On 9 Maj, 20:27, "David Joyner" <[EMAIL PROTECTED]> wrote:
> It turns out that next year it is very possible that all USNA freshamn will
> have
> an asus eee. The debate seems to be about the amount of ram it should have.
> I can borrow one next week. It has xandros linux 500M ram, 2G "hard
> d
Hallo,
I'm wondering what goes wrong with tis:
(sage 3.2 compiled from sources, ubuntu 8.04, quad core 2.4 GHz)
sage: for k in range(14,21):
: f=2^2^k+1;w=ecm.find_factor(f);[w[0],prod(w)==f]
:
[2, False]
[523923, False]
[1901173, False]
[2, False]
[2, False]
[30539, False]
[2, Fal
The old fashioned gmp-ecm interface:
sage: ecm.find_factor(2^2^7+1)
[59649589127497217, 5704689200685129054721]
sage: ecm.get_last_params()
{'B1': '19929', 'B2': '3804582', 'poly': 'x^1', 'sigma': '1643647236'}
the proposed, new one:
sage: import sage.libs.libecm
sage: from sage.libs.libecm impo
Hello
My question is
connected with file http://modular.fas.harvard.edu/ent/ent_py
and especially with checking the associativity law of addition on ell.
curves.
When I was trying to perform the same calculations in Sage I observed
some surprising (me) behaviour.
Enclosed is the corresponding Sa
Thanks to John Cremona and Paul Zimmermann
I'm impressed, I didn't expect such quick response from leading
specialists
in the field. Thank you very much!
The answers were extremly interesting an concrete but I can't agree
with last John Cremona's statement:
"we have answered the original question!
Paul
Im impressed again. Thank you so much
I had only a rough idea and you are realy effective in SAGE (too).
This time I have no additional concrete questions
but I'm strongly interested in your general opinion
concerning the comparison MAPLE-SAGE (any links?)
Andrzej Chrzeszczyk
On 11 Sty, 23:
Paul
Have you noticed that your SAGE code is much faster tha MAPLE's?
Your final questions are interesting but not easy to me
Andrzej Chrzeszczyk
On 12 Sty, 16:27, achrzesz <[EMAIL PROTECTED]> wrote:
> Paul
> Im impressed again. Thank you so much
> I had only a rough id
If you dont want factor you can use
n12 = numerator((s1-s2).rational_simplify())
On 12 Sty, 16:53, achrzesz <[EMAIL PROTECTED]> wrote:
> Paul
> Have you noticed that your SAGE code is much faster tha MAPLE's?
> Your final questions are interesting but not easy to me
> And
Sty, 21:57, achrzesz <[EMAIL PROTECTED]> wrote:
> If you dont want factor you can use
> n12 = numerator((s1-s2).rational_simplify())
>
> On 12 Sty, 16:53, achrzesz <[EMAIL PROTECTED]> wrote:
>
> > Paul
> > Have you noticed that your SAGE code is much faster tha MAPL
Dear Carl,
I like your code; it is elegant and realy quick
but it seems that finishing your code
with Paul Zimmermann's approach
I2 = singular(I).groebner()
#print I.reduce(n12);
print singular.reduce((n12), I2)
(althout less elegant)
is a little bit faster
(0.06 -> 0.05 on my comp. :)
I want a
over Fraction
Field of Multivariate Polynomial Ring in a, b, x1, x2, x3 over
Rational Field by the ideal (y1^2 - x1^3 - a*x1 - b, y2^2 - x2^3 -
a*x2 - b, y3^2 - x3^3 - a*x3 - b)
but
E = EllipticCurve(S, [a,b])
does not work (in the present implementation)
Andrzej
On 15 Sty, 08:35, achrze
One can also use scipy (faster) or mpmath (very slow)
sage: import scipy.integrate
sage: scipy.integrate.dblquad(lambda x,y:abs(cos(x+y)),0,pi,lambda x:
0,lambda x:pi)
(6.2831850310568189, 8.0696816340264377e-08)
sage: n(2*pi)
6.28318530717959
sage: from mpmath import *
sage: mp.dps = 50; mp.pre
sage: s=solve(3*x^3-9*x+10,x,solution_dict=True)
sage: ns=[n(s[k][x]) for k in range(3)]
sage: ns
[1.06780542232902 - 1.84949324407141*I, 0.0277635108030695 +
