virtually always choose the earliest possibility in the
"milestone" menue. Having bugfix releases would require a change of
attitude. People should tick 4.5.3 *only* if they have a bugfix.
Otherwise, they should tick 4.6 or 5.0. But then it may even be worth
to change the milestone menu. Perhaps:
  "bugfix only" (without mentioning a number, as this will always go
into the earliest possible release),
  "minor addition: 4.5.3" (There is no change in existing code and
little new code, so, it may be safe to consider early inclusion - but
care has to be taken, as it is more than a bugfix)
  "minor addition: 4.5.4" (dito)
  "major addition: 4.6" (There is much testing required, as there is
change in old code or there is much new code)
  "critical change: 5.x" (in contrast to an addition, a change might
not be fully compatible with Sage-4.x and will thus not go in before
version 5.0)

At this point, a question on the current milestones: What is the
meaning of the milestones "sage-invalid/duplicate/wontfix" and "sage-
i18n"? The former looks more like a resolution (not a milestone) of a
ticket, and the latter is totally obscure to me.

Cheers,
Simon

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Re: [sage-support] Re: solve() problem

2010-08-23 Thread robin hankin
Hello everyone

thanks for the help here.

In Mathematica,  Reduce[] works like Solve, except that it returns a
Boolean  list of possible solutions.  I use it to check what
the necessary  conditions for the"real"  solution to work:

MMA> Reduce[a*x == b, {x}]

MMA>  (b == 0 && a == 0) || (a != 0 && x == b/a)


best wishes

rksh




On Fri, Aug 20, 2010 at 1:14 AM, kcrisman  wrote:
>
>
> On Aug 19, 5:39 pm, robin hankin  wrote:
>> Hello Simon
>>
>> thanks for this. One problem
>> with the solution you mention is that I can't do the
>> general case.  What I need is the sage equivalent
>> of mathematica's Reduce[] function.
>>
>
> I think that solve() is the closest that comes to this (though
> admittedly I am no Mma expert).
>
> It turns out that even in Maxima straight up, this doesn't work
> (either with solve() or to_poly_solve()).  I think maybe it doesn't
> know how to handle the conjugate() piece. There are however a lot of
> solvers in Maxima, so it's possible that one of them will do it
> (perhaps with a certain flag set.  You're also right that doing the
> general case doesn't quite work - even if one puts that
> p^2+q^2==r^2+s^2, so to speak.
>
> I've wanted to put more work into exposing Maxima functionality like
> this but have not been able make the time, because if we're going to
> hook in deeper we need to do it right.  But solving non-linear systems
> like this is probably one of the places we'd like to improve the most.
>
>
> - kcrisman
>
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-- 
Robin Hankin
Uncertainty Analyst
hankin.ro...@gmail.com

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