FrédéricC's profile - activity

How can I plot a list of points in space where the points are colored by their height?

The following code:

biglist = [(0, 0, 12), (0, 1, 19), (0, 2, 24), (0, 3, 30), (0, 4, 33), (0, 5, 35),
(0, 6, 38), (0, 7, 40), (0, 8, 41), (0, 9, 43), (0, 10, 44), (0, 11,
44), (0, 12, 44), (0, 13, 44)]

cm = colormaps.autumn
cf = lambda (x,y,z): z/100 % 1

list_plot3d(biglist, color=(cm,cf), point_list=True)

produces the following error:

/Applications/SageMath-7.2.app/Contents/Resources/sage/local/lib/python2\
.7/site-packages/matplotlib-1.5.1-py2.7-macosx-10.7-x86_64.egg/matplotli\
b/cbook.py:137: MatplotlibDeprecationWarning: The matplotlib.delaunay
module was deprecated in version 1.4. Use matplotlib.tri.Triangulation
instead.
  warnings.warn(message, mplDeprecation, stacklevel=1)
/Applications/SageMath-7.2.app/Contents/Resources/sage/local/lib/python2\
.7/site-packages/numpy-1.11.0-py2.7-macosx-10.7-x86_64.egg/numpy/lib/fun\
ction_base.py:2558: RuntimeWarning: invalid value encountered in
true_divide
  c /= stddev[:, None]
/Applications/SageMath-7.2.app/Contents/Resources/sage/local/lib/python2\
.7/site-packages/numpy-1.11.0-py2.7-macosx-10.7-x86_64.egg/numpy/lib/fun\
ction_base.py:2559: RuntimeWarning: invalid value encountered in
true_divide
  c /= stddev[None, :]
Traceback (click to the left of this block for traceback)
...
KeyError: 'popitem(): dictionary is empty'

I am trying to plot alcoves for in a rank 3 affine root system with some of those alcoves highlighted by having all faces drawn and the others only shown as a wire frame.

The manual on visualising root systems at sagemath.org is quite useful, but I have some effects show that I don't understand.

For some reason while the fundamental alcove will have all faces shown many of the others have not, that is, some faces are missing. Below you find one example code that I have done. For the chosen seq one face is missing, the red one. For other choices of seq one might even see only one face drawn. How do I force to have all faces shown?

L = RootSystem(["A",3,1]).ambient_space()
P = RootSystem(["A",3,1]).weight_space(extended=True)
Lambda = P.fundamental_weights()
W = L.weyl_group()
W0=W.classical()
plot_options = L.plot_parse_options()
seq=[2,3,1,2]  
t = 1*Lambda[1]-1*Lambda[2]+1*Lambda[3]
Alcoves=[W.from_reduced_word(w.reduced_word()) for w in W0]
p = L.plot_fundamental_chamber("classical")
p += L.plot_fundamental_weights()
p += L.plot_alcoves(alcoves=Alcoves, wireframe=True)
p += L.plot_alcoves(alcoves=[W.from_reduced_word(seq)])
p += L.plot_alcoves(alcoves=[W.from_reduced_word([])])
p += plot_options.family_of_vectors({t: L(t)})
p.show(frame=False)

This looks like the error that appears when calling "var" inside python, not inside sage..

Here is what I get with sage 8.7.beta2. This seems to be correct. Which version of sage are you using ?

sage: x = QQ[['x']].0
sage: f = x.cos()
sage: f.pade(2,4)
(-244/3*x^2 + 200)/(x^4 + 56/3*x^2 + 200)
sage: f.pade(2,4)(x)
1 - 1/2*x^2 + 1/24*x^4 - 1/720*x^6 - 17/216000*x^8 + 463/32400000*x^10 - 9139/9720000000*x^12 + 23771/1458000000000*x^14 + 1390687/437400000000000*x^16 - 24818093/65610000000000000*x^18 + O(x^20)
sage: f
1 - 1/2*x^2 + 1/24*x^4 - 1/720*x^6 + 1/40320*x^8 - 1/3628800*x^10 + 1/479001600*x^12 - 1/87178291200*x^14 + 1/20922789888000*x^16 - 1/6402373705728000*x^18 + O(x^20)

Like that

sage: R=GF(2)['x,y']
sage: x,y=R.gens()
sage: I=R.ideal([1+x*y,x+y])
sage: I.vector_space_dimension()
2

try ZZ(test)//2

Hello,

i am calculating the quotient of a really big number using the operator // the fact is: if the big number is in a variable, let's say x, and i write x//2, it won't work (it'll return x/2). But if i copy/paste the big number and write //2 at the end, it works.

