Ticket #11888: trac_11888-doctests.patch
| File trac_11888-doctests.patch, 7.0 KB (added by , 8 years ago) |
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sage/functions/log.py
# HG changeset patch # Parent b0c867efcf3e990324fa4b22c20166aa78f67187 # User Keshav Kini <keshav.kini@gmail.com> # Date 1326194143 -28800 trac #11888: fix docstring, doctests diff --git a/sage/functions/log.py b/sage/functions/log.py
a b 443 443 444 444 class Function_lambert_w(BuiltinFunction): 445 445 r""" 446 The principlebranch of the Lambert W function `W_0(z)`.446 The principal branch of the Lambert W function `W_0(z)`. 447 447 448 This function satisfies the equation:448 This function satisfies the equation 449 449 450 450 .. math:: 451 451 452 452 z = W_0(z) e^{W_0(z)} 453 453 454 IMPUT:454 INPUT: 455 455 456 456 - ``z`` - a complex number 457 457 458 458 ALGORITHM: 459 459 460 460 Numerical evaluation is handled using the mpmath library. 461 461 462 462 REFERENCES: 463 463 464 464 - http://en.wikipedia.org/wiki/Lambert_W_function 465 465 466 466 EXAMPLES:: 467 467 468 469 470 471 472 473 468 sage: lambert_w(1.0) 469 0.567143290409784 470 sage: lambert_w(-1).n() 471 -0.318131505204764 + 1.33723570143069*I 472 sage: lambert_w(-1.5 + 5*I) 473 1.17418016254171 + 1.10651494102011*I 474 474 475 476 475 sage: lambert_w(RealField(100)(1)) 476 0.56714329040978387299996866221 477 477 478 479 480 481 482 478 sage: S = solve(e^(5*x)+x==0, x, to_poly_solve=True) 479 sage: z = S[0].rhs(); z 480 -1/5*lambert_w(5) 481 sage: N(z) 482 -0.265344933048440 483 483 484 484 Check the defining equation numerically at `z=5`:: 485 485 486 sage: N(lambert_w(5)*exp(lambert_w(5)) - 5) 487 0.000000000000000 486 sage: N(lambert_w(5)*exp(lambert_w(5)) - 5) 487 0.000000000000000 488 """ 488 489 489 """490 490 def __init__(self): 491 491 """ 492 492 See the docstring for :meth:`Function_lambert_w`. -
sage/symbolic/random_tests.py
diff --git a/sage/symbolic/random_tests.py b/sage/symbolic/random_tests.py
a b 14 14 15 15 sage: from sage.symbolic.random_tests import _mk_full_functions 16 16 sage: [f for (one,f,arity) in _mk_full_functions()] 17 [Ei, abs, arccos, arccosh, arccot, arccoth, arccsc, arccsch, 18 arcsec , arcsech, arcsin, arcsinh, arctan, arctan2, arctanh,19 binomial, ceil, conjugate, cos, cosh, cot, coth, csc, csch,20 di ckman_rho, dilog, dirac_delta, elliptic_e, elliptic_ec,21 elliptic_ eu, elliptic_f, elliptic_kc, elliptic_pi, erf, exp,22 factorial, floor, heaviside, imag_part, integrate,23 kronecker_delta, log, polylog, real_part, sec, sech, sgn, sin,24 sinh, tan, tanh, unit_step, zeta,zetaderiv]17 [Ei, abs, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, 18 arcsech, arcsin, arcsinh, arctan, arctan2, arctanh, binomial, ceil, 19 conjugate, cos, cosh, cot, coth, csc, csch, dickman_rho, dilog, 20 dirac_delta, elliptic_e, elliptic_ec, elliptic_eu, elliptic_f, 21 elliptic_kc, elliptic_pi, erf, exp, factorial, floor, heaviside, 22 imag_part, integrate, kronecker_delta, lambert_w, log, polylog, 23 