|
3 | 3 |
|
4 | 4 | lazy_import('sage.functions.piecewise', 'piecewise')
|
5 | 5 | lazy_import('sage.functions.error', ['erf', 'erfc', 'erfi', 'erfinv',
|
6 |
| - 'fresnel_sin', 'fresnel_cos']) |
| 6 | + 'fresnel_sin', 'fresnel_cos']) |
7 | 7 |
|
8 |
| -from sage.functions.trig import ( sin, cos, sec, csc, cot, tan, |
9 |
| - asin, acos, atan, |
10 |
| - acot, acsc, asec, |
11 |
| - arcsin, arccos, arctan, |
12 |
| - arccot, arccsc, arcsec, |
13 |
| - arctan2, atan2) |
| 8 | +from sage.functions.trig import (sin, cos, sec, csc, cot, tan, |
| 9 | + asin, acos, atan, |
| 10 | + acot, acsc, asec, |
| 11 | + arcsin, arccos, arctan, |
| 12 | + arccot, arccsc, arcsec, |
| 13 | + arctan2, atan2) |
14 | 14 |
|
15 |
| -from sage.functions.hyperbolic import ( tanh, sinh, cosh, coth, sech, csch, |
16 |
| - asinh, acosh, atanh, acoth, asech, acsch, |
17 |
| - arcsinh, arccosh, arctanh, arccoth, arcsech, arccsch ) |
| 15 | +from sage.functions.hyperbolic import (tanh, sinh, cosh, coth, sech, csch, |
| 16 | + asinh, acosh, atanh, acoth, asech, acsch, |
| 17 | + arcsinh, arccosh, arctanh, arccoth, arcsech, arccsch) |
18 | 18 |
|
19 |
| -reciprocal_trig_functions = {'sec': cos, 'csc': sin, 'cot': tan, 'sech': cosh, 'csch': sinh, 'coth': tanh} |
| 19 | +reciprocal_trig_functions = {'sec': cos, 'csc': sin, |
| 20 | + 'cot': tan, 'sech': cosh, 'csch': sinh, 'coth': tanh} |
20 | 21 |
|
21 | 22 |
|
22 |
| -from sage.functions.other import ( ceil, floor, abs_symbolic, sqrt, real_nth_root, |
23 |
| - arg, real_part, real, frac, |
24 |
| - factorial, binomial, |
25 |
| - imag_part, imag, imaginary, conjugate, cases, |
26 |
| - complex_root_of) |
| 23 | +from sage.functions.other import (ceil, floor, abs_symbolic, sqrt, real_nth_root, |
| 24 | + arg, real_part, real, frac, |
| 25 | + factorial, binomial, |
| 26 | + imag_part, imag, imaginary, conjugate, cases, |
| 27 | + complex_root_of) |
27 | 28 |
|
28 |
| -from sage.functions.log import (exp, exp_polar, log, ln, polylog, dilog, lambert_w, harmonic_number) |
| 29 | +from sage.functions.log import (exp, exp_polar, log, ln, |
| 30 | + polylog, dilog, lambert_w, harmonic_number) |
29 | 31 |
|
30 | 32 | from sage.functions.transcendental import (zeta, zetaderiv, zeta_symmetric, hurwitz_zeta,
|
31 |
| - dickman_rho, stieltjes) |
| 33 | + dickman_rho, stieltjes) |
32 | 34 |
|
33 | 35 | from sage.functions.bessel import (bessel_I, bessel_J, bessel_K, bessel_Y,
|
34 |
| - Bessel, struve_H, struve_L, hankel1, hankel2, |
| 36 | + Bessel, struve_H, struve_L, hankel1, hankel2, |
35 | 37 | spherical_bessel_J, spherical_bessel_Y,
|
36 | 38 | spherical_hankel1, spherical_hankel2)
|
37 | 39 |
|
38 | 40 | from sage.functions.special import (spherical_harmonic, elliptic_e,
|
39 |
| - elliptic_f, elliptic_ec, elliptic_eu, |
40 |
| - elliptic_kc, elliptic_pi, elliptic_j) |
| 41 | + elliptic_f, elliptic_ec, elliptic_eu, |
| 42 | + elliptic_kc, elliptic_pi, elliptic_j) |
41 | 43 |
|
42 | 44 | from sage.functions.jacobi import (jacobi, inverse_jacobi, jacobi_nd, jacobi_ns, jacobi_nc,
|
43 |
| - jacobi_dn, jacobi_ds, jacobi_dc, jacobi_sn, jacobi_sd, |