1.24902476648341*I, -1.09556893313209 +
0.600468477588001*I] # no real solution, no conjugate
solutions
sage: x=CC[x].0
sage:
Thank you for explanation Francois
Note however that the additional option can change Maxima's behavior
sage: s=solve(3*x^3-9*x
+10==0,x,solution_dict=True,to_poly_solve='force')
sage: [n(t[x]) for t in s]
[1.06780542232902 - 0.648556288895405*I, #
-2.13561076604555, # POOR PRECISION
1.067805
SAGE:
sage: s=solve(3*x^3-9*x+10==0,x,solution_dict=True)
sage: [n(t[x]) for t in s]
[1.06780542232902 - 1.84949324407141*I,
0.0277635108030695 + 1.24902476648341*I,
-1.09556893313209 + 0.600468477588001*I]
# WRONG!
sage: s=solve(3*x^3-9*x+10==0,x,
solution_dict=True,to_poly_solve='force')
sage
sage: f0(x) = 0
sage: f = Piecewise([[(0,1),f0]])
sage: numerical_integral(f,0,1)
(0.0, 0.0)
Andrzej Chrzeszczyk
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For more options, v
Naive work-around
sage: [SR(0).integral(x,0,1),SR(1).integral(x,1,2),SR(2*x).integral(x,
2,3)]
[0, 1, 5]
sage: sum(_)
6
Andrzej Chrzeszczyk
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Less naive (?) workaround
def piecewise_lin_int(list_of_functions):
li=[SR(y[0]).integral(x,y[1],y[2]) for y in list_of_functions]
return sum(li)
print piecewise_lin_int([[0,0,1],[1,1,2],[2*x,2,3]])
Andrzej Chrzeszczyk
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def piecewise_lin_int(list_of_functions):
li=[SR(y[0]).integral(x,y[1],y[2]) for y in list_of_functions]
return sum(li)
#Example
print piecewise_lin_int([[0,0,1],[1,1,2],[2*x,2,3]])
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| Sage Version 4.6.2, Release Date: 2011-02-25 |
| Type notebook() for the GUI, and license() for information.|
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sage: inverse_mod(2,990)
-
I'm not sure if this is relevant but
sage: power_mod(2,-1,990)
also gives helpful error message
and checking for exponent -1 is not necessary
A Ch
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Just for Fun
sage: maxima('factor(3*x^2*y*z + x*y*z + y*z = 0)/(y*z)')
3*x^2+x+1=0
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Also:
sage: s=SR(result)
sage: type(s)
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import scipy.integrate
import matplotlib.pyplot as plt
import numpy
a=1.0
b=2.0
def fun(t):
if t<=-b:
return -a
elif fhttp://groups.google.com/group/sage-support
URL: http://www.sagemath.org
Of course
N=100 in "my" code and repeated
x0=[[0.5*k,0.5*k] for k in range(-10,10)]
in Marshall one are superfluous :)
Andrzej Chrzeszczyk
On 21 Mar, 13:58, kcrisman wrote:
> On Mar 20, 9:55 pm, Marshall Hampton wrote:
>
>
>
> > Slightly more Sage-ified version of the above very nice solution
Also introducing lambda function wasn't necessary:
import scipy.integrate
a=1.0
b=2.0
def fun(t):
if t<=-b:
return -a
elif fhttp://groups.google.com/group/sage-support
URL: http://www.sagemath.org
sage: f0(x)=x^2
sage: f = piecewise([[(0,1), f0]])
sage: f(0.5)
0.250
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sage: %time maxima('makelist(elliptic_ec(0.1*k),k,0,10)')
CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.01 s
[%pi/2,1.530757636897764,1.489035058095852,1.445363064412665,
1.399392138897432,1.350643881047676,1.298428035046913,
1.241670567945823,1.178489924327839,1.104774732704073,1
Oops
sage: %time pts=maxima('makelist(elliptic_ec(0.01*k),k,0,100)')
CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.05 s
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Conversion to sage list:
sage: pts0=map(n,pts)
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URL: htt
