Listing: Listing

1:# source_full.py output   (python 3.13.5, sympy 1.14.0, exact QQ arithmetic)
3:CHECK xvi_common.py is byte-identical to XVI-K-artifacts/xvi_common.py: True
5:CHECK R_{1,mu nu} and R_{2,mu nu} (eq:finite-curvature) are symmetric: True
6:CHECK symmetry in (mu,nu) of J_3: True
7:CHECK symmetry in (mu,nu) of 2C_2 dd sigma: True
8:CHECK symmetry in (mu,nu) of -2M_2 d sigma: True
9:# number of monomials of ell_3 (printed representative, eq:ell3): 1398
10:CHECK S1: Euler_gamma(sigma ell_3) = sigma J_3 + 2 C_2 dd sigma - 2 M_2 d sigma for all 10 components (XII-C thm:actualsource, symbolic in the 2-jets of gamma and sigma): True
11:CHECK S1': Euler_gamma(ell_3) = J_3 of eq:J3 (sign: +, convention dS = int E^{mu nu} d gamma_{mu nu}): True
12:CHECK finite exact test: ell_3 (this script) equals XVI-K's xvi_common.ell3_of on two random s-dependent fields gamma(x^1): True
13:# C_2 summand, unpolarized: (gamma-degree, derivatives on gamma, sigma-jet orders, foreign) -> #monomials: {(2, 0, (2,), False): 546}
14:CHECK quadratic homogeneity of the unpolarized C_2 summand: True
15:CHECK C_2 summand is linear in the sigma-jet of order exactly 2: True
16:CHECK C_2 summand: every monomial carries exactly 0 derivative(s) on gamma: True
17:CHECK C_2 summand contains no foreign generator (no residual metric, no psi): True
18:CHECK C_2 summand is not identically zero: True
19:# M_2 summand, unpolarized: (gamma-degree, derivatives on gamma, sigma-jet orders, foreign) -> #monomials: {(2, 1, (1,), False): 1152}
20:CHECK quadratic homogeneity of the unpolarized M_2 summand: True
21:CHECK M_2 summand is linear in the sigma-jet of order exactly 1: True
22:CHECK M_2 summand: every monomial carries exactly 1 derivative(s) on gamma: True
23:CHECK M_2 summand contains no foreign generator (no residual metric, no psi): True
24:CHECK M_2 summand is not identically zero: True
25:# J_3 summand, unpolarized: (gamma-degree, derivatives on gamma, sigma-jet orders, foreign) -> #monomials: {(2, 2, (0,), False): 1068}
26:CHECK quadratic homogeneity of the unpolarized J_3 summand: True
27:CHECK J_3 summand is linear in the sigma-jet of order exactly 0: True
28:CHECK J_3 summand: every monomial carries exactly 2 derivative(s) on gamma: True
29:CHECK J_3 summand contains no foreign generator (no residual metric, no psi): True
30:CHECK J_3 summand is not identically zero: True
31:CHECK rational coefficients (ring over QQ): True
32:CHECK every monomial of J_D carries total derivative weight 2 (on sigma and gamma together): True
33:# J_3 monomial types by derivative orders of the two gamma factors: {(0, 2): 534, (1, 1): 534}
34:CHECK J_3 contains both gamma*dd gamma and d gamma*d gamma monomials, and nothing else: True
96:CHECK bilinearity after polarization: every monomial of s_C_2[X,Y] is exactly linear in the X-jet and in the Y-jet, times a sigma-jet: True
97:CHECK slot symmetry P_{C_2,ij}^{ab,mu nu} = P_{C_2,ji}^{ba,mu nu}: True
98:# nonzero ordered coefficients P_{C_2,ij}^{ab,mu nu} (mu<=nu) by (|a|,|b|): {(0, 0): 688}  total 688
99:CHECK bilinearity after polarization: every monomial of s_M_2[X,Y] is exactly linear in the X-jet and in the Y-jet, times a sigma-jet: True
100:CHECK slot symmetry P_{M_2,ij}^{ab,mu nu} = P_{M_2,ji}^{ba,mu nu}: True
101:# nonzero ordered coefficients P_{M_2,ij}^{ab,mu nu} (mu<=nu) by (|a|,|b|): {(0, 1): 1152, (1, 0): 1152}  total 2304
102:CHECK bilinearity after polarization: every monomial of s_J_3[X,Y] is exactly linear in the X-jet and in the Y-jet, times a sigma-jet: True
103:CHECK slot symmetry P_{J_3,ij}^{ab,mu nu} = P_{J_3,ji}^{ba,mu nu}: True
104:# nonzero ordered coefficients P_{J_3,ij}^{ab,mu nu} (mu<=nu) by (|a|,|b|): {(0, 2): 534, (1, 1): 996, (2, 0): 534}  total 2064
105:CHECK C_2: source-slot derivative orders (|a|,|b|) = (0,0) only: True
106:CHECK M_2: source-slot derivative orders (|a|,|b|) in {(1,0),(0,1)}, both occur: True
107:CHECK J_3: source-slot derivative orders (|a|,|b|) in {(2,0),(0,2),(1,1)}, all occur: True
108:CHECK every P_{C_2} is a rational linear form in the sigma-jet of order 2 (no other y-dependence): True
109:CHECK every P_{M_2} is a rational linear form in the sigma-jet of order 1 (no other y-dependence): True
110:CHECK every P_{J_3} is a rational linear form in the sigma-jet of order 0 (no other y-dependence): True
111:# C_2: ordered source-slot placements (a,b) occurring: 1
112:# M_2: ordered source-slot placements (a,b) occurring: 8
113:# J_3: ordered source-slot placements (a,b) occurring: 36
114:CHECK S3: C_2-only polarized source equals XVI-K's xvi_common.polar_s(X,Y,dd sigma) identically (symbolic): True
116:CHECK S3': on the XVI-K dual-slot tensors X=-P B^i, Y=-P B^j (all 55 pairs) the C_2 summand equals XVI-K's s(-P B^i,-P B^j; dd sigma): True
117:CHECK S2a: C_1 = C_2 = 0 at gamma = psi eta: True
118:CHECK S2b: Gamma_2 = -psi Gamma_1 at gamma = psi eta: True
119:CHECK S2c: D_sigma|_{gamma=psi eta} = -psi[eta^{mu nu} d_rho sigma d^rho psi + d^mu sigma d^nu psi + d^nu sigma d^mu psi] (XII-C eq:full-trace-sector): True
120:CHECK S2d: eta_{mu nu} D_sigma^{mu nu}|_{gamma=psi eta} = -6 (d_mu sigma) psi d^mu psi (XII-B eq:input-trace): True
134:# total runtime 53.3s
135:ALL CHECKS PASSED