[sage-support] Plotting gamma function
Hi all, I'm a SAGE newbie, (but I have experience with python). In the sage reference manual is the example: P = plot(cos, -5, 5, thickness=5, rgbcolor=(0.5,1,0.5)) P # show it which works just fine, but if I replace "cos" with "gamma": P = plot(gamma, -5, 5, thickness=5, rgbcolor=(0.5,1,0.5)) P # show it I get: Exception (click to the left for traceback):P # show it ... TypeError: 'float' object is unsubscriptable Why can't I plot the gamma function??? Thanks for any light you shine on this, Jim Clark --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: clearing the denominator of a rational polynomial
Thank you Justin and Carl. Martin Albrecht came up with a solution:
sage: Z.numerator().reduce(I2)
0
David
On Mar 6, 6:32 pm, Carl Witty <[EMAIL PROTECTED]> wrote:
> On Mar 6, 11:20 am, David <[EMAIL PROTECTED]> wrote:
>
> > I am trying to use the reduce() command on a rational pollynomial. I
> > first clear the denominator by multiplying by the denominator but when
> > I use reduce() I get an error. When I print out the polynomial it is
> > no longer rational but SAGE doesn't like it. I would appriciate any
> > advice. Below is an example script with ouput. Thank you.
>
> The resulting polynomial does not print as rational, but Sage still
> considers it to be a rational polynomial with denominator 1. (You can
> see this by printing parent(Z).)
>
> The general principle for this sort of situation in Sage is that you
> should be able to get the polynomial you want by treating your ring as
> a function and calling your rational polynomial; that is, I would
> expect R1(Z) to give you your polynomial. Unfortunately, it doesn't;
> I've reported this as a bug here:http://sagetrac.org/sage_trac/ticket/2411
>
> Instead, there's a somewhat ugly workaround you can use: R1(str(Z))
> converts your polynomial to a string, then parses it again, giving you
> a polynomial in the correct ring. And R1(str(Z)).reduce(I2) returns
> 0.
>
>
>
>
>
> > Untitled
> > system:sage
>
> > {{{id=0|
> > R1 = PolynomialRing(RationalField(),9,
> > ["x0","x1","x2","y0","y1","y2","a0","a1","a2"], "lex")
> > x0,x1,x2,y0,y1,y2,a0,a1,a2=R1.gens()
> > X=[
> > x0*y0 - x2*y1 + x1*y2,
> > a2*y0 + a1*y1 - a0*y2,
> > a1*x0 - a0*x1 - a2*x2
> > ]
> > I=R1.ideal(X)
> > I2 = I.groebner_basis()
> > print X[2].reduce(I2)
> > Y=X[2]/a1
> > Z=a1*Y
> > print Z
> > print Z.reduce(I2)
> > ///
>
> > 0
>
> > -x1*a0 + x0*a1 - x2*a2
>
> > Traceback (most recent call last):
> > File "", line 1, in
> > File "/home/notebook/sage_notebook/worksheets/admin/61/code/3.py",
> > line 17, in
> > exec compile(ur'print Z.reduce(I2)' + '\n', '', 'single')
> > File "/usr/local/sage/data/extcode/sage/", line 1, in
>
> > TypeError: reduce() takes exactly 1 argument (2 given)
>
> > }}}
>
> > {{{id=1|
>
> > }}}
>
> Carl- Hide quoted text -
>
> - Show quoted text -
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[sage-support] Re: MAC PC configuration problem.
Yi Qiang wrote:
> The problem is that the notebook is never launched to bound to a
> specific interface. Could you please file a trac# against this?
>
> The specific issue is that in twistedconf.tac, we start the server like so:
>
> strports.service('tls:8000:privateKey=/Users/yqiang/.sage/notebook/private.pem:certKey=/Users/yqiang/.sage/notebook/public.pem',
>
> factory)
>
> It should read something like
>
> strports.service('tls:8000:interface=127.0.0.1:privateKey=/Users/yqiang/.sage/notebook/private.pem:certKey=/Users/yqiang/.sage/notebook/public.pem',
>
> factory)
>
> to only listen on localhost.
>
> Someone more familiar with the notebook should probably write the patch,
> since the behavior of this should depend on what the user specifies when
> launching the notebook.
>
> Cheers,
> Yi
Yi and William,
I just posted a patch up at http://trac.sagemath.org/sage_trac/ticket/2423
Could one of you review it? It seems to solve the problem for me and
allows notebook(address=whatever) to work as expected as well.
