ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 03 Apr 2021 20:34:41 +0200Evaluating a form field at a point on vectorshttps://ask.sagemath.org/question/56483/evaluating-a-form-field-at-a-point-on-vectors/I am having trouble matching up terminology in my textbook (Hubbard's *Vector Calculus*) against SageMath operators. I'd like to understand how to solve the following example problem with Sage:
> Let `phi = cos(x z) * dx /\ dy` be a 2-form on `R^3`. Evaluate it at the point `(1, 2, pi)` on the vectors `[1, 0, 1], [2, 2, 3]`.
The expected answer is:
```
cos (1 * pi) * Matrix([1, 2], [0, 2]).det() = -2
```
So far I have pieced together the following:
E.<x,y,z> = EuclideanSpace(3, 'E')
f = E.diff_form(2, 'f')
f[1, 2] = cos(x * z)
point = E((1,2,pi), name='point')
anchor = f.at(point)
v1 = vector([1, 0, 1])
v2 = vector([2, 2, 3])
show(anchor(v1, v2))
which fails with the error:
> `TypeError: the argument no. 1 must be a module element`
To construct a vector in `E`, I tried:
p1 = E(v1.list())
p2 = E(v2.list())
show(anchor(p1, p2))
but that fails with the same error. What's the right way to construct two vectors in `E`?ripple_carrySat, 03 Apr 2021 20:34:41 +0200https://ask.sagemath.org/question/56483/