[sage-support] Re: Partial Fraction Expansion for Polynomials with complex factors
If the factors are complex conjugates then it is already in partial fraction form. On Thursday, August 1, 2013 1:50:32 PM UTC+8, Rakhi Warriar wrote: > > I have the following function: > > f(x) = 1 > > x^2 + 4*x + 13 > > I need to find its partial fraction expansion. As the factors are complex > conjugates, I am not able to do using partial_fraction(). How can I find > this? > > Commands: > x = CC['x'].0 > f = 1/(x^2 + 4*x+ 13) > f.partial_fraction() > this gives error: > Traceback (click to the left of this block for traceback) > ... > AttributeError: 'FractionFieldElement_1poly_field' object has no > attribute 'partial_fraction' > > System used: Ubuntu 12.04, 32 bit, Intel Core i5 procesor > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
[sage-support] Re: Partial Fraction Expansion for Polynomials with complex factors
On Thursday, August 1, 2013 1:50:32 AM UTC-4, Rakhi Warriar wrote: > I have the following function: > > f(x) = 1 > > x^2 + 4*x + 13 > > I need to find its partial fraction expansion. As the factors are complex > conjugates, I am not able to do using partial_fraction(). How can I find > this? > > Commands: > x = CC['x'].0 > f = 1/(x^2 + 4*x+ 13) > f.partial_fraction() > this gives error: > Traceback (click to the left of this block for traceback) > ... > AttributeError: 'FractionFieldElement_1poly_field' object has no > attribute 'partial_fraction' > With Sage 5.10: sage: P.=CC[] sage: f=1/(x^2+4*x+13) sage: f 1.00/(x^2 + 4.00*x + 13.0) sage: f.partial_fraction_decomposition() (0, [(-0.167*I)/(x + 2.00 - 3.00*I), 0.167*I/(x + 2.00 + 3.00*I)]) sage: f.partial_fraction_decomposition()[1] [(-0.167*I)/(x + 2.00 - 3.00*I), 0.167*I/(x + 2.00 + 3.00*I)] sage: sum(f.partial_fraction_decomposition()[1]) 1.00/(x^2 + 4.00*x + 13.0) sage: f == sum(f.partial_fraction_decomposition()[1]) True sage: -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
[sage-support] Re: Partial Fraction Expansion for Polynomials with complex factors
Thanks rickhg12hs. Rakhi On Thursday, August 1, 2013 1:28:53 PM UTC+5:30, rickhg12hs wrote: > > On Thursday, August 1, 2013 1:50:32 AM UTC-4, Rakhi Warriar wrote: > >> I have the following function: >> >> f(x) = 1 >> >> x^2 + 4*x + 13 >> >> I need to find its partial fraction expansion. As the factors are complex >> conjugates, I am not able to do using partial_fraction(). How can I find >> this? >> >> Commands: >> x = CC['x'].0 >> f = 1/(x^2 + 4*x+ 13) >> f.partial_fraction() >> this gives error: >> Traceback (click to the left of this block for traceback) >> ... >> AttributeError: 'FractionFieldElement_1poly_field' object has no >> attribute 'partial_fraction' >> > With Sage 5.10: > > sage: P.=CC[] > sage: f=1/(x^2+4*x+13) > sage: f > 1.00/(x^2 + 4.00*x + 13.0) > sage: f.partial_fraction_decomposition() > (0, > [(-0.167*I)/(x + 2.00 - 3.00*I), > 0.167*I/(x + 2.00 + 3.00*I)]) > sage: f.partial_fraction_decomposition()[1] > [(-0.167*I)/(x + 2.00 - 3.00*I), > 0.167*I/(x + 2.00 + 3.00*I)] > sage: sum(f.partial_fraction_decomposition()[1]) > 1.00/(x^2 + 4.00*x + 13.0) > sage: f == sum(f.partial_fraction_decomposition()[1]) > True > sage: > > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
[sage-support] Re: Disturbing Equality (from askSAGE)
No - because sqrt is multivalued, the answer can be, and in this case is, > multivalued: sometimes true and sometimes false. This isn't desperately > helpful, or course, and can be cast in other ways in terms of the defect > > If a boolean is "sometimes true and sometimes false" it is false and that is what I want sage to give back. Sage does not have "multi-valued booleans" I believe. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-support] Re: Disturbing Equality (from askSAGE)
On 1 August 2013 11:10, chris wuthrich wrote:
>
>
>> No - because sqrt is multivalued, the answer can be, and in this case is,
>> multivalued: sometimes true and sometimes false. This isn't desperately
>> helpful, or course, and can be cast in other ways in terms of the defect
>>
> If a boolean is "sometimes true and sometimes false" it is false and that is
> what I want sage to give back. Sage does not have "multi-valued booleans" I
> believe.
I mostly agree, but in the following:
sage: var('a b')
(a, b)
sage: bool(a==a)
True
sage: bool(a==a+1)
False
sage: bool(a==a*a)
False # bad? it is True for a=0,1
sage: bool(b*a==a*b)
True
sage: bool((a+b)^2==a^2+2*a*b+b^2)
True
sage: bool(sqrt(a)^2==a)
True #bad? is is False for all a<0
I don't like seeing True unless the expression is a tautology, i.e. an
identity, and I don't like seeing False unless it is always false (the
negation of a tautology. This is a different questions from the one
about branches of sqrt.