sage: %time pts=maxima('makelist(elliptic_ec(float(1/(1+0.01*k))),k,
1,100)')
CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.05 s
sage: pts0=[RR(x) for x in pts]
On 28 Mar, 15:39, ObsessiveMathsFreak
wrote:
> > sage: %time pts=maxima('makelist(elliptic_ec(0.01*k),k,0,100)')
> > s
sage: from scipy.special import ellipk
sage: time pts=[ellipk(1.0/(1.0+0.01*k)) for k in srange(0,1,0.01)]
CPU times: user 0.02 s, sys: 0.00 s, total: 0.02 s
Wall time: 0.02 s
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sa
of course k in range(1,101)
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If you mean complete elliptic integrals of the second kind then:
sage: from scipy.special import ellipe
sage: time pts=[ellipe(1.0/(1.0+0.01*k)) for k in range(1,101)]
CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s
Wall time: 0.02 s
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If you need more precision,you can also use mpmath
sage: from mpmath import *
sage: time pts=[ellipe(1.0/(1.0+0.01*k)) for k in range(1,101)]
CPU times: user 0.03 s, sys: 0.00 s, total: 0.03 s
Wall time: 0.03 s
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sage: maxima('solve([imagpart(x)=0,imagpart(sqrt(-x^2-1))=0],
[x])').sage()
[]
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In instalatiopn guide you can find:
SAGE_ATLAS_LIB - if you have an installation of ATLAS on your system
and you want Sage to use it instead of building and installing its own
version of ATLAS, set this variable to be the parent directory of your
ATLAS installation: it should have a subdirectory l
sage: gp_console()
? \p 100
realprecision = 115 significant digits (100 digits displayed)
? a=matrix(3,3,k,m,random(1.0))+I*matrix(3,3,k,m,random(1.0));
? m=a*conj(a)~;
? mateigen(m)
On 30 Mar, 18:20, Jason Grout wrote:
> On 3/30/11 10:44 AM, Ben123 wrote:
>
>
>
> > Hello. I've written a sa
eigenvectors of ttdag in PARI/GP, pass results back to sage
>
> Thanks for the help,
>
> On Mar 30, 2:45 pm, achrzesz wrote:
>
> > sage: gp_console()
> > ? \p 100
> > realprecision = 115 significant digits (100 digits displayed)
> > ? a=matrix(3,3,k,m,random(1
Since GP/PARI default precision is 38 (on my system)
(and I dont know how to set \p 100 from sage)
it would be probably better to replace
precision_digits=30
by
precision_digits=38
On 30 Mar, 23:03, achrzesz wrote:
> # NO WARRANTY
> precision_digits=30
> nop=5 # rank of matrix
>
().transpose()
m=gp(ttdag)
gp('default(realprecision,100)')
ev=gp.mateigen(m).sage()
print ev[:-1]
On 31 Mar, 11:47, achrzesz wrote:
> Since GP/PARI default precision is 38 (on my system)
> (and I dont know how to set \p 100 from sage)
> it would be probably better to replace
> pr
]
On 31 Mar, 12:14, achrzesz wrote:
> #NOT CHECKED
> precision_digits=100
> nop=5 # rank of matrix
> MS_nop_comp=MatrixSpace(ComplexField(precision_digits),nop,nop)
> tmat=MS_nop_comp(0) # zero-ize the values
> ttdag=MS_nop_comp(0)
> for a in range(nop):
> for b in rang
sage: import time
sage: time.asctime(time.localtime())
'Thu Mar 31 15:36:30 2011'
On 31 Mar, 15:15, kcrisman wrote:
> This could be useful:sage: import datetime
> sage: datetime.datetime.now()
> datetime.datetime(2011, 3, 31, 9, 13, 0, 932345)
> And there are lots of methods and string formatting
sage: import scipy as sc
sage: map(floor,sc.arange(0.0,1.2,0.1))
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]
On 1 Kwi, 21:17, ObsessiveMathsFreak
wrote:
> Thanks for that, but I've run into another issue. I don't know whether
> this is related to the sequence syntax or not
>
> sage: for n in [0.0,0.1,..
