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]) > >> >> > >> >> -- > >> >> 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+un...@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. 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/c41fa5b9-047a-4150-a28a-c10bab1d840en%40googlegroups.com.