I tried to demonstrate Cayley Hamilton in Sage, but failed. Here is what I
tries:
sage: f = function('f')
sage: m = matrix([[f(i,j) for j in range(2)] for i in range(2)])
sage: p=SR[x](m.characteristic_polynomial('x'))
sage: p.subs(x=m)
[(f(0, 0) - x)*(f(1, 1) - x) - f(0, 1)*f(1, 0)
0]
[
I would do something like this:
sage: m = matrix([[var('x%s%s'%(i,j)) for j in range(2)] for i in range(2)]); m
[x00 x01]
[x10 x11]
sage: m.characteristic_polynomial().polynomial(QQ).subs(x=m)
[0 0]
[0 0]
--Mike
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Martin Rubey wrote:
> I tried to demonstrate Cayley Hamilton in Sage, but failed. Here is what I
> tries:
>
Alternatively, you could do everything in polynomial rings:
sage: R.=QQ[]
sage: m=matrix(R, 2, [x1,x2,x3,x4])
sage: m
[x1 x2]
[x3 x4]
sage: m.charpoly()
x^2 + (-x1 - x4)*x - x2*x3 + x1*
Jason Grout <[EMAIL PROTECTED]> writes:
> Martin Rubey wrote:
> > I tried to demonstrate Cayley Hamilton in Sage, but failed. Here is what I
> > tries:
> >
> > sage: f = function('f')
> > sage: m = matrix([[f(i,j) for j in range(2)] for i in range(2)])
> > sage: p=SR[x](m.characteristic_polynom
Martin Rubey wrote:
> I tried to demonstrate Cayley Hamilton in Sage, but failed. Here is what I
> tries:
>
> sage: f = function('f')
> sage: m = matrix([[f(i,j) for j in range(2)] for i in range(2)])
> sage: p=SR[x](m.characteristic_polynomial('x'))
> sage: p.subs(x=m)
>
> [(f(0, 0) - x)*(f(1,
A week older and still not smarter...
Sorry for the noise, but I am still trying to find a way of getting
useful latex output for equations that contain decimal numbers. It
seems that the previous posts passed below the radars of those that
might know the answer, so I am trying to push it to the s
There are a number of interact examples on the wiki (such as the Gram-
Schmidt one at http://wiki.sagemath.org/interact/linear_algebra) that
work around this problem by casting to a field of low precision, for
example doing something like
latex(RealField(8)(0.6))
produces "0.60".
Hope that help
Dear all,
I want to use simplify and pretty_print (or show or latex) to display
pretty equations. However, in some cases, simplify_full() adds a
factor of 1.0 to the equation, which prints as an ugly
1.0 in latex. Is this a bug? Example:
vp = (exp(17.27*x/(x+237.3)));
pretty_print(
On Mon, Nov 17, 2008 at 7:12 AM, Marshall Hampton <[EMAIL PROTECTED]> wrote:
>
> There are a number of interact examples on the wiki (such as the Gram-
> Schmidt one at http://wiki.sagemath.org/interact/linear_algebra) that
> work around this problem by casting to a field of low precision, for
> e
Jason Grout <[EMAIL PROTECTED]> writes:
> > Why is your coefficients different from mine?
>
>
> I specifically asked for the coefficient of "x". You just asked for the
> coefficients, but didn't specify what variable was the variable of your
> polynomial.
OK, I think I understand now: Sage
Martin Rubey wrote:
> Jason Grout <[EMAIL PROTECTED]> writes:
>
>> Martin Rubey wrote:
>>> I tried to demonstrate Cayley Hamilton in Sage, but failed. Here is what I
>>> tries:
>>>
>>> sage: f = function('f')
>>> sage: m = matrix([[f(i,j) for j in range(2)] for i in range(2)])
>>> sage: p=SR[x](
If a is your real number, and then a._latex_?? will point you in the
direction that you need to go. It leads to the _latex_ function for
which there really isn't anything deep going on.
If all you care about is truncating zeros, then following changes will do:
diff -r 07a824fa8f2b sage/rings/re
Marshall Hampton wrote:
> There are a number of interact examples on the wiki (such as the Gram-
> Schmidt one at http://wiki.sagemath.org/interact/linear_algebra) that
> work around this problem by casting to a field of low precision, for
> example doing something like
>
> latex(RealField(8)(0.6
Martin Rubey wrote:
> Jason Grout <[EMAIL PROTECTED]> writes:
>
>>> Why is your coefficients different from mine?
>>
>> I specifically asked for the coefficient of "x". You just asked for the
>> coefficients, but didn't specify what variable was the variable of your
>> polynomial.
>
> OK, I t
I am confused about the polymake module. Does this module allow you
to do everything in polymake or just the particular functions listed
in the sage reference manual. Thanks.
