Hi Alan! On Wed, Dec 2, 2009 at 3:48 PM, Alan Bromborsky <abro...@verizon.net> wrote: > Alan Bromborsky wrote: >> Vinzent Steinberg wrote: >> >>> On 1 déc, 21:28, Scott<scotta_2...@yahoo.com> wrote: >>> >>> >>>> Is there a sympy function for making symbolic tensors? >>>> Basically I want to treat 3x3 rotation tensor symbol that is constant >>>> inside of an integral while preserving the tensor algebra (A*B .ne. >>>> B*A). The 3x3 rotain tensor is multiplied by a 3x1 position tenosr >>>> which is integrated. >>>> >>>> Is there a built in function for converting a 3*1 tensor to a skew >>>> antisymetric cross product matrix then back again? >>>> V/R >>>> >>>> Scott >>>> >>>> >>> This is one of our oldest issues: >>> http://code.google.com/p/sympy/issues/detail?id=16 >>> >>> You may have a look at the geometric algebra module, but there are no >>> tensors in sympy yet. >>> >>> Vinzent >>> >>> -- >>> >>> You received this message because you are subscribed to the Google Groups >>> "sympy" group. >>> To post to this group, send email to sy...@googlegroups.com. >>> To unsubscribe from this group, send email to >>> sympy+unsubscr...@googlegroups.com. >>> For more options, visit this group at >>> http://groups.google.com/group/sympy?hl=en. >>> >>> >>> >>> >>> >> In geometric algebra rotations are done via rotors (spinors) as follows: >> >> For a the rotation of a vector x around an axis u (|u| = 1) through >> an angle theta, the rotor is: >> >> R = cos(theta)-I*u*sin(theta) >> >> where I is the pseudo scalar (I=i*j*k if i, j, and k are orthogonal >> basis vectors and * the geometric product). >> The components of I*u form a rank 2 antisymmetric tensor. The >> reverse of R, rev(R) is: >> >> rev(R) = cos(theta)+I*u*sin(theta) >> >> The rotated x, x' is then: >> >> x' = R*x*rev(R) >> >> where again * is the geometric product. >> >> What domain (path, area, or volume) do you want to integrate >> R*x*rev(R) over? >> >> -- >> >> You received this message because you are subscribed to the Google Groups >> "sympy" group. >> To post to this group, send email to sy...@googlegroups.com. >> To unsubscribe from this group, send email to >> sympy+unsubscr...@googlegroups.com. >> For more options, visit this group at >> http://groups.google.com/group/sympy?hl=en. >> >> >> >> > Here is your example: > > First the code - > > #!/usr/bin/python > > import sys > import os,sympy,time > from sympy.galgebra.GA import * > from sympy import cos,sin > set_main(sys.modules[__name__]) > > if __name__ == '__main__': > > make_symbols('a x y z') > MV.setup('e',metric='[1,1,1]',coords=[x,y,z]) > MV.set_str_format(1) > u = MV('u','vector') > x = MV('x','vector') > print u > print x > print MV.I*u > R = cos(a)-MV.I*u*sin(a/2) > Rrev = R.rev() > print R > print Rrev > MV.set_str_format(2) > rot_x = R*x*Rrev > rot_x.simplify() > print rot_x > > Second the result - > > u__x*e_x+u__y*e_y+u__z*e_z > > x__x*e_x+x__y*e_y+x__z*e_z > > u__z*e_xe_y-u__y*e_xe_z+u__x*e_ye_z > > cos(a/2)-u__z*sin(a/2)*e_x^e_y+u__y*sin(a/2)*e_x^e_z-u__x*sin(a/2)*e_y^e_z > > cos(a/2)+u__z*sin(a/2)*e_x^e_y-u__y*sin(a/2)*e_x^e_z+u__x*sin(a/2)*e_y^e_z > > (-2*u__z*x__y*cos(a/2)*sin(a/2)+2*u__y*x__z*cos(a/2)*sin(a/2)+x__x*cos(a/2)**2+x__x*u__x**2*sin(a/2)**2-x__x*u__y**2*sin(a/2)**2-x__x*u__z**2*sin(a/2)**2+2*u__x*u__y*x__y*sin(a/2)**2+2*u__x*u__z*x__z*sin(a/2)**2)*e_x > +(-2*u__x*x__z*cos(a/2)*sin(a/2)+2*u__z*x__x*cos(a/2)*sin(a/2)+x__y*cos(a/2)**2+x__y*u__y**2*sin(a/2)**2-x__y*u__x**2*sin(a/2)**2-x__y*u__z**2*sin(a/2)**2+2*u__x*u__y*x__x*sin(a/2)**2+2*u__y*u__z*x__z*sin(a/2)**2)*e_y > +(-2*u__y*x__x*cos(a/2)*sin(a/2)+2*u__x*x__y*cos(a/2)*sin(a/2)+x__z*cos(a/2)**2+x__z*u__z**2*sin(a/2)**2-x__z*u__x**2*sin(a/2)**2-x__z*u__y**2*sin(a/2)**2+2*u__x*u__z*x__x*sin(a/2)**2+2*u__y*u__z*x__y*sin(a/2)**2)*e_z > > In the previous post I forgot you had to use the half-angle!
thanks for this, I am always intrigued how well you handle the geometric algebra and that you are able to handle all problems that people (including myself) raise with tensors. It's really cool, I am glad we have it in sympy. Ondrej -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sy...@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
