Friedrich Hagedorn wrote: > On Mon, Oct 06, 2008 at 06:26:11PM -0400, Alan Bromborsky wrote: > >> Yes almost, but can you suppress the (x1,x2,x3) in the output so that >> the output would be >> >> A*dB/dx1+B*dA/dx1 ? >> > > I dont think that > > dA/dx1 > > is a good idea for a CAS. This notation means the partial derivative of > A(x1, x2, x3) in respect to x1. But x1 is only a 'local symbol' in the > function A. The following terms are equivalent > > diff( A(x1, x2, x3), x1) == diff( A(b, c, e), b) > > == diff( A(x, y, z), x) > > Thats why there is an other notation > > diff(A, 1) > > means the partial derivative of A in respect to the first Argument of A. > This notation it unique but not so convinient to read. > > By, > > Friedrich > > PS.: What is your original problem? > > > > > I am calculating the geometric derivative of a multivector field. The most general field for space time (4 basis vectors) can have 16 real coefficients that are a function of the 4-position vector x = (x0,x1,x2,x3) (note that x0=ct). There are one scalar, 4 vector, 6 bivector, 4 trivector, and one pseudoscalar coefficents. Lets just consider the bivector coefficients B^{ij} which are functions of x. The standard notation for the derivatives of B^{ij} would be \partial_{k}B^{ij}. I am looking for a notation that duplicates the standard notation as closely as possible both when printed out and in the python program. I know from context that B^{ij} is a function of x and do not want to have B^{ij}(x0,x1,x2,x3) repeated over and over in a long expression especially if the B^{ij} are themselves expressed as functions of implicit and explicit functions. For example if B^{12} = x0*g^{12}(x0,x1,x2,x3)+x1*f^{12}(x0,x1,x2,x3) , having the (x0,x1,x2,x3) appear in every implicit function and in every derivative of a implicit function would be confusing, especially in long expressions containing many terms.
For reference the most general multivector field is written in terms of the real coefficients a, B^{ij}, T^{lmn}, and p using the summation convention with j<k and l<m<n: A = a +v^{i}\gamma_{i}+B^{jk}\gamma_{k}\gamma_{k}+T^{lmn}\gamma_{l}\gamma_{m}\gamma_{n}+ p\gamma_{0}\gamma_{1}\gamma_{2}\gamma_{3} where the space time basis vectors are \gamma_{0}, \gamma_{1}, \gamma_{2},\and gamma_{3} and the geometric products of the basis vectors are completely antisymmetric. --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sympy?hl=en -~----------~----~----~----~------~----~------~--~---