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GeezerVison is showing github.com — python-docs-ru/library/cmath.po at 3.13 · python/python-docs-ru Expand file tree/ Copy pathcmath.poMore file actions 522 lines (398 loc) · 13.3 KB / Copy pathcmath.poFile metadata and controls522 lines (398 loc) · 13.3 KB 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 # SOME DESCRIPTIVE TITLE. # Copyright (C) 2001 Python Software Foundation # This file is distributed under the same license as the Python package. # FIRST AUTHOR <EMAIL@ADDRESS>, YEAR. # # Translators: # python-doc bot, 2025 # #, fuzzy msgid "" msgstr "" "Project-Id-Version: Python 3.15\n" "Report-Msgid-Bugs-To: \n" "POT-Creation-Date: 2026-11-01 18:39+0000\n" "PO-Revision-Date: 2025-09-16 00:00+0000\n" "Last-Translator: python-doc bot, 2025\n" "Language-Team: Russian (https://app.transifex.com/python-doc/teams/5390/" "ru/)\n" "MIME-Version: 1.0\n" "Content-Type: text/plain; charset=UTF-8\n" "Content-Transfer-Encoding: 8bit\n" "Language: ru\n" "Plural-Forms: nplurals=4; plural=(n%10==1 && n%100!=11 ? 0 : n%10>=2 && " "n%10<=4 && (n%100<12 || n%100>14) ? 1 : n%10==0 || (n%10>=5 && n%10<=9) || " "(n%100>=11 && n%100<=14)? 2 : 3);\n" msgid ":mod:`!cmath` --- Mathematical functions for complex numbers" msgstr "" msgid "" "This module provides access to mathematical functions for complex numbers. " "The functions in this module accept integers, floating-point numbers or " "complex numbers as arguments. They will also accept any Python object that " "has either a :meth:`~object.__complex__` or a :meth:`~object.__float__` " "method: these methods are used to convert the object to a complex or " "floating-point number, respectively, and the function is then applied to the " "result of the conversion." msgstr "" msgid "" "For functions involving branch cuts, we have the problem of deciding how to " "define those functions on the cut itself. Following Kahan's \"Branch cuts " "for complex elementary functions\" paper, as well as Annex G of C99 and " "later C standards, we use the sign of zero to distinguish one side of the " "branch cut from the other: for a branch cut along (a portion of) the real " "axis we look at the sign of the imaginary part, while for a branch cut along " "the imaginary axis we look at the sign of the real part." msgstr "" msgid "" "For example, the :func:`cmath.sqrt` function has a branch cut along the " "negative real axis. An argument of ``-2-0j`` is treated as though it lies " "*below* the branch cut, and so gives a result on the negative imaginary " "axis::" msgstr "" msgid "" ">>> cmath.sqrt(-2-0j)\n" "-1.4142135623730951j" msgstr "" msgid "" "But an argument of ``-2+0j`` is treated as though it lies above the branch " "cut::" msgstr "" msgid "" ">>> cmath.sqrt(-2+0j)\n" "1.4142135623730951j" msgstr "" msgid "**Conversions to and from polar coordinates**" msgstr "" msgid ":func:`phase(z) <phase>`" msgstr "" msgid "Return the phase of *z*" msgstr "" msgid ":func:`polar(z) <polar>`" msgstr "" msgid "Return the representation of *z* in polar coordinates" msgstr "" msgid ":func:`rect(r, phi) <rect>`" msgstr "" msgid "Return the complex number *z* with polar coordinates *r* and *phi*" msgstr "" msgid "**Power and logarithmic functions**" msgstr "" msgid ":func:`exp(z) <exp>`" msgstr "" msgid "Return *e* raised to the power *z*" msgstr "" msgid ":func:`log(z[, base]) <log>`" msgstr "" msgid "Return the logarithm of *z* to the given *base* (*e* by default)" msgstr "" msgid ":func:`log10(z) <log10>`" msgstr "" msgid "Return the base-10 logarithm of *z*" msgstr "" msgid ":func:`sqrt(z) <sqrt>`" msgstr "" msgid "Return the square root of *z*" msgstr "" msgid "**Trigonometric functions**" msgstr "" msgid ":func:`acos(z) <acos>`" msgstr "" msgid "Return the arc cosine of *z*" msgstr "" msgid ":func:`asin(z) <asin>`" msgstr "" msgid "Return the arc sine of *z*" msgstr "" msgid ":func:`atan(z) <atan>`" msgstr "" msgid "Return the arc tangent of *z*" msgstr "" msgid ":func:`cos(z) <cos>`" msgstr "" msgid "Return the cosine of *z*" msgstr "" msgid ":func:`sin(z) <sin>`" msgstr "" msgid "Return the sine of *z*" msgstr "" msgid ":func:`tan(z) <tan>`" msgstr "" msgid "Return the tangent of *z*" msgstr "" msgid "**Hyperbolic functions**" msgstr "" msgid ":func:`acosh(z) <acosh>`" msgstr "" msgid "Return the inverse hyperbolic cosine of *z*" msgstr "" msgid ":func:`asinh(z) <asinh>`" msgstr "" msgid "Return the inverse hyperbolic sine of *z*" msgstr "" msgid ":func:`atanh(z) <atanh>`" msgstr "" msgid "Return the inverse hyperbolic tangent of *z*" msgstr "" msgid ":func:`cosh(z) <cosh>`" msgstr "" msgid "Return the hyperbolic cosine of *z*" msgstr "" msgid ":func:`sinh(z) <sinh>`" msgstr "" msgid "Return the hyperbolic sine of *z*" msgstr "" msgid ":func:`tanh(z) <tanh>`" msgstr "" msgid "Return the hyperbolic tangent of *z*" msgstr "" msgid "**Classification functions**" msgstr "" msgid ":func:`isfinite(z) <isfinite>`" msgstr "" msgid "Check if all components of *z* are finite" msgstr "" msgid ":func:`isinf(z) <isinf>`" msgstr "" msgid "Check if any component of *z* is infinite" msgstr "" msgid ":func:`isnan(z) <isnan>`" msgstr "" msgid "Check if any component of *z* is a NaN" msgstr "" msgid ":func:`isclose(a, b, *, rel_tol, abs_tol) <isclose>`" msgstr "" msgid "Check if the values *a* and *b* are close to each other" msgstr "" msgid "**Constants**" msgstr "" msgid ":data:`pi`" msgstr "" msgid "*π* = 3.141592..." msgstr "" msgid ":data:`e`" msgstr "" msgid "*e* = 2.718281..." msgstr "" msgid ":data:`tau`" msgstr "" msgid "*τ* = 2\\ *π* = 6.283185..." msgstr "" msgid ":data:`inf`" msgstr "" msgid "Positive infinity" msgstr "" msgid ":data:`infj`" msgstr "" msgid "Pure imaginary infinity" msgstr "" msgid ":data:`nan`" msgstr "" msgid "\"Not a number\" (NaN)" msgstr "" msgid ":data:`nanj`" msgstr "" msgid "Pure imaginary NaN" msgstr "" msgid "Conversions to and from polar coordinates" msgstr "" msgid "" "A Python complex number ``z`` is stored internally using *rectangular* or " "*Cartesian* coordinates. It is completely determined by its *real part* " "``z.real`` and its *imaginary part* ``z.imag``." msgstr "" msgid "" "*Polar coordinates* give an alternative way to represent a complex number. " "In polar coordinates, a complex number *z* is defined by the modulus *r* and " "the phase angle *phi*. The modulus *r* is the distance from *z* to the " "origin, while the phase *phi* is the counterclockwise angle, measured in " "radians, from the positive x-axis to the line segment that joins the origin " "to *z*." msgstr "" msgid "" "The following functions can be used to convert from the native rectangular " "coordinates to polar coordinates and back." msgstr "" msgid "" "Return the phase of *z* (also known as the *argument* of *z*), as a float. " "``phase(z)`` is equivalent to ``math.atan2(z.imag, z.real)``. The result " "lies in the range [-\\ *π*, *π*], and the branch cut for this operation lies " "along the negative real axis. The sign of the result is the same as the " "sign of ``z.imag``, even when ``z.imag`` is zero::" msgstr "" msgid "" ">>> phase(-1+0j)\n" "3.141592653589793\n" ">>> phase(-1-0j)\n" "-3.141592653589793" msgstr "" msgid "" "The modulus (absolute value) of a complex number *z* can be computed using " "the built-in :func:`abs` function. There is no separate :mod:`!cmath` " "module function for this operation." msgstr "" msgid "" "Return the representation of *z* in polar coordinates. Returns a pair ``(r, " "phi)`` where *r* is the modulus of *z* and *phi* is the phase of *z*. " "``polar(z)`` is equivalent to ``(abs(z), phase(z))``." msgstr "" msgid "" "Return the complex number *z* with polar coordinates *r* and *phi*. " "Equivalent to ``complex(r * math.cos(phi), r * math.sin(phi))``." msgstr "" msgid "Power and logarithmic functions" msgstr "" msgid "" "Return *e* raised to the power *z*, where *e* is the base of natural " "logarithms." msgstr "" msgid "" "Return the logarithm of *z* to the given *base*. If the *base* is not " "specified, returns the natural logarithm of *z*. There is one branch cut, " "from 0 along the negative real axis to -∞." msgstr "" msgid "" "Return the base-10 logarithm of *z*. This has the same branch cut " "as :func:`log`." msgstr "" msgid "" "Return the square root of *z*. This has the same branch cut as :func:`log`." msgstr "" msgid "Trigonometric functions" msgstr "" msgid "" "Return the arc cosine of *z*. There are two branch cuts: One extends right " "from 1 along the real axis to ∞. The other extends left from -1 along the " "real axis to -∞." msgstr "" msgid "" "Return the arc sine of *z*. This has the same branch cuts as :func:`acos`." msgstr "" msgid "" "Return the arc tangent of *z*. There are two branch cuts: One extends from " "``1j`` along the imaginary axis to ``∞j``. The other extends from ``-1j`` " "along the imaginary axis to ``-∞j``." msgstr "" msgid "Return the cosine of *z*." msgstr "" msgid "Return the sine of *z*." msgstr "" msgid "Return the tangent of *z*." msgstr "" msgid "Hyperbolic functions" msgstr "" msgid "" "Return the inverse hyperbolic cosine of *z*. There is one branch cut, " "extending left from 1 along the real axis to -∞." msgstr "" msgid "" "Return the inverse hyperbolic sine of *z*. There are two branch cuts: One " "extends from ``1j`` along the imaginary axis to ``∞j``. The other extends " "from ``-1j`` along the imaginary axis to ``-∞j``." msgstr "" msgid "" "Return the inverse hyperbolic tangent of *z*. There are two branch cuts: One " "extends from ``1`` along the real axis to ``∞``. The other extends from " "``-1`` along the real axis to ``-∞``." msgstr "" msgid "Return the hyperbolic cosine of *z*." msgstr "" msgid "Return the hyperbolic sine of *z*." msgstr "" msgid "Return the hyperbolic tangent of *z*." msgstr "" msgid "Classification functions" msgstr "" msgid "" "Return ``True`` if both the real and imaginary parts of *z* are finite, and " "``False`` otherwise." msgstr "" msgid "" "Return ``True`` if either the real or the imaginary part of *z* is an " "infinity, and ``False`` otherwise." msgstr "" msgid "" "Return ``True`` if either the real or the imaginary part of *z* is a NaN, " "and ``False`` otherwise." msgstr "" msgid "" "Return ``True`` if the values *a* and *b* are close to each other and " "``False`` otherwise." msgstr "" msgid "" "Whether or not two values are considered close is determined according to " "given absolute and relative tolerances. If no errors occur, the result will " "be: ``abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)``." msgstr "" msgid "" "*rel_tol* is the relative tolerance -- it is the maximum allowed difference " "between *a* and *b*, relative to the larger absolute value of *a* or *b*. " "For example, to set a tolerance of 5%, pass ``rel_tol=0.05``. The default " "tolerance is ``1e-09``, which assures that the two values are the same " "within about 9 decimal digits. *rel_tol* must be nonnegative and less than " "``1.0``." msgstr "" msgid "" "*abs_tol* is the absolute tolerance; it defaults to ``0.0`` and it must be " "nonnegative. When comparing ``x`` to ``0.0``, ``isclose(x, 0)`` is computed " "as ``abs(x) <= rel_tol * abs(x)``, which is ``False`` for any ``x`` and " "rel_tol less than ``1.0``. So add an appropriate positive abs_tol argument " "to the call." msgstr "" msgid "" "The IEEE 754 special values of ``NaN``, ``inf``, and ``-inf`` will be " "handled according to IEEE rules. Specifically, ``NaN`` is not considered " "close to any other value, including ``NaN``. ``inf`` and ``-inf`` are only " "considered close to themselves." msgstr "" msgid ":pep:`485` -- A function for testing approximate equality" msgstr "" msgid "Constants" msgstr "" msgid "The mathematical constant *π*, as a float." msgstr "" msgid "The mathematical constant *e*, as a float." msgstr "" msgid "The mathematical constant *τ*, as a float." msgstr "" msgid "Floating-point positive infinity. Equivalent to ``float('inf')``." msgstr "" msgid "" "Complex number with zero real part and positive infinity imaginary part. " "Equivalent to ``complex(0.0, float('inf'))``." msgstr "" msgid "" "A floating-point \"not a number\" (NaN) value. Equivalent to " "``float('nan')``. See also :data:`math.nan`." msgstr "" msgid "" "Complex number with zero real part and NaN imaginary part. Equivalent to " "``complex(0.0, float('nan'))``." msgstr "" msgid "" "Note that the selection of functions is similar, but not identical, to that " "in module :mod:`math`. The reason for having two modules is that some users " "aren't interested in complex numbers, and perhaps don't even know what they " "are. They would rather have ``math.sqrt(-1)`` raise an exception than " "return a complex number. Also note that the functions defined in :mod:`!" "cmath` always return a complex number, even if the answer can be expressed " "as a real number (in which case the complex number has an imaginary part of " "zero)." msgstr "" msgid "" "A note on branch cuts: They are curves along which the given function fails " "to be continuous. They are a necessary feature of many complex functions. " "It is assumed that if you need to compute with complex functions, you will " "understand about branch cuts. Consult almost any (not too elementary) book " "on complex variables for enlightenment. For information of the proper " "choice of branch cuts for numerical purposes, a good reference should be the " "following:" msgstr "" msgid "" "Kahan, W: Branch cuts for complex elementary functions; or, Much ado about " "nothing's sign bit. In Iserles, A., and Powell, M. (eds.), The state of the " "art in numerical analysis. Clarendon Press (1987) pp165--211." msgstr "" msgid "module" msgstr "" msgid "math" msgstr "" |
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