This work is funded by TUBITAK 1001 Program, Grant Number 123R114.
Copy the file NPDerivatives.sage into your directory and load it by
load("NPDerivatives.sage")
Please see the file Coordinate_Free_Example.ipynb as an example.
- Defined parameters:
-- alpha, beta, epsilon, gamma, kappa, mu, nu, pi, rho, sigma, tau
-- lambda, defined as "lambdaa". Displays as LaTeX
-- Phi00, Phi01, Phi02, Phi10, Phi11, Phi12, Phi20, Phi21, Phi22, Lambda
-- Psi0, Psi1, Psi2, Psi3, Psi4
- Commands:
- General:
-- "showall" function: The function to show all NP parameters.
-- "opconj" function: Special function for conjugation. (If conjugate is used, derivatives in the l and n directions also become complex).
- Derivatives:
-- Defined as Dl (D), Dn (Capital Delta), Dm (small delta), and Dmbar (small deltabar).
-- Derivatives can be nested.
- Commutators, such that they equal zero (X input):
-- Dn_Dl_com(X): [Dn,Dl]
-- Dm_Dl_com(X): [Dm,Dl]
-- Dm_Dn_com(X): [Dm, Dn]
-- Dmbar_Dm_comNP(X): [Dmbar, Dm]
- NPeqs():
-- Calculates and writes the NP equations such that they equal zero.
-- Outputs can be used in the form NP1, .., NP18.
- Bianchi():
-- Calculates and writes Bianchi identities such that they equal 0.
-- Outputs can be used in the form BI1, ..., BI11.
- Transformations defined in the Carmeli and Kaye paper (z input):
-- CKAdo(z): A. Null Rotation about l (Do transformation and the parameters will change)
-- CKBdo(z): B. Boost in l-n Plane and Spatial Rotation in m-mbar Plane (Do transformation and the parameters will change)
-- CKCdo(z): C. Null Rotation about n (Do transformation and the parameters will change)
-- CKAsee(z): A. Null Rotation about l (See the results of the transformation and the parameters will not change)
-- CKBsee(z): B. Boost in l-n Plane and Spatial Rotation in m-mbar Plane (See the results of the transformation and the parameters will not change)
-- CKCsee(z): C. Null Rotation about n (See the results of the transformation and the parameters will not change)