I try to avoid using symbolic expressions at all costs because of
things like this. After setting x = a==a+1 os that x has type
sage.symbolic.expression.Expression we have bool(x) is False, but I
don't know how bool(x) is evaluated. The documentation says that
bool(x) returns False because x is not always True, but
bool(x.negation()) is True even though x.negation() is 'a != a^2'
which is *not* always True. So that is surely a bug, anyway.
John
>
>
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Re: [sage-support] Re: Disturbing Equality (from askSAGE)
probably this is the same:
(rhs - lhs).full_simplify()
returns zero for wrong stuff.
On Thu, Aug 01, 2013 at 12:11:06PM +0100, John Cremona wrote:
> On 1 August 2013 11:10, chris wuthrich wrote:
> >
> >
> >> No - because sqrt is multivalued, the answer can be, and in this case is,
> >> multivalued: sometimes true and sometimes false. This isn't desperately
> >> helpful, or course, and can be cast in other ways in terms of the defect
> >>
> > If a boolean is "sometimes true and sometimes false" it is false and that is
> > what I want sage to give back. Sage does not have "multi-valued booleans" I
> > believe.
>
> I mostly agree, but in the following:
>
> sage: var('a b')
> (a, b)
> sage: bool(a==a)
> True
> sage: bool(a==a+1)
> False
> sage: bool(a==a*a)
> False # bad? it is True for a=0,1
> sage: bool(b*a==a*b)
> True
> sage: bool((a+b)^2==a^2+2*a*b+b^2)
> True
> sage: bool(sqrt(a)^2==a)
> True #bad? is is False for all a<0
>
> I don't like seeing True unless the expression is a tautology, i.e. an
> identity, and I don't like seeing False unless it is always false (the
> negation of a tautology. This is a different questions from the one
> about branches of sqrt.
>
> I try to avoid using symbolic expressions at all costs because of
> things like this. After setting x = a==a+1 os that x has type
> sage.symbolic.expression.Expression we have bool(x) is False, but I
> don't know how bool(x) is evaluated. The documentation says that
> bool(x) returns False because x is not always True, but
> bool(x.negation()) is True even though x.negation() is 'a != a^2'
> which is *not* always True. So that is surely a bug, anyway.
>
> John
>
> >
> >
> > --
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> >
> >
>
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Re: [sage-support] Re: Disturbing Equality (from askSAGE)
On Thu, Aug 01, 2013 at 05:32:29PM +0300, Georgi Guninski wrote: > probably this is the same: > (rhs - lhs).full_simplify() > returns zero for wrong stuff. > > .full_simplify() appears better than bool: sage: ex=a*a-a sage: ex.full_simplify() a^2 - a sage: (sqrt(a)^2-a).full_simplify() 0 -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
[sage-support] Re: Sage Notebook, Chrome Browser, & SELinux Alert
On 2013-07-30, Jason Grout wrote: > On 7/29/13 8:11 PM, rickhg12hs wrote: >> Sage 5.10 Notebook, Fedora 17 with SELinux set to Enforcing. >> >> SELinux is preventing /opt/google/chrome/chrome from 'write' >> accesses on the directory /home/MyHomeDir/.sage. >> >> Is this expected? Should I allow write access by creating a local >> exception for SELinux? >> > > I can't imagine why Chrome needs access to ~/.sage. isn't it where the Sage notebook files are kept? Dima > > Jason > > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
[sage-support] Re: Sage Notebook, Chrome Browser, & SELinux Alert
On 8/1/13 1:22 PM, Dima Pasechnik wrote: On 2013-07-30, Jason Grout wrote: On 7/29/13 8:11 PM, rickhg12hs wrote: Sage 5.10 Notebook, Fedora 17 with SELinux set to Enforcing. SELinux is preventing /opt/google/chrome/chrome from 'write' accesses on the directory /home/MyHomeDir/.sage. Is this expected? Should I allow write access by creating a local exception for SELinux? I can't imagine why Chrome needs access to ~/.sage. isn't it where the Sage notebook files are kept? Yes, but the browser shouldn't be changing those. All changes should be shuttled through the backend webserver. Jason -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
[sage-support] Re: configuring tachyon's camera center
On Wednesday, July 31, 2013 4:09:45 PM UTC-7, Oscar Lazo wrote:
>
> Hello dear sage users!
>
> I would like to view a 3d plot from a specific viewpoint using tachyon.
>
It requires a bit of surgery. Presently, viewpoint and direction are not
part of the configurable scenery parameters (and they clearly should be).
The just get hard-wired into the input to tachyon. You can intercept the
scenery string, however, and edit it to your liking before sending it to
the raytracer:
var('s')
spiral=parametric_plot3d((cos(s),sin(s),s/8),
(s,-16*pi,16*pi),aspect_ratio=1,plot_points=200)
S=spiral.tachyon()
S=S.replace('center 2.3 2.4 2.0','center 0.0 0.0 0.0')
S=S.replace('viewdir -2.3 -2.4 -2.0','viewdir 0.0 1.0 1.0')
tachyon_rt(S)
in the notebook, this now just displays. From the command line, you'd have
to view the just produced `sage.png`.
Be careful. for non-standard viewing directions, you may have to add some
backdrop planes to avoid looking into a big black abyss.
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