Jason
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[sage-support] Re: Set question
On Fri, Mar 7, 2008 at 10:57 AM, William Stein <[EMAIL PROTECTED]> wrote: > > On Fri, Mar 7, 2008 at 7:35 AM, David Joyner <[EMAIL PROTECTED]> wrote: > > > > Hi: > > Is there a reason why Set only applies to hashable elements? > > Set is implemented using the Python language's builtin set type, which > in turn requires that elements by hashable. Since SAGE's uniq also required the elements to be hashable, I wonder if anyone things that the above routine should replace it? > > > > It is faster than > > http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/52560 > > at removing duplicates from a list (which is what I need) but does not > > apply, for example, to lists of matrices: > > FYI -- If you make the matrices immutable then you can hash them. Thanks. > > > > > > > > sage: MS = MatrixSpace(GF(7),2,2) > > sage: A = MS.identity_matrix() > > sage: B = 2*A > > sage: L = [A,A,B] > > sage: Set(L) > > > --- > > Traceback (most recent call > last) > > > > /mnt/drive_hda1/sagefiles/sage-2.10.3.rc2/ in () > > > > > /home/wdj/wdj/sagefiles/sage-2.10.3.rc2/local/lib/python2.5/site-packages/sage/sets/set.py > > in Set(X) > > 78 raise TypeError, "Element has no defined underlying set" > > 79 elif isinstance(X, (list, tuple, set, frozenset)): > > ---> 80 return Set_object_enumerated(frozenset(X)) > > 81 try: > > 82 if X.is_finite(): > > > > /mnt/drive_hda1/sagefiles/sage-2.10.3.rc2/matrix_modn_dense.pyx in > > sage.matrix.matrix_modn_dense.Matrix_modn_dense.__hash__() > > > > /mnt/drive_hda1/sagefiles/sage-2.10.3.rc2/matrix_dense.pyx in > > sage.matrix.matrix_dense.Matrix_dense._hash() > > > > : mutable matrices are unhashable > > > > > > - David Joyner > > > > > > > > > > > -- > William Stein > Associate Professor of Mathematics > University of Washington > http://wstein.org > > > > --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Set question
On Fri, Mar 7, 2008 at 7:35 AM, David Joyner <[EMAIL PROTECTED]> wrote: > > Hi: > Is there a reason why Set only applies to hashable elements? Set is implemented using the Python language's builtin set type, which in turn requires that elements by hashable. > It is faster than > http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/52560 > at removing duplicates from a list (which is what I need) but does not > apply, for example, to lists of matrices: FYI -- If you make the matrices immutable then you can hash them. > > > sage: MS = MatrixSpace(GF(7),2,2) > sage: A = MS.identity_matrix() > sage: B = 2*A > sage: L = [A,A,B] > sage: Set(L) > --- > Traceback (most recent call last) > > /mnt/drive_hda1/sagefiles/sage-2.10.3.rc2/ in () > > > /home/wdj/wdj/sagefiles/sage-2.10.3.rc2/local/lib/python2.5/site-packages/sage/sets/set.py > in Set(X) > 78 raise TypeError, "Element has no defined underlying set" > 79 elif isinstance(X, (list, tuple, set, frozenset)): > ---> 80 return Set_object_enumerated(frozenset(X)) > 81 try: > 82 if X.is_finite(): > > /mnt/drive_hda1/sagefiles/sage-2.10.3.rc2/matrix_modn_dense.pyx in > sage.matrix.matrix_modn_dense.Matrix_modn_dense.__hash__() > > /mnt/drive_hda1/sagefiles/sage-2.10.3.rc2/matrix_dense.pyx in > sage.matrix.matrix_dense.Matrix_dense._hash() > > : mutable matrices are unhashable > > > - David Joyner > > > > -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Set question
Hi: Is there a reason why Set only applies to hashable elements? It is faster than http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/52560 at removing duplicates from a list (which is what I need) but does not apply, for example, to lists of matrices: sage: MS = MatrixSpace(GF(7),2,2) sage: A = MS.identity_matrix() sage: B = 2*A sage: L = [A,A,B] sage: Set(L) --- Traceback (most recent call last) /mnt/drive_hda1/sagefiles/sage-2.10.3.rc2/ in () /home/wdj/wdj/sagefiles/sage-2.10.3.rc2/local/lib/python2.5/site-packages/sage/sets/set.py in Set(X) 78 raise TypeError, "Element has no defined underlying set" 79 elif isinstance(X, (list, tuple, set, frozenset)): ---> 80 return Set_object_enumerated(frozenset(X)) 81 try: 82 if X.is_finite(): /mnt/drive_hda1/sagefiles/sage-2.10.3.rc2/matrix_modn_dense.pyx in sage.matrix.matrix_modn_dense.Matrix_modn_dense.__hash__() /mnt/drive_hda1/sagefiles/sage-2.10.3.rc2/matrix_dense.pyx in sage.matrix.matrix_dense.Matrix_dense._hash() : mutable matrices are unhashable - David Joyner --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Bug converting real numbers to integers?
