I think sage solving is based on maxima, and I've noticed that Maxima has
always had this problem with non-linear equations.
If you set it up as follows:
eq = x == sqrt(1 + x)
solns = solve(eq^2,x); solns
You will get:
[x == -1/2*sqrt(5) + 1/2, x == 1/2*sqrt(5) + 1/2]
Of course, then you have
Unfortunately, that method could produce extraneous solutions. There
is an additional constraint from the original equation that x=0 since
the square root of something must be =0 (no complex number is a
solution, either). That is missing from x^2-x-1=0. Is there a way
to make Sage check it
Which is why I did the sanity checking in the last step. I admit n( ) on
lhs() and rhs() is ugly, but I'm sure others could suggest ways to check for
equality in an equation.
On the other hand, you didn't mention in the original problem that x had to
be in the reals. :D
Joal Heagney
--
To
On Apr 9, 2011, at 22:23 , nkulmati wrote:
Hi All, I am a newbie to Sage. My main purpose is to write scripts
(algorithms). That is, I am not interested in the answer-question
approach of the notebook, but I want to write and execute .sage
files using sage just as I do with .m files using
Here's a one-liner to filter the solutions:
filter((lambda x: n(eq.subs(x).lhs()) == n(eq.subs(x).rhs())),solns
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Here's a one liner to filter the solutions.
filter((lambda x: n(eq.subs(x).lhs()) == n(eq.subs(x).rhs())),solns)
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sage: solve(x==sqrt(x+1),x,to_poly_solve='force')
[x == 1/2*sqrt(5) + 1/2]
On 10 Kwi, 09:01, ancienthart joalheag...@gmail.com wrote:
Here's a one liner to filter the solutions.
filter((lambda x: n(eq.subs(x).lhs()) == n(eq.subs(x).rhs())),solns)
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Partial seems useful, thank you. The Lambda solutions also work.
But what IS lambda anyway? I don't see that its doing anything other
than being syntactic verbose.
On Apr 9, 7:24 am, Jason Grout jason-s...@creativetrax.com wrote:
On 4/8/11 2:00 PM, John H Palmieri wrote:
On Friday, April
I'm completely unable to get the scipy special functions module to
work. In addition, it seems to cause chaos on my system once imported
sage: import scipy
sage: from scipy.special import *
sage: scipy.special.lpn(1,1)
---
Thanks. Does this just slow things down, or does it change the
output?
There are at least three alternatives to imagemagick. One is to use
javascript to animate frames; the result wouldn't be saveable though.
There's a 2-year-old ticket for this that no one ever got quite right:
I'm completely unable to get the scipy special functions module to
work. In addition, it seems to cause chaos on my system once imported
sage: import scipy
sage: from scipy.special import *
sage: scipy.special.lpn(1,1)
I'd avoid your second line in Sage, which pulls everything in
Hi,
I wonder if it is possible to do root locus plots in sage?
The root locus plot of a complex function is basically the zero locus
of the imaginary part but it should be equipped
with various markings.
Regards,
Michel
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To
On Sunday, April 10, 2011 6:36:08 AM UTC-7, Marshall Hampton wrote:
Finally, what I do currently is to use ffmpeg. Because of patent and
license issues I think this cannot be part of the standard Sage, but
it does a great job and is very flexible. For larger movies this is
crucial,
lambda x : f(x) should read the function which maps x to f(x). It
has nothing to do with symbolic computations, and exists in Python.
note that lambda x : x^2 is exactly the same as lambda y : y^2,
which is mathematically very sound. Using the symbolic ring however,
if x and y are formal
I realize that my 4th paragraph (specifically the implicit
replacement...) is not very truthful. It may be a good first
explanation, but there's a more technical answer if you (or anyone)
cares for one.
when you try
plot( foo, ...)
