I tried using Sage to compute the Galois group of a polynomial of
degree 12, using the following code:
p= -98298717579910546875000 +
36091888356881423583984375* x -
1193313058398713452148437500* x^2 + 754759543928715527343750*
x^3 + 1582754650853547656250* x^4 -
On Feb 1, 8:59 am, William Stein [EMAIL PROTECTED] wrote:
On Jan 31, 2008 7:59 AM, pgdoyle [EMAIL PROTECTED] wrote:
On Jan 31, 12:29 am, William Stein [EMAIL PROTECTED] wrote:
On Jan 30, 2008 3:48 PM, pgdoyle [EMAIL PROTECTED] wrote:
I would like to take the Taylor series
On Jan 31, 12:29 am, William Stein [EMAIL PROTECTED] wrote:
On Jan 30, 2008 3:48 PM, pgdoyle [EMAIL PROTECTED] wrote:
I would like to take the Taylor series of a matrix. But I find I
can't even put a Taylor polynomial into a matrix without its being
simplified.
sage: f=-x/(2*x-4
On Jan 31, 8:05 am, John Cremona [EMAIL PROTECTED] wrote:
You could try substituting x+1 for x first, then do what you want, and
substitute back at the end,
I would expect the auto-simplification to happen at that last step
too, but you would be able to (say) replace x by (x-1) in the
I would like to take the Taylor series of a matrix. But I find I
can't even put a Taylor polynomial into a matrix without its being
simplified.
sage: f=-x/(2*x-4); f
-x/(2*x - 4)
sage: g=taylor(f,x,1,1); g
1/2 + x - 1
sage: matrix(1,[g])
[x - 1/2]
sage: m=matrix(1,[f]); m
[-x/(2*x - 4)]
sage:
On Jan 22, 2:17 pm, Carl Witty [EMAIL PROTECTED] wrote:
'Integer' is a Sage type. This means it has lots of useful
mathematical convenience methods (like .is_square()), it participates
in the coercion model, etc. Also, 'Integer' is implemented with GMP,
and 'long' is not, so 'Integer' is
sage: var(x)
x
sage: time sum(((x+sin(i))/x+(x-sin(i))/x).rational_simplify() for i
in xrange(100))
200
CPU time: 5.29 s, Wall time: 39.10 s
sage: time maxima('sum(ratsimp((x+sin(i))/x+(x-sin(i))/x),i,1,100)')
200
CPU time: 0.02 s, Wall time: 0.55 s
Those times above are
The following behavior is not what I want or expect for the ordering
of terms when Sage displays a polynomial:
sage: 1-x
1 - x
sage: 1+x
x + 1
sage: 1-x^2
1 - x^2
sage: 1+x^2
x^2 + 1
sage: 1+x-x^2
-x^2 + x + 1
sage: 1+x+x^2
x^2 + x + 1
Is there some way to let Sage know that I'd prefer a
I'm having problems doing symbolic computations in Sage. Calls to
rational_simplify() seem to take about .2 seconds each. Working
directly in Maxima is about 100 times faster. Mathematica is
something like 500 times faster.
In Sage, where does the time go? Is there something I can do right
That said, I *do* want to change the implementation
so that any time a cell is changed and the cursor leaves the cell
or save close is clicked, the changed version is sent back to the
server. I think Tom Boothby has argued against this,
which is why it hasn't happened already.
I think it
I'm looking for advice about how to speed up the attached Sage
program.
I've been commissioned to write an article for a popular math journal
debunking the notion that `seven shuffles suffice'. This article will
feature a computation done in Sage of the exact probability of winning
`New Age
On Dec 18, 12:51 pm, pgdoyle [EMAIL PROTECTED] wrote:
Changes to my Sage notebooks are not always getting saved. I'm
running Sage 2.9 from Firefox 2.0.0.11 on Mac OS 10.4.11 on a PowerMac
G5.
I've tried this now on with Safari instead of Firefox, and on a Linux
box instead of the Mac
Changes to my Sage notebooks are not always getting saved. I'm
running Sage 2.9 from Firefox 2.0.0.11 on Mac OS 10.4.11 on a PowerMac
G5.
Simplest case:
If I fire up a new worksheet, enter 2+2, then `Save and Close', when I
reopen the worksheet, it's empty.
If I fire up a new worksheet, enter
The vector v2 doesn't display properly in the attached Sage output.
Or rather, the free module element v2.
(Should I be worried that I got a free module element when I expected
a vector, or will everything work out for the best?)
Cheers,
Peter
---
sage:
Let me simplify the question.
Is there a better way to get Mathematica to go off and compute a
Bessel function for me than this:
def math_bessel_K(nu,x):
m=mathematica('N[BesselK['+str(mathematica(nu))
+','+str(mathematica(x))+'],20]')
return m.sage()
Cheers,
Peter
To get back to the question of argument order, it seems strange to me
that
pari(2).besselk(3)
should meant K_2(3) rather than K_3(2).
sage: pari(2).besselk(3)
0.06151045847174203765682007145
sage: bessel_K(2,3)
0.0615104584717420
bessel_K(nu,x) is written K_nu(x) because the first argument nu
Say I want to get Mathematica to compute some function that Sage can't
compute for me. What is the best way to pipe the arguments into
Mathematica, and then get the answer back into the world of sage?
Here's what I tried:
sage: def math_bessel_K(nu,x):
...
I told a colleague about sage, wondering if he would see it as a
viable
alternative to matlab for numerical work. This was his response:
I don't know SAGE - it looks great. I'm looking forward to trying it once
things settle down.
I've used python for a project and it was excellent. I think
In[7]:= Pi + E // N + 5 // N
Out[7]= (5. + N)[5.85987]
Gees -- what in the heck does (5. + N)[5.85987] mean?
It means 5.+N applied to 5.85987. (In Mathematica f[x] is how you
would express applying f to x).
And here's why:
In[8]:= a+b//c+d//e
Out[8]= e[(c + d)[a + b]]
So Pi + E // N
On Dec 7, 10:17 pm, Mike Hansen [EMAIL PROTECTED] wrote:
I think what confusing is the following:
In[1]:= Pi // N
Out[1]= 3.14159
In[2]:= Pi // N + 2
Out[2]= (2 + N)[Pi]
What does it mean in Mathematica to add 2 to N? Does it just treat N
as a formal symbol when you add 2 to it N?
Mike,
Thanks for the help - much appreciated!
On Dec 3, 9:30 pm, Mike Hansen [EMAIL PROTECTED] wrote:
If you just need to substitute, you can do:
sage: m.subs(x=1)
[-1 -1]
[-1 0]
If you want to apply a more general map to the coefficients, then you can do:
sage: m.apply_map(lambda
I'm trying to wean myself from Mathematica. Here are some issues I've
been
wrestling over with SAGE. I apologize in advance for not showing the
sage output, which I'm sure there is some easy way to generate
automatically
from this file.
1) Taylor series of a rational function.
This works:
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