Define a differential form recursively

rfauffar
21 ●5

I have the following code:

n=3;
x = list(var('x_%d' % i) for i in (1..2*n));
U = CoordinatePatch(x);
F = DifferentialForms(U);
w = DifferentialForm(F,2);
  for j in range(2*n-1):
     for k in range(2*n-1):
        w[j,k]=j+k;
w;

It's supposed to define a differential form whose (j,k)th member is j+k, but this code just returns the 0 differential form. I've tried many variations using for, while, etc., but none seem to work. I suspect it's because a differential form is stored as a dictionary, but since I'm a beginner in Sage, I have no idea what to do. Any help is appreciated.

answered 11 years ago

kcrisman
12252 ●42 ●136 ●255

I seem to get something reasonable here, not the zero form.

??????????????????????????????????????????????????????????????????????
? Sage Version 5.12, Release Date: 2013-10-07                        ?
? Type "notebook()" for the browser-based notebook interface.        ?
? Type "help()" for help.                                            ?
??????????????????????????????????????????????????????????????????????
sage: n=3;
sage: x = list(var('x_%d' % i) for i in (1..2*n));
sage: U = CoordinatePatch(x);
sage: F = DifferentialForms(U);
sage: w = DifferentialForm(F,2);
sage:   for j in range(2*n-1):
....:          for k in range(2*n-1):
....:                 w[j,k]=j+k;
....:         
sage: w
-1*dx_1/\dx_2 + -3*dx_2/\dx_3 + 0*dx_1/\dx_1 + 0*dx_4/\dx_4 + 0*dx_3/\dx_3 + 0*dx_5/\dx_5 + -5*dx_2/\dx_5 + -2*dx_1/\dx_3 + -4*dx_2/\dx_4 + -5*dx_3/\dx_4 + -4*dx_1/\dx_5 + -6*dx_3/\dx_5 + -3*dx_1/\dx_4 + -7*dx_4/\dx_5 + 0*dx_2/\dx_2

I will point out that perhaps you are using 1-based counting, but Python starts counting at 0. Is this what you are looking for?

sage: for j in range(2*n-1):
....:     for k in range(2*n-1):
....:         w[j,k] = j+1+k+1
....:         
sage: w
-3*dx_1/\dx_2 + -5*dx_2/\dx_3 + 0*dx_1/\dx_1 + 0*dx_4/\dx_4 + 0*dx_3/\dx_3 + 0*dx_5/\dx_5 + -7*dx_2/\dx_5 + -4*dx_1/\dx_3 + -6*dx_2/\dx_4 + -7*dx_3/\dx_4 + -6*dx_1/\dx_5 + -8*dx_3/\dx_5 + -5*dx_1/\dx_4 + -9*dx_4/\dx_5 + 0*dx_2/\dx_2

I don't know whether the negatives are what you want or not, nor why the necessarily zero differentials are even included, but I've never used this functionality before, so you will have to peruse the documentation for technical points like this.

link

add a comment

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Define a differential form recursively

1 Answer

Your Answer

Question Tools

Stats

Related questions

Define a differential form recursively savecancel

1 Answer