then the first thing sage does is evaluate foo once. It has to
Ugghh It looks like scipy wasn't quite what I was looking for. All
I really need is a way of evaluating generalised legendre functions of
the first and second kind. I've actually found a package in sympy that
does this
If numerical tools are sufficient then:
sage: from mpmath import *
sage: mp.dps = 15; mp.pretty = True
sage: legendre(1,0.5)
0.5
sage: legenq(1,0,0.5)
-0.725346927832973
On 10 Kwi, 20:17, ObsessiveMathsFreak obsessivemathsfr...@gmail.com
wrote:
Ugghh It looks like scipy wasn't quite what I
On Sun, Apr 10, 2011 at 11:17 AM, ObsessiveMathsFreak
obsessivemathsfr...@gmail.com wrote:
Ugghh It looks like scipy wasn't quite what I was looking for. All
I really need is a way of evaluating generalised legendre functions of
the first and second kind. I've actually found a package in
Or:
sage: import scipy.special
sage: scipy.special.legendre(1,0.5)
poly1d([ 1., 0.])
sage: scipy.special.lqn(int(1),float(0.5))
(array([ 0.54930614, -0.72534693]), array([ 1., 1.21597281]))
On 10 Kwi, 20:17, ObsessiveMathsFreak obsessivemathsfr...@gmail.com
wrote:
Ugghh It looks
Hi
I don't know why the function A=H.point() at the followe program
for the finite field with size 101^5 don't work.
But for the finite field with size 101^2 it work.
sage: k.x=GF(101^5,'x');
sage: x=polygen(k);
sage: H = HyperellipticCurve(x^5 + 12*x^4 + 13*x^3 + 15*x^2 + 33*x);
sage: J =
Hi
I don't know why the function A=H.point() at the followe program
for the finite field with size 101^5 don't work.
But for the finite field with size 101^2 there is no problem.
sage: k.x=GF(101^5,'x');
sage: x=polygen(k);
sage: H = HyperellipticCurve(x^5 + 12*x^4 + 13*x^3 + 15*x^2 + 33*x);
Or simply legendre_P, legendre_Q
On 10 Kwi, 21:26, achrzesz achrz...@wp.pl wrote:
Or:
sage: import scipy.special
sage: scipy.special.legendre(1,0.5)
poly1d([ 1., 0.])
sage: scipy.special.lqn(int(1),float(0.5))
(array([ 0.54930614, -0.72534693]), array([ 1., 1.21597281]))
On 10
On Apr 10, 2011, at 12:35 , Foad Khoshnam wrote:
Hi
I don't know why the function A=H.point() at the followe program
for the finite field with size 101^5 don't work.
But for the finite field with size 101^2 it work.
Could you be a little more specific? it doesn't work is not a lot to go on
On Apr 10, 4:46 pm, John H Palmieri jhpalmier...@gmail.com wrote:
On Sunday, April 10, 2011 6:36:08 AM UTC-7, Marshall Hampton wrote:
Finally, what I do currently is to use ffmpeg. Because of patent and
license issues I think this cannot be part of the standard Sage, but
it does a great
The mpmath import seems to work, but I am unable to plot the resulting
functions. I get an error about too many values to unpack.
from mpmath import *
plot(lambda x: legenp(1,0,x),(x,-1,1))
Traceback (click to the left of this block for traceback)
...
ValueError: too many values to unpack
On
Workaround:
list_plot([(x,legenp(2,0,x)) for x in
srange(-1,1,0.1)],plotjoined=True)
On 10 Kwi, 23:47, ObsessiveMathsFreak obsessivemathsfr...@gmail.com
wrote:
The mpmath import seems to work, but I am unable to plot the resulting
functions. I get an error about too many values to unpack.
from
On Sunday, April 10, 2011 8:46:51 AM UTC-7, John H Palmieri wrote:
On Sunday, April 10, 2011 6:36:08 AM UTC-7, Marshall Hampton wrote:
Finally, what I do currently is to use ffmpeg. Because of patent and
license issues I think this cannot be part of the standard Sage, but
it does a
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