On Mar 7, 12:42 am, Nikos Apostolakis <[EMAIL PROTECTED]> wrote: > Carl Witty <[EMAIL PROTECTED]> writes: > > Didier mentioned floor(); if you actually want to round, instead of > > taking the floor, then this works (even though it's a little verbose): > > sage: ZZ((num*100).round()) > > I thought that `floor' is what I was looking for: I want to get the > integer that appears in screen as output to the command > > sage: RealField(12).random_element(1,9.99)*100 > > as an element of ZZ. However this doesn't seem to work in all > cases! For example: > > , > | sage: foo = RealField(16).random_element(20,99.99)*100 > | sage: foo > | 2036. > | sage: floor(foo) > | 2035 > | sage: foo.round() > | 2036. > ` You can see the exact true value of a floating-point number with foo.exact_rational(). For printing, the code determines a number of digits which is (deliberately) slightly too low to represent floating-point numbers of that precision; then it rounds to the nearest printable value. For example, 1.0/49*49 prints as 1.00, even though the floating-point number you get is actually 9007199254740991/9007199254740992 or 0.99988897769753748434595763683319091796875 . You can see the number printed with enough digits to distinguish adjacent floating-point numbers like this: sage: (1.0/49*49).str(truncate=False) '0.99989' floor gives the greatest integer which is <= the given floating-point number: sage: floor(1.0/49*49) 0 round gives the integer which is closest to the given floating-point number: sage: round(1.0/49*49) 1.00 except that it gives that integer in the form of a floating-point number. (IMHO, this is a bug, which I've reported here: http://trac.sagemath.org/sage_trac/ticket/2421) This rounding-off when printing floating-point numbers was supposed to reduce confusion for people who don't care about floating-point numbers, and who would be surprised (and would complain) if 1.0/49*49 did not print as 1.0. Unfortunately, as in your case, this comes at the cost of increasing confusion for people who do care about floating- point numbers; I don't know how to decide if the tradeoff is worth it. Carl --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Bug converting real numbers to integers?
Carl Witty <[EMAIL PROTECTED]> writes:
> On Mar 6, 2:48 pm, Nikos Apostolakis <[EMAIL PROTECTED]> wrote:
>> > I can confirm this. I think numbers are rounded up when they are
>> > printed, which leads to confusion:
>> > {{{
>> > sage: num = RealField(12).random_element(1,9.99)*100
>> > sage: num
>> > 406.
>> > }}}
>>
>> > But num is actually ~405.725! :
>> > {{{
>> > sage: num -406
>> > -0.375
>>
>> > }}}
>>
>> > And so ZZ(num) will fail, as it should, since num ~ 405.725.
>>
>> Hm, I see! This behavior is very confusing. Wouldn't you say it *is*
>> a bug?
>
> I'm not sure which part you're talking about: are you complaining that
> this particular number prints as an integer even though it isn't
> exactly, or that coercion to ZZ fails?
>
I guees the former. I found it confusing that *all* numbers that
one gets by doing
sage: RealField(12).random_element(1,9.99)*100
appear to be integers, while in fact are not. I would expect that
if something looks like an integer then it should be able to be
coerced to be an integer. So, I guess, I am complaining for the
latter as well :).
> For the former, I disclaim responsibility. :) The decision to round-
> off floating-point numbers was made before I started working on Sage;
> I don't really care one way or the other.
>
> For the latter: I think that coercion to ZZ should fail. Regardless
> of how the number prints, it really is not an integer.
>
>> Anyway to get what I expected to get I can do something like
>>
>> sage: Integer(sage_eval(str(num))*100)
>> 318
>>
>> but it seems like an ugly hack. Is there another way?
>
> Didier mentioned floor(); if you actually want to round, instead of
> taking the floor, then this works (even though it's a little verbose):
> sage: ZZ((num*100).round())
I thought that `floor' is what I was looking for: I want to get the
integer that appears in screen as output to the command
sage: RealField(12).random_element(1,9.99)*100
as an element of ZZ. However this doesn't seem to work in all
cases! For example:
,
| sage: foo = RealField(16).random_element(20,99.99)*100
| sage: foo
| 2036.
| sage: floor(foo)
| 2035
| sage: foo.round()
| 2036.
`
I feel very confused. Perhaps I should get some sleep :(
Nikos
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[sage-support] Re: Error related with singular, gap and resultant
Dear William, On Mar 5, 11:51 pm, "William Stein" <[EMAIL PROTECTED]> wrote: > Regarding whether or not your problem would be a bug, > *anything* that's not obviously supposed to mess up the interfaces > that does mess them up (without a big error appearing) is a bug, > and I want to fix it. I'm really glad if you can reliably replicate the > problem, since that makes it vastly easier to fix. Since there exist at least two computers on which the error can be reproduced, i made it a ticket #2419; i thought it wouldn't hurt. Of course i understand that it is hardly fixable if no developer is able to reproduce it. Yours Simon --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