I don't understand it. I wanted to post a picture as example, but it seems that i need more karma to do it... so instead i put a copy/paste of the problem at the end of this post. The variable's name is "test", so i first print it, then do the //2; as you can see it doesn't work, i got the same number with /2 at the end. Then i copy/paste the number and use //2 again and here it works. The point is: when i use it in a programm, i can't copy/paste the number, it'll be in a variable. And then it fails.

sage: test
837852367160941686882182203279810821534331590056292182065749220359229900094799322306853693706463088872767820405170018794451898101765853614283153521412505365960228304480760794688517092896652646155467604050167410281621256684893277033624912312765082826592417694451712096609637026970174504593832198908321736540951
sage: test//2
837852367160941686882182203279810821534331590056292182065749220359229900094799322306853693706463088872767820405170018794451898101765853614283153521412505365960228304480760794688517092896652646155467604050167410281621256684893277033624912312765082826592417694451712096609637026970174504593832198908321736540951/2
sage: 83785236716094168688218220327981082153433159005629218206574922035922990009479932230685369370646
....: 30888727678204051700187944518981017658536142831535214125053659602283044807607946885170928966526
....: 46155467604050167410281621256684893277033624912312765082826592417694451712096609637026970174504
....: 593832198908321736540951//2
418926183580470843441091101639905410767165795028146091032874610179614950047399661153426846853231544436383910202585009397225949050882926807141576760706252682980114152240380397344258546448326323077733802025083705140810628342446638516812456156382541413296208847225856048304818513485087252296916099454160868270475

giac gives an answer, but this answer fails to be converted to sage

What can not be decoded is 未命名

i use a windows laptop with Chinese. i download the windows installer, and install the sage 8.5 successfully. it can run sage(shell) correctly, but when i launch the jupyter, something wrong with it.

"sage -n" use the cmd to start a server, i got

File "/opt/sagemath-8.5/src/bin/sage-notebook", line 268, in 
launcher(unknown)
File "/opt/sagemath-8.5/src/bin/sage-notebook", line 142, in init
super(SageNBExport, self).init(argv)
File "/opt/sagemath-8.5/src/bin/sage-notebook", line 100, in init
main(argv)
File "/opt/sagemath-8.5/local/lib/python2.7/site-packages/jupyter_core/application.py", line 266, in launch_instance
return super(JupyterApp, cls).launch_instance(argv=argv, **kwargs)
File "/opt/sagemath-8.5/local/lib/python2.7/site-packages/traitlets/config/application.py", line 657, in launch_instance
app.initialize(argv)
File "", line 2, in initialize
File "/opt/sagemath-8.5/local/lib/python2.7/site-packages/traitlets/config/application.py", line 89, in catch_config_error
app.print_help()
File "/opt/sagemath-8.5/local/lib/python2.7/site-packages/traitlets/config/application.py", line 385, in print_help
self.print_subcommands()
File "/opt/sagemath-8.5/local/lib/python2.7/site-packages/traitlets/config/application.py", line 377, in print_subcommands
print(os.linesep.join(lines))
UnicodeDecodeError: 'ascii' codec can't decode byte 0xe5 in position 4: ordinal not in range(128)

so i try some solutions, i can skip this step, but i got stuck in the jupyter launch step:

Could not decode '\xe6\x9c\xaa\xe5\x91\xbd\xe5\x90\x8d' for unicode trait 'untitled_notebook' of a LargeFileManager instance.

i know there is something wrong with the coding in python (and there are many problems when software operate with Chinese), but i can't find the right way to solve it

or more precisely in the python used by sage, which can be the system's python, depending on the way you installed sage.