real_part, sec, sech, sgn, sin, sinh, tan, tanh, unit_step, zeta, 24 zetaderiv] 25 25 26 26 Note that this doctest will fail whenever a Pynac function is added or 27 27 removed. In that case, it is very likely that the doctests for … … 234 234 sage: from sage.symbolic.random_tests import * 235 235 sage: set_random_seed(2) 236 236 sage: random_expr(50, nvars=3, coeff_generator=CDF.random_element) 237 (euler_gamma - v3^(-e) + (v2 - factorial(-e/v2))^(((2.85879036573 - 1.18163393202*I)*v2 + (2.85879036573 - 1.18163393202*I)*v3)*pi - 0.247786879678 + 0.931826724898*I)*arccsc((0.891138386848 - 0.0936820840629*I)/v1) - (0.553423153995 - 0.5481180572*I)*v3 + 0.149683576515 - 0.155746451854*I)*v1 + arccsch(pi + e)*elliptic_f(khinchin*v2, 1.4656989704 + 0.863754357069*I) 237 -v1*elliptic_kc((0.0666829501658 + 0.206976992303*I)/(v3 + e))/v3 + 238 heaviside(arccosh(-(abs(v2 - 239 floor(-v3))^(-real_part(elliptic_e(-0.703991792631 + 0.750156228797*I, 240 -(1.21734510331 - 1.22580558833*I)*pi*v1)))*e^(arctan2(imag_part(v2) - 241 imag_part(floor(-v3)), real_part(v2) - 242 real_part(floor(-v3)))*imag_part(elliptic_e(-0.703991792631 + 243 0.750156228797*I, -(1.21734510331 - 244 1.22580558833*I)*pi*v1)))*sin(-log(abs(v2 - 245 floor(-v3)))*imag_part(elliptic_e(-0.703991792631 + 0.750156228797*I, 246 -(1.21734510331 - 1.22580558833*I)*pi*v1)) - arctan2(imag_part(v2) - 247 imag_part(floor(-v3)), real_part(v2) - 248 real_part(floor(-v3)))*real_part(elliptic_e(-0.703991792631 + 249 0.750156228797*I, -(1.21734510331 - 250 1.22580558833*I)*pi*v1)))*imag_part(arccsc((0.891138386848 - 251 0.0936820840629*I)/v1)) - abs(v2 - 252 floor(-v3))^(-real_part(elliptic_e(-0.703991792631 + 0.750156228797*I, 253 -(1.21734510331 - 1.22580558833*I)*pi*v1)))*e^(arctan2(imag_part(v2) - 254 imag_part(floor(-v3)), real_part(v2) - 255 real_part(floor(-v3)))*imag_part(elliptic_e(-0.703991792631 + 256 0.750156228797*I, -(1.21734510331 - 257 1.22580558833*I)*pi*v1)))*cos(-log(abs(v2 - 258 floor(-v3)))*imag_part(elliptic_e(-0.703991792631 + 0.750156228797*I, 259 -(1.21734510331 - 1.22580558833*I)*pi*v1)) - arctan2(imag_part(v2) - 260 imag_part(floor(-v3)), real_part(v2) - 261 real_part(floor(-v3)))*real_part(elliptic_e(-0.703991792631 + 262 0.750156228797*I, -(1.21734510331 - 263 1.22580558833*I)*pi*v1)))*real_part(arccsc((0.891138386848 - 264 0.0936820840629*I)/v1)) + v3^(-0.48519994364 - 0.485764091302*I) + 265 0.0909404921682*real_part(v3)/(real_part(v3)^2 + imag_part(v3)^2) + 266 0.281538203756*imag_part(v3)/(real_part(v3)^2 + imag_part(v3)^2) - 267 0.647983235144*real_part(v1) - 1.20665952957*imag_part(v1))*v1)) 238 268 sage: random_expr(5, verbose=True) 239 About to apply dirac_delta to [1] 240 About to apply arccsch to [0] 241 About to apply <built-in function add> to [0, arccsch(0)] 242 arccsch(0) 269 About to apply <built-in function mul> to [v1, e] 270 About to apply <built-in function div> to [v1*e, 1] 271 v1*e 243 272 """ 244 273 vars = [(1.0, sage.calculus.calculus.var('v%d' % (n+1))) for n in range(nvars)] 245 274 if ncoeffs is None:
