plenty to read in http://docs.sympy.org/latest/modules/galgebra/GA.html
had to dig to see what to import import sympy from sympy import * from sympy.galgebra import * from sympy.galgebra.ga import * some references said to from sympy.galgebra.GAsympy import * which doesn't exist or at least doesn't exist now. I will play around with it, thanks, but now I am curious about free algebra quotients a little. On Sat, Jul 26, 2014 at 8:27 PM, David Joyner <wdjoy...@gmail.com> wrote: > Have you looked at what sympy already has for Clifford algebras? > > > On Saturday, July 26, 2014, Stephen Kauffman <strangerl...@gmail.com> > wrote: > >> I attempted to create a Clifford Algebra for space-time with the gamma >> matrices using the FreeAlgebraQuotient in analogy to the example for >> constructing a quarternion algebra from the documentation with the code: >> >> PRGA=FreeAlgebra(QQ,4,'g') >> F = PRGA.monoid() >> g0,g1,g2,g3 = F.gens() >> mons = [ F(1), g0, g1, g2, g3, g0*g1, g0*g2, g0*g3, g1*g2, g2*g3, g3*g1, >> g0*g1*g2*g3*g0, g0*g1*g2*g3*g1, g0*g1*g2*g3*g2, g0*g1*g2*g3*g3, g0*g1*g2*g3] >> G0=diagonal_matrix([1,1,1,1,-1,-1,-1,-1]) #8x8 gamma matrices >> ZR=matrix(2,2,0) >> EE=diagonal_matrix([1,1]) >> II=matrix([[0,1],[-1,0]]) >> >> G1=block_matrix([[ZR,ZR,ZR,EE],[ZR,ZR,EE,ZR],[ZR,-EE,ZR,ZR],[-EE,ZR,ZR,ZR]],subdivide=False) >> >> G2=block_matrix([[ZR,ZR,ZR,-II],[ZR,ZR,II,ZR],[ZR,II,ZR,ZR],[-II,ZR,ZR,ZR]],subdivide=False) >> >> G3=block_matrix([[ZR,ZR,EE,ZR],[ZR,ZR,ZR,-EE],[-EE,ZR,ZR,ZR],[ZR,EE,ZR,ZR]],subdivide=False) >> mats = [G0,-G1,-G2,-G3] >> ST.<g0,g1,g2,g3> = FreeAlgebraQuotient(PRGA, mons, mats) >> ST >> >> Free algebra quotient on 4 generators ('g0', 'g1', 'g2', 'g3') and >> dimension 16 over Rational Field >> >> everything looked promising here but when I type >> >> g0*g1 >> >> Traceback (click to the left of this block for traceback) >> ... >> TypeError: unsupported operand parent(s) for '*': 'Vector space of >> dimension 16 over Rational Field' and 'Full MatrixSpace of 8 by 8 dense >> matrices over Integer >> Ring' >> >> I expected sage to parrot back >> >> g0*g1 >> >> Seems like we ought to be able to use a Free Algebra and the code: >> >> PRGA=FreeAlgebra(QQ,4,'g') >> MG=matrix(PRGA.gens()) >> MGG=MG.transpose()*MG >> Metric = diagonal_matrix([1,-1,-1,-1]) >> MGGM=MGG+MGG.transpose()-2*Metric >> [MGGM[i,j] for i in range(4) for j in range(4)] >> >> [-2 + 2*g0^2, g0*g1 + g1*g0, g0*g2 + g2*g0, g0*g3 + g3*g0, g0*g1 + >> g1*g0, 2 + 2*g1^2, g1*g2 + g2*g1, g1*g3 + g3*g1, g0*g2 + g2*g0, g1*g2 + >> g2*g1, 2 + 2*g2^2, >> g2*g3 + g3*g2, g0*g3 + g3*g0, g1*g3 + g3*g1, g2*g3 + g3*g2, 2 + 2*g3^2] >> >> and use this like an ideal. Sage is Clifford averse. >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sage-support" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to sage-support+unsubscr...@googlegroups.com. >> To post to this group, send email to sage-support@googlegroups.com. >> Visit this group at http://groups.google.com/group/sage-support. >> For more options, visit https://groups.google.com/d/optout. >> > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To post to this group, send email to sage-support@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.