sage: plot(lambda w:arg(1/(I*w) + 1/2 + (I*w)) ,(w,0,5),
axes_labels=['$Frequency$', '$Phase$'])
On 4 Kwi, 22:41, Renan Birck Pinheiro wrote:
> Hello,
>
> I define a complex-valued function, and then want to plot its absolute
> value and argument:
>
> w = var('w')
> V(omega) = 1/(I*omega) + 1/2 +
Or:
sage: plot(lambda x: h(x,3), (x, 0, 4),exclude=[2])
On 8 Kwi, 21:00, John H Palmieri wrote:
> On Friday, April 8, 2011 11:03:14 AM UTC-7, ObsessiveMathsFreak wrote:
>
> > I have a python type function taking two variables is defined in such
> > a say that accidental evaluation is a possibili
This works for me:
p1=plot(x^2, (x, -pi, pi),label="f")
G=graphics_array(((p1,p1),(p1,p1)))
G.show(figsize=[8,8])
On 8 Kwi, 18:54, ObsessiveMathsFreak
wrote:
> I'm encountering a problem with graphics_array and latex use in plots.
> The following command works fine
>
> p1=plot(x^2, (x, -pi, pi),
sage: solve(x==sqrt(x+1),x,to_poly_solve='force')
[x == 1/2*sqrt(5) + 1/2]
On 10 Kwi, 09:01, ancienthart 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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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
wrote:
> Ugghh It looks like scipy wasn't quite what I was looking for. All
> I reall
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
wrote:
> Ugghh It looks like scipy wasn't quite what I
Or simply legendre_P, legendre_Q
On 10 Kwi, 21:26, achrzesz 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]))
t *
>
> 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 Apr 10, 8:38 pm, achrzesz wrote:
>
> > Or simply legendre_P, legendre_Q
>
> Unfortunately, the
sage: reset()
sage: import mpmath
sage: plot(lambda x: mpmath.legenp(2,0,x),(x,-1,1))
On 11 Kwi, 00:34, achrzesz wrote:
> Workaround:
> list_plot([(x,legenp(2,0,x)) for x in
> srange(-1,1,0.1)],plotjoined=True)
> On 10 Kwi, 23:47, ObsessiveMathsFreak
> wrote:
>
> > Th
I'm not sure but:
sage: solve(x==sqrt(x+1),x,to_poly_solve='use_grobner=True')
[x == 1/2*sqrt(5) + 1/2]
On 11 Kwi, 12:24, ancienthart wrote:
> Now THAT seriously needs to be made clearer in the documentation, including
> some examples.
> Also, how to use use_grobner because use_grobner=True don't
to_poly_solve([(x-5)^2+y^2-16, (y-3)^2+x^2-9], [x,y],
use_grobner=true);
works in wxmaxima 0.8.7 but does not in maxima_console()
On 11 Kwi, 13:06, achrzesz wrote:
> I'm not sure but:
> sage: solve(x==sqrt(x+1),x,to_poly_solve='use_grobner=True')
> [x == 1/2*sqrt(5) + 1
sage: solve([(x-5)^2+y^2-16, (y-3)^2+x^2-9],
[x,y],to_poly_solve='use_grobner=True')
[[x == -9/68*sqrt(55) + 135/68, y == -15/68*sqrt(5)*sqrt(11) +
123/68], [x == 9/68*sqrt(55) + 135/68, y == 15/68*sqrt(5)*sqrt(11) +
123/68]]
On 11 Kwi, 13:29, achrzesz wrote:
> to_poly_solve([(x-5)
Oops!
