p.dot(p)
a**2 + b**2 + c**2
dot(p,p)
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
i am confused. why does this happen?
Oscar schrieb am Montag, 25. Oktober 2021 um 12:35:47 UTC+2:
> 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 <and...@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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> .
> >> >
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