U 9%e@sdZddlmZddlmZddlZeZej Z ejZej Z ej Z ej Z ej Z ejZeZej ZdddZdd d ZdddZdddZdddZdddZdS)aS When you need to use random numbers in SymPy library code, import from here so there is only one generator working for SymPy. Imports from here should behave the same as if they were being imported from Python's random module. But only the routines currently used in SymPy are included here. To use others import ``rng`` and access the method directly. For example, to capture the current state of the generator use ``rng.getstate()``. There is intentionally no Random to import from here. If you want to control the state of the generator, import ``seed`` and call it with or without an argument to set the state. Examples ======== >>> from sympy.core.random import random, seed >>> assert random() < 1 >>> seed(1); a = random() >>> b = random() >>> seed(1); c = random() >>> assert a == c >>> assert a != b # remote possibility this will fail ) is_sequence)as_intNcCs tj||dtj||ddS)Naversion)rngseed_assumptions_rngrr P/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/sympy/core/random.pyr ,sr Fc Cs^ddlm}ddlm}t||t||}} |s>||| S||d|d||| d|dS)a Return a random complex number. To reduce chance of hitting branch cuts or anything, we guarantee b <= Im z <= d, a <= Re z <= c When rational is True, a rational approximation to a random number is obtained within specified tolerance, if any. r)I) nsimplifyT)rational tolerance)sympy.core.numbersrZsympy.simplify.simplifyruniform) rbcdrrrrABr r r random_complex_number1s    rư>c sddlm}ddlmddlm} fdd||fD\}}|dkrT|j|jB}nt||rd|g}tt |fdd |D} | |  } | |  } | | | |S) a  Test numerically that f and g agree when evaluated in the argument z. If z is None, all symbols will be tested. This routine does not test whether there are Floats present with precision higher than 15 digits so if there are, your results may not be what you expect due to round- off errors. Examples ======== >>> from sympy import sin, cos >>> from sympy.abc import x >>> from sympy.core.random import verify_numerically as tn >>> tn(sin(x)**2 + cos(x)**2, 1, x) True r)Symbolsympifycompc3s|]}|VqdS)Nr ).0irr r Ysz%verify_numerically..Ncsg|]}tqSr )r)r"_)rrrrr r ^sz&verify_numerically..) Zsympy.core.symbolrZsympy.core.sympifyrrr!Z free_symbols isinstancelistzipsubsn) fgztolrrrrrr!ZrepsZz1Zz2r )rrrrrr verify_numericallyDs    "r0c Cs\ddlm}ddlm}t||||} |||| } |||| } || | |S)a Test numerically that the symbolically computed derivative of f with respect to z is correct. This routine does not test whether there are Floats present with precision higher than 15 digits so if there are, your results may not be what you expect due to round-off errors. Examples ======== >>> from sympy import sin >>> from sympy.abc import x >>> from sympy.core.random import test_derivative_numerically as td >>> td(sin(x), x) True rr ) Derivative) rr!Zsympy.core.functionr1rdiffr*Zdoit_numericallyr+) r,r.r/rrrrr!r1Zz0f1f2r r r test_derivative_numericallyds   r5cs^|dkr tSt|tr$t|tSt|rRt|}|d|ffdd StddS)a8Return a randrange generator. ``seed`` can be * None - return randomly seeded generator * int - return a generator seeded with the int * list - the values to be returned will be taken from the list in the order given; the provided list is not modified. Examples ======== >>> from sympy.core.random import _randrange >>> rr = _randrange() >>> rr(1000) # doctest: +SKIP 999 >>> rr = _randrange(3) >>> rr(1000) # doctest: +SKIP 238 >>> rr = _randrange([0, 5, 1, 3, 4]) >>> rr(3), rr(3) (0, 1) Ncs|dkrd|}}t|t|}}||}|dkr.givez!_randrange got an unexpected seed) randranger'intrr rr(reverser7r r r>r _randrange~s  rDcs\|dkr tSt|tr$t|tSt|rPt|}||ffdd StddS)a:Return a randint generator. ``seed`` can be * None - return randomly seeded generator * int - return a generator seeded with the int * list - the values to be returned will be taken from the list in the order given; the provided list is not modified. Examples ======== >>> from sympy.core.random import _randint >>> ri = _randint() >>> ri(1, 1000) # doctest: +SKIP 999 >>> ri = _randint(3) >>> ri(1, 1000) # doctest: +SKIP 238 >>> ri = _randint([0, 5, 1, 2, 4]) >>> ri(1, 3), ri(1, 3) (1, 2) Ncst|t|}}||}|dkr*tdz |}Wntk rRtdYnX||krh|krpnn|S|||SdS)Nrz_randint got empty rangez_randint sequence was too shortr6r:r>r r r?s z_randint..givez_randint got an unexpected seed) randintr'rArr rr(rBr7rCr r>r _randints   rF)Nr)rr rrFN)Nrrr rr)rrr rr)N)N)__doc__Zsympy.utilities.iterablesrZsympy.utilities.miscrrandom_randomRandomrchoicerEr@sampleshufflerr Z_assumptions_shuffler rr0r5rDrFr r r r s&      5