without "to_poly_solve='use_grobner=True'"
also works
On 11 Kwi, 13:37, achrzesz wrote:
> sage: solve([(x-5)^2+y^2-16, (y-3)^2+x^2-9],
> [x,y],to_poly_solve='use_grobner=True')
> [[x == -9/68*sqrt(55) + 135/68, y == -15/68*sqrt(5)*sqrt(11) +
> 123/
)')
%union([x=-(9*sqrt(55)-135)/68,y=-(3*5^(3/2)*sqrt(11)-123)/68],
[x=(9*sqrt(55)+135)/68,y=(3*5^(3/2)*sqrt(11)+123)/68])
> Oops!
> without "to_poly_solve='use_grobner=True'"
> also works
>
> On 11 Kwi, 13:37, achrzesz wrote:
>
> > sage: solve(
Maxima functions are OK
but mpmath is not as slow as one can think
sage: time list_plot([(x,mpmath.legenq(2,0,x)) for x in
srange(-0.99,1.01,0.05)],plotjoined=True)
+list_plot([(x,mpmath.legenp(2,0,x)) for x in
srange(-0.99,1.01,0.1)],plotjoined=True)
CPU times: user 0.20 s, sys: 0.00 s, total: 0.2
Is your function usable?
def mplegp(n,m,x):
V=mpmath.legenp(n,m,x)
return float(V.real)+I*float(V.imag)
sage: time plot(lambda x:mplegp(2.1,0,x).real(),(x,-1,1))
CPU times: user 0.87 s, sys: 0.00 s, total: 0.87 s
Wall time: 0.87 s
On 13 Kwi, 19:48, ObsessiveMathsFreak
wrote:
> On Apr 12, 8:5
Or:
sage: import sage.libs.mpmath.all as mpmath
sage: V=mpmath.call(mpmath.legenp,2.1,0,-2);V
5.83105230126368 + 1.89579005740338*I
sage: type(V)
On 13 Kwi, 23:45, Fredrik Johansson
wrote:
> On Apr 13, 7:48 pm, ObsessiveMathsFreak
>
>
>
> wrote:
> > On Apr 12, 8:52 pm, ObsessiveMathsFreak
>
> >
In 64bit 4.6.2 fedora13 Dell Vostro 1720
sage: numerical_integral(lambda x: cos(2*x)*cos(x), 0, pi)
(4.4478052108155282e-17, 1.3516940761795953e-14)
sage: plot(cos(2*x)*cos(x), (x, 0, pi))
Maxima and Wolfram alpha: 0
sage: integral(cos(2*x)*cos(x), x, 0, pi)
4/3
On 15 Kwi, 05:27, Dan Drake wr
To be more precise:
Maxima 5.23.2 gives 0
Sage 4.6.2 has 5.22.1 (and gives 4/3)
On 15 Kwi, 06:00, achrzesz wrote:
> In 64bit 4.6.2 fedora13 Dell Vostro 1720
> sage: numerical_integral(lambda x: cos(2*x)*cos(x), 0, pi)
> (4.4478052108155282e-17, 1.3516940761795953e-14)
> sage: plot(
Without additional assumption that x is constant
the limit is not zero (take for example x=(1/2)^(1/(n+1))
(W... alpha:
Assuming[x=const,x<1,x>0];Limit[x^(n+1)/(1-x),n->+Infinity] 0 OK,
Assuming[x<1,x>0];Limit[x^(n+1)/(1-x),n->+Infinity] unevaluated OK)
On 15 Kwi, 06:00, Dan Drake wrote:
> Why d
One can discuss if in limits of f(x,n) as n-->oo
x may depend on n or not but in the following version:
sage: assume(x>-0.99,x<0.99)
sage: n=var('n')
sage: sage: limit(x^(n+1)/(1-x), n=infinity)
-limit(x^(n + 1), n, +Infinity)/(x - 1)
sage: assume(x>0)
sage: sage: limit(x^(n+1)/(1-x), n=infinit
In W... alpha
Assuming[x>-0.99,x<0.99];Limit[x^(n+1)/(1-x),n->+Infinity]
remains unevaluated, so Maxima, Sage are nol alone
On 16 Kwi, 08:18, achrzesz wrote:
> One can discuss if in limits of f(x,n) as n-->oo
