marco's profile - activity

If you try to show() a sage.plot.graphics.Graphics object, you will find something extremely bizarre: there is a white border around the .png image which is 30 pixels wide (on some sides, 31 pixels wide). There is no documentation of this and it seems to be impossible to remove with any documented options to show() or to the settings of a Graphics object.

Does anyone know how to get rid of this bug?

The best thing I came up with was to do

show(MyObject, axes=False, axes_pad=0)

This only reduced the number of pixels but didn't remove the border entirely.
Also note that you can sometimes make the graphics object transparent (though not through show()), but this does not remove the border, it only makes it transparent, which causes even more problems when I pipe this into other software.

Example:

polygon([(0,0),(1,0),(1,1),(0,1)],aspect_ratio=1,axes=False,figsize=1,axes_pad=0)

yields:

Why is the absolute value of the exponential of z:

f = fast_callable(exp(z).abs(),domain=CDF,vars='z')

about twice as fast as the exponential of the real part of z:

g = fast_callable(exp(z.real()), domain=CDF, vars='z')

Should I ignore this kind of thing in sage, or is there a good reason in this particular case?

Data:

z = var('z')
f = fast_callable(exp(z).abs(),domain=CDF,vars='z')
g = fast_callable(exp(z.real()), domain=CDF, vars='z') 
timeit('f(4+2*I)')

625 loops, best of 3: 2.94 µs per loop

timeit('g(4+2*I)')

625 loops, best of 3: 5.87 µs per loop

Non-fast_callable times, in case you are interested:

z = var('z')
fs(z) = exp(z).abs()
gs(z) = exp(z.real())
timeit('fs(4+2*I)')

625 loops, best of 3: 1.02 ms per loop

timeit('gs(4+2*I)')

625 loops, best of 3: 988 µs per loop

I have been using Sage through the notebook interface. I usually keep my other working documents in sync using Dropbox. What do you think is an efficient way of working on notebooks from different computers? Currently I export and import .sws files. I thought of perhaps changing the DATA path to a folder on Dropbox, but I don't know enough about the internals of Sage to see if this would be a horrible idea.

This is more of a general question about whether we can do with Sage what we normally do as mathematicians on paper and in our minds. For example, if I do

V = VectorSpace(QQ,4)

W = VectorSpace(QQ,4)

V==W

I get: True. This is quite disturbing - while V and W are isomorphic they should not be identical. As I understand it, a vectorspace over QQ for Sage is just QQ^4, that's it. In other words, the Linear algebra package, while excellent, is not really about vector spaces but rather about arrays of numbers.

Any thoughts on this desire of mine to have a genuine "coordinate-free" approach?

I would like to do a computation in Sage involving formal power series but I believe some (all?) steps may be impossible:

1. define a couple of formal power series in two variables (x,y) by defining the coefficient function a(m,n) (the coefficients involve gamma functions and such, and are rational). As far as I can see there is no way to do even this step in Sage.

2. do a change of variables, something like (x,y) = (g(x,y),y), obtaining new power series. The function g(x,y) may be a polynomial or possibly itself an infinite power series.

3. multiply the resulting power series

4. Simplify the expression for the coefficients of the resulting power series c(m,n) in terms of classical quantities like gamma functions.

Which of these steps do you believe is possible in Sage? I could write my own software to deal with formal power series properly, but then I would not be able to recognize or simplify the resulting coefficients.

As an example:

1. h(x,y) is a sum of (m!)(4^n)x^m y^n with indices running from 0 to infinity, and k(x,y) is a sum of (m+n)x^m y^n,

2. do a substitution H(x,y) = h(x,exp(xy)y)

3. multiply H*k

4. simplify the coefficients of H*k.

sage: type(airy_ai)
<type 'function'>
sage: type(gamma)
<type 'function'>
sage: type(sin)
<class 'sage.functions.trig.Function_sin'>
sage: type(log_gamma)
<class 'sage.functions.other.Function_log_gamma'>

Actually, this is somewhat misleading, since gamma uses

sage: type(sage.functions.other.gamma1)
<class 'sage.functions.other.Function_gamma'>

under the hood, but I hope you get the point.

See also Trac 12455 for this very issue - maybe you can help?

This helps but actually gives an even better example of my problem: sage: type(airy_ai); type(gamma) type 'function' type 'function' sage: taylor(gamma(x),x,1) -(x - 1)*euler_gamma + 1 sage: taylor(airy_ai(x),x,2) TypeError: Cannot evaluate symbolic expression to a numeric value.

Sorry for the wording of the question. Functions in sage.functions.special, such as airy_ai, seem not to be true functions, e.g. you can't apply taylor() to them. On the other hand, maxima.airy_ai seems to be OK. How can I tell what "status" a function has, or whether I can pass it to operations such as taylor()?

taylor(maxima.airy_ai(x),x,0,4)

-1/363^(2/3)x^4/gamma(1/3) + 1/183^(1/3)x^3/gamma(2/3) - 1/33^(2/3)x/gamma(1/3) + 1/3*3^(1/3)/gamma(2/3)

taylor(sage.functions.special.airy_ai(x),x,0,4)

Traceback (click to the left of this block for traceback) ... TypeError: Cannot evaluate symbolic expression to a numeric value.

thanks, that makes it even easier.

One thing that seems to work is to start the sage notebook from the terminal session with

sage: notebook('/Users/.../Dropbox/Sage')

to create a notebook in the specified directory and then use the same command for any other linked computer. I've tried this out and it seems to work perfectly using Dropbox.

I think the plot must contain the information of its dimensions, so perhaps we can programmatically do this

This seems to be a feature from matplotlib. You can try your best, turning off everything in matplotlib like this:

import matplotlib.pyplot as plt
plt.plot(range(10), range(10))
plt.axis('off')
plt.savefig('/tmp/a.png', bbox_inches='tight')

The outcome of the plot will be the same as the following code in Sage:

list_plot(range(10), plotjoined=True, axes=False)

So there is not much that can be done on Sage side. Eventually, the generation of the figure and the saving is handled by matplotlib.

Update:

There is a way to do it in matplotlib.

sage: import matplotlib.pyplot as plt
sage: plt.plot(range(10), range(10), '-o')
sage: plt.subplots_adjust(left=0, right=1, top=1, bottom=0)
sage: plt.axis('off')
sage: plt.savefig('/tmp/a.png', bbox_inches=0)