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See: SymPy vs. Sage (from the SymPy GitHub Wiki).

On pp. 152-3 of Hydon's Symmetry Methods for Differential Equations (2000 ed.), he lists some computer packages for symmetry-finding. This related Mathematica StackExchange question mentions the SYM Mathematica package and Maple's DEtools/symgen. Does SAGE have anything similar for doing symmetry-finding?

I'm getting this issue with the Sage 7.5.1 release.

Unfortunately that didn't work for me.

How do I deal with large, hex numbers in Sage (say ones with 256 or 512 bytes)? How would I import them from a CSV file?

(cf. this related answer)

What about the comments here? Are those options good, too?

This is what I expected for an answer. I'm not looking for how to do every detail of such an implementation, but where to start. Thus, you've answered my question. thank you

How would I implement Lie-admissible algebras in Sage?

A Lie-admissible algebra is "A (non-associative) algebra (cf. Non-associative rings and algebras) whose commutator algebra becomes a Lie algebra." Read more.

Lie-admissible algebras are classified as 17D25 on MSC2010.

Oh, yes, using a windowing function is a good idea. thanks

Just ignore it. It's a self-signed cert because I'm too cheap to buy a CA-issued one…

How do I interpolate (up-sample) a discrete function so that I can perform a more refined FFT spectral analysis on it?

(Note: By default, NumPy's FFT command produces a list of the same dimension as the input list.)

thanks

They key is to use hist2d:

import matplotlib as mpl
import matplotlib.pyplot as plt

px,py = x,y

nx = ny = 100 #number of bins in x,y directions
x_bins = np.linspace(px.min(), px.max(), nx+1)
y_bins = np.linspace(py.min(), py.max(), ny+1)

plt.xlabel('Nonce');
plt.ylabel('Hash ($\log_{10}$)');
plt.title(r'2-D Histogram of First '+str(len(x))+' Valid Nonces and Hashes');

plt.hist2d(px, py, [x_bins,y_bins], norm=mpl.colors.LogNorm());

plt.savefig('Density Plot (log colorscale).png')
plt.close();

This produces a nice plot:

Actually, hist2d is what I was looking for.

Actually, I want to do this for discrete values, not functions, so a need to use histogram2d, as here.

I'm using Sage with KDE Cantor on Linux.

Here's what I did, and it works very well:

import csv
    mylist=[]
    with open('~/Downloads/datasmall.txt', 'rb') as csvfile:
         data = csv.reader(csvfile)
         for row in data:
             mylist.append([int(row[1]),float.fromhex(row[2])])

How can I make a 2-D density plot of a list of values in Sage?

I'd like to make something like this: (image source)

I'm dealing with over 300,000 points, and

p = Graphics()

for n in range(len(mylist)):
    
    p += point((mylist[n][0], mylist[n][1]),color=hue(n/len(mylist)))

is somewhat slow…

Any tips to speed this up?

thanks