> x may depend on n or not but in the following version:
>
>
sage: R.=PolynomialRing(QQ,'x,y,z')
sage: w=3/5*x*y+5*y+3*z
sage: w.monomials()
[x*y, y, z]
sage: w1=3*x^2
sage: w1.monomials()
[x^2]
On 16 Kwi, 07:00, tvn wrote:
> given an expression f of the form c1*t1 + c2*t2 + .. +cn*tn, I want to
> extract from f the list of 'terms' [t1..tn] .. is there
I must correct myself
W... alpha:
Assuming[x>-0.99,Assuming[x<0.99,Limit[x^(n+1)/(1-x),n->+Infinity]]
gives correct answer 0
On 16 Kwi, 09:27, achrzesz wrote:
> In W... alpha
> Assuming[x>-0.99,x<0.99];Limit[x^(n+1)/(1-x),n->+Infinity]
> remains unevaluated, so Maxima
In the last post one can replace 0.99 by 1
but I wanted to exclude the following situation:
sage: n=var('n')
sage: x=var('x')
sage: x=(1/2)^(1/(n+1))
sage: limit(x^(n+1)/(1-x),n=+oo)
+Infinity # OK
On 16 Kwi, 15:36, achrzesz wrote:
> I must correct myself
> W...
http://ask.sagemath.org/question/335/multiple-3d-plots-in-one-panel-graphics_array-and
On 17 Kwi, 02:46, ObsessiveMathsFreak
wrote:
> Currently in sage 3D I can graph 3D plots in the same output, but not
> side by side.
>
> p1=plot3d(lambda x, y: x^2 + y^2, (-2,2), (-2,2))
> p2=plot3d(lambda x, y
sage: numerical_integral(lambda t:imaginary(gamma(1-I*t)),-15,15)
(0.0, 5.3925521851144085e-15)
On 18 Kwi, 00:02, Ian Petrow wrote:
> Also, imaginary(gamma(1.+I*5)), say, works fine as long as it's not
> inside a numerical integral
>
> Ian
>
> On Apr 17, 2:57 pm, Ian Petrow wrote:
>
> > Hello Ev
Hello nkulmati
If you want to get rid of virtualization
maybe you should try Linux version without instalation
burning Live-CD first
The present version fits into memory and after (rather long)
start process the CD can be removed
It works quite satisfactory (if you have >=2GB RAM)
The native Lin
Artifical workaround:
sage: R.=QQ[]
sage: w=3*x^2+4*x
sage: w.monomials()
[x^2, x]
On 29 Kwi, 00:28, tvn wrote:
> Hi, the monimals function you suggested doesn't work for the below case
> where I want to extract the terms [x^2,x] from the given expression
> 3*x^2+4*x .
>
> sage: type(x)
>
Maybe a series of implicit_plot3d with w=w0,w1,...
will be helpful?
On 5 Maj, 19:12, kcrisman wrote:
> On May 5, 12:25 pm, ObsessiveMathsFreak
>
> wrote:
> > I currently have a function of three variables w=f(x,y,z), which I
> > would like to plot in 3D if possible (e.g. via coloured plots)
>
>
It seems that Maxima has problem here but mpmath has not:
sage: from mpmath import *
sage: mp.pretty=True
sage: quad(lambda x:(x^2)*exp(x)/(1+exp(x))^2,[-inf,+inf])
3.28986813369645
sage: n(pi^2/3)
3.28986813369645
A Ch
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``list_plot`` takes either a single list of data, a list of tuples,
or a dictionary and plots the corresponding points.