This can be found using len(v)

you can import any python module that is installed in sage's own python.

Not exactly Markdown, but close to it, you can discover the syntax by editing a post and clicking on the icons on top of the edit section (e.g. B, I, planet, ", 101010, picture,...).

For example bild is obtained with **, italic with *, and so on.

Regarding formatting Sage, you can have a monospaced code either with the button 101010, or by adding 4 spaces at the beginning of very code line.

I edited your other question, you can check the markup by editing it.

I am interested to compute: ``torsion subgroups of Jacobian abelian variety J_0(p^2) defined over fields bigger than rationals."

The command: Upto p=11 it is fine after that if you give

J0(169).qbar_torsion_subgroup().field_of_definition()

gives the error:

``AttributeError                            Traceback (most recent call last)
<ipython-input-1-0f46a1a51624> in <module>()
      1 A = J0(Integer(169))
      2 A.qbar_torsion_subgroup()
----> 3 A.field_of_definition()
      4 J0(Integer(169)).qbar_torsion_subgroup().field_of_definition()"

Can somebody kindly tell me why Sage can compute upto p=11?

See

k.modulus?

syntax error, the brackets are not right. You are trying to iterate over QQ...

The long-term plan is to move Sage to Python 3. Here's a couple Trac metatickets that show the progress:

• https://trac.sagemath.org/ticket/15980
• https://trac.sagemath.org/ticket/16052
• https://trac.sagemath.org/ticket/26212

In the mean time, just be aware of the major changes between the two versions and write Python 3-compatible code as much as possible.

I just learnt python3. But i came to know after installing sage that it use python2? Do I have a future in sage? I don't prefer to use the cloud, but the package i have?

What should I do now?

There is a known issue with volume computations when coefficients are in RR. Try if possible to use coefficients in QQ.

See https://trac.sagemath.org/ticket/18214 for the known bug.

Well, this is sort of a known problem.. https://trac.sagemath.org/ticket/14885

There is something for permutations:

sage: Permutations.options(mult='r2l',display='cycle')
sage: a=Permutation([(1,2),(3,)]);a
(1,2)
sage: b=Permutation([(2,3),(1,)]);b
(2,3)
sage: a*b
(1,2,3)

But this does not seem to be available for SymmetricGroup.

Maybe using

sage: E(8)*E(8).conjugate()
1

to make your own norm method for vectors ?

Which version of sage ? Which OS (windows© or not windows©) ? How did you install sage ? etc..

Maybe like that:

hex(hash(R))

Like this:

M = FiniteSetMaps(["a", "b"], [3, 4, 5]); M

Did you look at the doc: numerical_integral?

typical sage+python3 error ; already fixed in the latest beta

It seems that currently the index set for reducible types can only be consecutive integers starting from 1.

sage: ct = CartanType("B3").subtype([1, 3])
sage: ct.index_set??

This is displayed also in the following example

sage: CartanType("A5").index_set()
(1, 2, 3, 4, 5)
sage: CartanType("A5").subtype([3,4]).index_set()
(3, 4)
sage: CartanType("A5").subtype([1,4]).index_set()
(1, 2)

So there is certainly room for improvement here.

in 8.5.b0:

sage: integral(sqrt(1+cos(x)**2), x).full_simplify()
1/6*sin(x)^3

Use something like that

sage: [v for v in IntegerVectors(n=4,k=3)]
[[4, 0, 0],
 [3, 1, 0],
 [3, 0, 1],
 [2, 2, 0],
 [2, 1, 1],
 [2, 0, 2],
 [1, 3, 0],
 [1, 2, 1],
 [1, 1, 2],
 [1, 0, 3],
 [0, 4, 0],
 [0, 3, 1],
 [0, 2, 2],
 [0, 1, 3],
 [0, 0, 4]]

The threejs works very well for me with a python3-built sage (on Ubuntu).

your px and py should be vectors, not matrices. Use vector(list2(2,5,6))

You should not use "make" for the moment.

See https://trac.sagemath.org/ticket/26212

Like that maybe

sage: K.<a>=QuadraticField(5)
sage: K.primes_of_bounded_norm(120)