I don't see the exception that you showed:
In [9]: O = CoordSys3D('O')
...: r = O.x*O.i + O.y*O.j + O.z*O.k
...: dot(r,r) # this works
...: O.x**2 + O.y**2 + O.z**2
...: from sympy import symbols
...: a, b, c = symbols("a, b, c")
...: p = a*O.i +b*O.j + c*O.k
...: p
...: a*O.i + b*O.j + c*O.k
...: dot(p,p) # this does not work
Out[9]:
2 2 2
a + b + c
--
Oscar
On Mon, 25 Oct 2021 at 11:28, Andreas Schuldei <andr...@schuldei.org> wrote:
>
>
> I am trying to figure out the basics here.
> I understand O.x, O.y and O.z have special meaning, first because they
> magically appear, just by instanciating O, and also because they seem to
> distinguish themselves from other generic symbols/skalars:
>
> O = CoordSys3D('O')
> r = O.x*O.i + O.y*O.j + O.z*O.k
> dot(r,r) # this works
> O.x**2 + O.y**2 + O.z**2
> from sympy import symbols
> a, b, c = symbols("a, b, c")
> p = a*O.i +b*O.j + c*O.k
> p
> a*O.i + b*O.j + c*O.k
> dot(p,p) # this does not work
> Traceback (most recent call last):
> File "<input>", line 1, in <module>
> File "C:\Users\Andreas
> Schuldei\PycharmProjects\lissajous-achse\venv\lib\site-packages\sympy\physics\vector\functions.py",
> line 31, in dot
> raise TypeError('Dot product is between two vectors')
> TypeError: Dot product is between two vectors
> p = a*O.x*O.i + b*O.y*O.j + c*O.z*O.k
> dot(p,p) # this does not work, either!
> Traceback (most recent call last):
> File "<input>", line 1, in <module>
> File "C:\Users\Andreas
> Schuldei\PycharmProjects\lissajous-achse\venv\lib\site-packages\sympy\physics\vector\functions.py",
> line 31, in dot
> raise TypeError('Dot product is between two vectors')
> TypeError: Dot product is between two vectors
>
> Why is this? What factors are allowed with vector components and unit vectors?
>
> I feel a little restricted if my only vector component variables allowed are
> O.x, O.y, and O.z.
> Oscar schrieb am Samstag, 23. Oktober 2021 um 16:49:10 UTC+2:
>>
>> A SymPy Vector is constructed algebraically from the unit vectors i, j
>> and k of the coordinate system. For a vector field you also use the
>> coordinate system base scalars x, y and z.
>>
>> In [11]: from sympy.vector import CoordSys3D, dot
>>
>> In [12]: O = CoordSys3D('O')
>>
>> In [13]: r = O.x*O.i + O.y*O.j + O.z*O.k
>>
>> In [14]: r
>> Out[14]: (x_O) i_O + (y_O) j_O + (z_O) k_O
>>
>> In [15]: dot(r, r)
>> Out[15]:
>> 2 2 2
>> x_O + y_O + z_O
>>
>> I often see confusion about this so clearly this is not very intuitive
>> and maybe it is not very clearly documented:
>> https://docs.sympy.org/latest/modules/vector/index.html
>>
>> I think there should be an easier way where you can just use a
>> "standard" coordinate system and just do:
>>
>> from sympy.vector.stdcoords import x, y, z, i, j, k
>> r = x*i + y*j + z*k
>> print(dot(r, r))
>>
>> The vector docs should just begin by showing how to do that and then
>> how to do simple calculations in a single coordinate system.
>>
>> --
>> Oscar
>>
>> On Sat, 23 Oct 2021 at 07:11, Andreas Schuldei <and...@schuldei.org> wrote:
>> >
>> > I am putting together the components of a vector field (a magnetic field,
>> > caused by a current in several conductors) in cartesian coordinates. The
>> > field is derived from calculating the rotation of its magnetic vector
>> > potential, which can be expressed as
>> >
>> > A_z = -Const * dot(r,a)(dot(r,r)
>> > A =(0,0,A_z
>> > and then the rot(A):
>> > B = curl(A)
>> >
>> > gives me (after some simplifications)
>> > u = (2 * C * r2 * (a1 * r1 + a2 * r2)) / np.square(r1*r1 + r2*r2) - (C *
>> > a2) / (r1*r1 + r2*r2)
>> > v = (C * a1) / (r1*r1 + r2*r2) - (2 * C * r1 * (a1 * r1 + a2 * r2)) /
>> > np.square(r1*r1 + r2*r2)
>> > w = 0
>> >
>> > with B(u,v,w) being the vector field I am interested in.
>> >
>> > My initial question ("How to create a vector") is mostly a sympy
>> > syntactical one. I look for a function like
>> >
>> > Sys = CoordSys3D("Sys")
>> > O = Sys.origin
>> > u = (2 * C * r2 * (a1 * r1 + a2 * r2)) / np.square(r1*r1 + r2*r2) - (C *
>> > a2) / (r1*r1 + r2*r2)
>> > v = (C * a1) / (r1*r1 + r2*r2) - (2 * C * r1 * (a1 * r1 + a2 * r2)) /
>> > np.square(r1*r1 + r2*r2)
>> > w = 0
>> > V = O.vector(u,v,w)
>> > ^^^^^^^^^^^^^^^^^^^
>> > where I can specify a vector, relative to a coordinate system, by its
>> > components. The O.vector() function would return a vector that can then
>> > safely be transformed into other (resting) coordinate systems.
>> >
>> > brombo schrieb am Freitag, 22. Oktober 2021 um 19:06:03 UTC+2:
>> >>
>> >> You might want to look at this link -
>> >>
>> >> https://galgebra.readthedocs.io/en/latest/
>> >>
>> >> Also if you could show me symbolically (not code) what you are doing
>> >> perhaps I could give you an example of how to do it in galgebra.
>> >>
>> >> On 10/22/21 3:15 AM, Andreas Schuldei wrote:
>> >>
>> >> I saw this
>> >> https://stackoverflow.com/questions/46993819/how-to-create-a-vector-function-in-sympy
>> >> which uses Matrix() as a workaround to create a vector. The author says,
>> >> that it can not be transformed between coordinate systems, like real
>> >> vectors, though.
>> >>
>> >> I need to transform my input and output vector from one coordinate system
>> >> to another (and back). How are vector functions done in that case? My
>> >> function is simple:
>> >>
>> >> def B_el(r_vec, I):
>> >> mu_0 = 4 * np.pi * 1e-7
>> >> a1 = -0.05
>> >> a2 = 0.0
>> >> C = mu_0 * I / np.pi
>> >> r1 = r_vec.i
>> >> r2 = r_vec.j
>> >> u = (2 * C * r2 * (a1 * r1 + a2 * r2)) / np.square(r1*r1 + r2*r2) - (C *
>> >> a2) / (r1*r1 + r2*r2)
>> >> v = (C * a1) / (r1*r1 + r2*r2) - (2 * C * r1 * (a1 * r1 + a2 * r2)) /
>> >> np.square(r1*r1 + r2*r2)
>> >> return Matrix([u, v, 0])
>> >>
>> >> --
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>> >> https://groups.google.com/d/msgid/sympy/8db840a8-20f9-47ac-a1c3-11b6658f00bfn%40googlegroups.com.
>> >
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>
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