######################################################################## #Clifford(1,4) #Flat space, no metric, just signature #All constants = 1 metric=[1 ,-1 ,-1 ,-1 ,-1] #Dimensions variables = (t, x, y, z, w) = symbols('t x y z w', real=True) myBasis='gamma_t gamma_x gamma_y gamma_z gamma_w' #Algebra sp5d = Ga(myBasis, g=metric, coords=variables,norm=True) (gamma_t, gamma_x, gamma_y, gamma_z, gamma_w) = sp5d.mv() (grad, rgrad) = sp5d.grads() #Imaginary unit imag=gamma_w imag.texLabel='i' #Associative Hyperbolic Quaternions ihquat=gamma_t jhquat=gamma_t*gamma_x*gamma_y*gamma_z*gamma_w khquat=gamma_x*gamma_y*gamma_z*gamma_w ihquat.texLabel='\\mathbf{i}' jhquat.texLabel='\\mathbf{j}' khquat.texLabel='\\mathbf{k}' #Quaternions iquat=gamma_y*gamma_z jquat=gamma_z*gamma_x kquat=gamma_x*gamma_y