sage: list_plot(data.tolist())
A Ch
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Example; intersection of an elipsoid and sphere:
var('x,y,z')
solve([x^2 +y^2+z^2 ==1,x^2+y^2+2*z^2 ==1],[x,y,z])
#[[x == r1, y == -sqrt(-r1^2 + 1), z == 0], [x == r2, y == sqrt(-r2^2
+ 1), z == 0]]
var('r1')
p1=parametric_plot3d([r1,-sqrt(-r1^2 + 1),0],
(-1,1),thickness=10,color='red')
p2=paramet
sage: assume(t,'real')
sage: solve(diff(myHH,t),t)
[t == 1/10*log(31)]
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t=var('t')
taum, tauh, m = var('taum, tauh, m')
f(t) = (1-e^(-t/taum))^m*(e^(-t/tauh))
d=diff(f(t),t)
d1=(d==0).full_simplify()
print d1.solve(t)
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Try something like this:
from mpmath import *
mp.dps = 30; mp.pretty = True
f=[lambda s00, s01, s10, s11, k, p:0.55*k*s00 + 0.6*k*s01 + 0.6*k*s10
+ 0.6*p*s01 + 0.6*p*s10 +0.55*p*s11 + 33*s00 + 33*s01 + 33*s10 +
33*s11 - 33.0,
lambda s00, s01, s10, s11, k, p:0.55*k*s00 + 0.6*k*s01 + 0.6*k*s10 +
3
Or:
sage: import numpy as np
sage: from numpy import linalg as LA
sage: a=np.random.rand(512,512)
sage: ainv=LA.inv(a)
sage: np.allclose(np.dot(ainv,a),np.eye(512))
True
Andrzej Chrzeszczyk
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On i5-661:
sage: timeit('ainv=LA.inv(a)')
5 loops, best of 3: 54.3 ms per loop
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sage: MS=MatrixSpace(RDF,512,512)
sage: A=MS.random_element()
sage: timeit('B=A.inverse()')
5 loops, best of 3: 41 ms per loop
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For more op
sage: (integrate( exp(-x^2/2)/sqrt(2*pi) * sign(x-1), x, -oo, 1 )
+integrate( exp(-x^2/2)/sqrt(2*pi) * sign(x-1), x, 1,
oo )).simplify_full()
-erf(1/2*sqrt(2))
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Also:
sage: n=var('n')
sage: assume(n,'integer')
sage: maxima('rectform(exp(%i*n*%pi))').sage().simplify_full()
(-1)^n
Andrzej Chrzeszczyk
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> For trivial cases, yeah, but consider
>
> parametric_plot((f(t-0.5j).real, f(t-0.5j).imag), (t,tmin,tmax))
>
> parametric_plot(ReIm(f(t-0.5j)), (t,tmin,tmax))
>
> --
For example:
sage: f(z)=[z.real(),z.imag()]
sage: t=var('t')
sage: parametric_plot(f(exp(I*(t-5*I))),(t,0,2*pi))
A colon is missing after range(20).
The following version works for me:
(but the indentation in this post may be broken)
x,y,z,t = var('x,y,z,t')
P = implicit_plot3d(x^2 +y^2 -z^2 ==1, (x,-3.2,3.2),(y,-3.2,3.2),
(z,-3,3),opacity=.2,color='blue')
for k in range(20):
P += parametric_plot3d([cos(
Also:
sage: T = Cylindrical('height', ['radius', 'azimuth'])
sage: r, theta, z = var('r theta z')
sage: plot3d(r*sin(1/r), (r, 0.0, 0.2), (theta, 0, 2*pi),
transformation=T,adaptive=True)
Andrzej Chrzeszczyk
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On Sep 28, 2:48 pm, flyingsquirrel wrote:
> I have a symmetric matrix that I want to diagonalize, such as
>
> x y z
> y 0 xy
> z xy xyz
>
> x, y, z being variables, and the base field is CC (complex numbers). I
> typed in the following:
>
> R.=CC[]
> m=matrix(R,[[x,y,z],[y,0,x*y],[z,x*
> It seems unreasonably annoying to plot a bunch of Bessel functions
> together. How can I work around this?