44 |
| - jacobi_sc, jacobi_cn, jacobi_cd, jacobi_cs, jacobi_am, |
45 |
| - inverse_jacobi_nd, inverse_jacobi_ns, inverse_jacobi_nc, |
46 |
| - inverse_jacobi_dn, inverse_jacobi_ds, inverse_jacobi_dc, |
47 |
| - inverse_jacobi_sn, inverse_jacobi_sd, inverse_jacobi_sc, |
48 |
| - inverse_jacobi_cn, inverse_jacobi_cd, inverse_jacobi_cs) |
| 45 | + jacobi_dn, jacobi_ds, jacobi_dc, jacobi_sn, jacobi_sd, |
| 46 | + jacobi_sc, jacobi_cn, jacobi_cd, jacobi_cs, jacobi_am, |
| 47 | + inverse_jacobi_nd, inverse_jacobi_ns, inverse_jacobi_nc, |
| 48 | + inverse_jacobi_dn, inverse_jacobi_ds, inverse_jacobi_dc, |
| 49 | + inverse_jacobi_sn, inverse_jacobi_sd, inverse_jacobi_sc, |
| 50 | + inverse_jacobi_cn, inverse_jacobi_cd, inverse_jacobi_cs) |
49 | 51 |
|
50 | 52 | from sage.functions.orthogonal_polys import (chebyshev_T,
|
51 |
| - chebyshev_U, |
52 |
| - gen_laguerre, |
53 |
| - gen_legendre_P, |
54 |
| - gen_legendre_Q, |
55 |
| - hermite, |
56 |
| - jacobi_P, |
57 |
| - laguerre, |
58 |
| - legendre_P, |
59 |
| - legendre_Q, |
60 |
| - ultraspherical, |
61 |
| - gegenbauer, |
62 |
| - krawtchouk, |
63 |
| - meixner, |
64 |
| - hahn) |
| 53 | + chebyshev_U, |
| 54 | + gen_laguerre, |
| 55 | + gen_legendre_P, |
| 56 | + gen_legendre_Q, |
| 57 | + hermite, |
| 58 | + jacobi_P, |
| 59 | + laguerre, |
| 60 | + legendre_P, |
| 61 | + legendre_Q, |
| 62 | + ultraspherical, |
| 63 | + gegenbauer, |
| 64 | + krawtchouk, |
| 65 | + meixner, |
| 66 | + hahn) |
65 | 67 |
|
66 | 68 | from sage.functions.spike_function import spike_function
|
67 | 69 |
|
68 | 70 | from sage.functions.prime_pi import legendre_phi, partial_sieve_function, prime_pi
|
69 | 71 |
|
70 | 72 | from sage.functions.wigner import (wigner_3j, clebsch_gordan, racah, wigner_6j,
|
71 |
| - wigner_9j, gaunt) |
| 73 | + wigner_9j, gaunt) |
72 | 74 |
|
73 | 75 | from sage.functions.generalized import (dirac_delta, heaviside, unit_step, sgn, sign,
|
74 |
| - kronecker_delta) |
| 76 | + kronecker_delta) |
75 | 77 |
|
76 | 78 | from sage.functions.min_max import max_symbolic, min_symbolic
|
77 | 79 |
|
78 | 80 | from sage.functions.airy import airy_ai, airy_ai_prime, airy_bi, airy_bi_prime
|
79 | 81 |
|
80 | 82 | from sage.functions.exp_integral import (exp_integral_e, exp_integral_e1, log_integral, li, Li,
|
81 |
| - log_integral_offset, |
82 |
| - sin_integral, cos_integral, Si, Ci, |
83 |
| - sinh_integral, cosh_integral, Shi, Chi, |
84 |
| - exponential_integral_1, Ei, exp_integral_ei) |
| 83 | + log_integral_offset, |
| 84 | + sin_integral, cos_integral, Si, Ci, |
| 85 | + sinh_integral, cosh_integral, Shi, Chi, |
| 86 | + exponential_integral_1, Ei, exp_integral_ei) |
85 | 87 |
|
86 | 88 | from sage.functions.hypergeometric import hypergeometric, hypergeometric_M, hypergeometric_U
|
87 | 89 |
|
88 | 90 | from sage.functions.gamma import (gamma, psi, beta, log_gamma,
|
89 |
| - gamma_inc, gamma_inc_lower) |
| 91 | + gamma_inc, gamma_inc_lower) |
90 | 92 |
|
91 | 93 | Γ = gamma
|
92 | 94 | ψ = psi
|
93 | 95 | ζ = zeta
|
| 96 | +del lazy_import |
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