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I'm trying to run the following:
sage: n=3; q=7; G=SL(n,q)
sage: for a in G:
: print a
:
it just got stuck there, nothing shows up (for a looong while)
this is Sage version 3.1.1
and if I try the same with q=4 it works (but it takes some time to start)
any ideas?
tinch
--~--~---
On Nov 17, 2008, at 9:34 AM, Martin Mereb wrote:
>
> I'm trying to run the following:
>
> sage: n=3; q=7; G=SL(n,q)
> sage: for a in G:
> : print a
> :
>
> it just got stuck there, nothing shows up (for a looong while)
> this is Sage version 3.1.1
>
> and if I try the same with q=4 i
Dear Marshall,
Thanks a lot for looking into this. I tried similar approaches as well,
and so did the original poster. However, as soon as you introduce a
symbolic variable into the equation, latex does weird things such as:
latex(RealField(8)(0.6)*x)
produces
"{0.6016000 x}"
Does thi
Any decimal number that goes into maxima turns into a 53-bit floating
point number (at least by default), which then turns into a 53 bit
MPFR coming out. The reason all the trailing 0's are exposed is to
show how much precision is known. Maxima (as far as I know) doesn't
have the concept o
Dear Team,
I have a couple of .pyx files and (sometimes trying to be a good boy)
I provided long doc strings with lots of doc tests.
However,
sage -t foo.pyx
fails by raising errors on *all* tests that involve any function from
'foo.pyx'.
First attempt:
Plainly use the function 'bar' from
I'm sorry I didn't ask more precisely..
Yes, that's what I actually meant to ask.
I want to save e.g. latex(x) to a .tex file.
I'm using Sage on Windows, with the VMware image.
Thanks for the reply!
Kinds regards,
Christoph
On 16 Nov., 19:54, "William Stein" <[EMAIL PROTECTED]> wrote:
> On Sun,
On Mon, Nov 17, 2008 at 11:28 AM, Christoph Bichler
<[EMAIL PROTECTED]> wrote:
>
> I'm sorry I didn't ask more precisely..
> Yes, that's what I actually meant to ask.
> I want to save e.g. latex(x) to a .tex file.
> I'm using Sage on Windows, with the VMware image.
Here's an example (without the
I see I expressed myself wrong
(I meant the problem was in the "for" line)
so what's going on is that gap is attempting to built first the whole
list and that is taking way too much time (right?)
are there any iterator that avoids that amount of memory and take the
elements "on the fly", like xran
On Mon, Nov 17, 2008 at 3:24 PM, Martin Mereb <[EMAIL PROTECTED]> wrote:
>
> I see I expressed myself wrong
> (I meant the problem was in the "for" line)
> so what's going on is that gap is attempting to built first the whole
> list and that is taking way too much time (right?)
> are there any ite
ok, thanks!
On Mon, Nov 17, 2008 at 2:39 PM, David Joyner <[EMAIL PROTECTED]> wrote:
>
> On Mon, Nov 17, 2008 at 3:24 PM, Martin Mereb <[EMAIL PROTECTED]> wrote:
>>
>> I see I expressed myself wrong
>> (I meant the problem was in the "for" line)
>> so what's going on is that gap is attempting to
The current interface to polymake is pretty minimal, a lot more could
be done to improve it. You need to install the polymake optional spkg
for it to work - this installs a full-fledged version of polymake that
you could use on its own as well. Last time I checked the spkg was
broken, but in a m
Its probably not necessary to note this, but on the slim chance it is
I'll point out that the regular expression module, re, is a standard
python module that is not imported by default so you have to do
sage: import re
before Robert's solution.
-mh
On Nov 17, 1:05 pm, Robert Bradshaw <[EMAIL P
Dear Mike,
Thanks a lot for that, this looks very promising. However, after
making the suggested change, the behaviour of latex() did not change.
Do I need to restart sage for the changes to take effect?
dummy._latex_?? reflects the changes made, but the 0s are still there
when I latex(dummy).
d
Hello,
On Mon, Nov 17, 2008 at 11:11 PM, Stan Schymanski <[EMAIL PROTECTED]> wrote:
>
> Dear Mike,
>
> Thanks a lot for that, this looks very promising. However, after
> making the suggested change, the behaviour of latex() did not change.
> Do I need to restart sage for the changes to take effec
Hi Robert,
Thanks, this explains what is going on. Would there be a way of
including the regular expressions procedure in the show() command? The
output of the line you proposed is a string, which doesn't show well
in show(). :)
Thanks again,
Stan
On Nov 17, 8:05 pm, Robert Bradshaw <[EMAIL PRO
Hi Mike,
This is great, it does exactly what I wanted. Thanks a lot! Are there
any potentially undesired side-effects of the changes in real_mpfr.pyx
or could this fix be included in future versions of sage?
Stan
On Nov 18, 8:14 am, "Mike Hansen" <[EMAIL PROTECTED]> wrote:
> Hello,
>
> On Mon,
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