>
> Dan
sage: pl=sum([plot(lambda x:bessel_J(x,n),(x,0,1)) for n in [1,2]])
sage: pl.show()
Andrzej Chrzeszczyk
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To u
The *indefinite* integral of zero is an arbitrary constant (not only
zero)
Compare more 'concrete' version
sage: y = function('y',x)
sage: a = 1 + diff(y,x) == 0
sage: var('t')
t
sage: assume(t>0)
sage: integrate(a,(x,0,t))
t - y(0) + y(t) == 0
Andrzej Chrzeszczyk
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This also works:
sage: k=var('k')
sage: sum('binomial(8,k)',k,0,8)
256
Andrzej Chrzeszczyk
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The exact integral
1/2*(erf(pi - 1/2*I) + erf(pi + 1/2*I))*sqrt(pi)*e^(-1/4)
contains *real* expression
(erf(pi - 1/2*I) + erf(pi + 1/2*I))
but maxima/sage can't check that it is real
In WolframAlpha one can check that
Im[Erf[Pi-1/2*I]+Erf[Pi+1/2*I]]
iz zero
Andrzej Chrzeszczyk
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To post
>
> We need to work on the numerical approximation stuff for the error
> function!
>
> Dan
More generally
in my opinion n() in complex domain needs improvement
For example (as I have mentioned)
sage: ((-1)^(1/3)).n()
0.500 + 0.866025403784439*I
leads to wrong solution
sage: s=solve
This version works for me:
r,z = var('r,z')
gro = 1.0
kro = 3.0
def f(r,z):
term1 = (1+(bessel_J(0, gro)/bessel_J(2,gro)))*(r/
kro)*(bessel_J(1, r)/bessel_J(1,gro))*cos(z)
term2 = -(bessel_J(0,r)/bessel_J(2, gro))*(r**2/kro**2)
return term1 + term2
p = contour_plot(f , (r, 0, 2.5), (z,
On Oct 22, 4:57 am, Gary Church wrote:
> Hello all,
>
> How can I evaluate
>
> integral(sin(x^2),x,0,2)
>
> to get a real value instead of the nasty expression involving erf() and I
> that it spits out at me?
>
> Thanks much,
> Gary
One can check that the "nasty expression" is real:
sage: w=in
> Is that "integrate_numerical" or "numerical_integral"?
sage: numerical_integral(sin(x^2),0,2)
(0.80477648934375612, 1.0932458096886601e-14)
Andrzej Chrzeszczyk
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On Oct 8, 10:05 am, achrzesz wrote:
> The exact integral
>
> 1/2*(erf(pi - 1/2*I) + erf(pi + 1/2*I))*sqrt(pi)*e^(-1/4)
>
> contains *real* expression
>
> (erf(pi - 1/2*I) + erf(pi + 1/2*I))
>
> but maxima/sage can't check that it is real
>
> In WolframAlph
On Oct 23, 11:33 pm, Eric Kangas wrote:
> Hi,
>
> I have one function that I need to plot in an array with different
> values for two constants. I would like to only have to repeat the
> function once, and go off of a string of different variables to
> produce this array. Is that even possible i
sage: maxima('batch(solve_rec)')
"/home/andy/Pobrane/sage-4.7.1/local/share/maxima/5.23.2/share/contrib/
solve_rec/solve_rec.mac"
sage: maxima('deq: u[n+2]=2*u[n + 1] + 8*u[n];')
u[n+2]=2*u[n+1]+8*u[n]
sage: maxima('sol:solve_rec(deq,u[n],u[0]=2,u[1]=7);')
u[n]=11*4^n/6-(-2)^(n-1)/3
Andrzej Chrze
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