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]) >> >> >> >> -- >> >> You received this message because you are subscribed to the Google Groups >> >> "sympy" group. >> >> To unsubscribe from this group and stop receiving emails from it, send an >> >> email to sympy+un...@googlegroups.com. >> >> To view this discussion on the web visit >> >> https://groups.google.com/d/msgid/sympy/8db840a8-20f9-47ac-a1c3-11b6658f00bfn%40googlegroups.com. >> > >> > -- >> > You received this message because you are subscribed to the Google Groups >> > "sympy" group. >> > To unsubscribe from this group and stop receiving emails from it, send an >> > email to sympy+un...@googlegroups.com. >> > To view this discussion on the web visit >> > https://groups.google.com/d/msgid/sympy/9797a914-06a6-4f8e-a99f-5403504862bfn%40googlegroups.com. > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/49cefd33-34db-4c97-9010-cc9be4f1f131n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sympy" group. 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