B [^$@sddlmZmZddlmZddlmZddlmZddl m Z m Z ddl m Z ddlmZmZmZmZddlmZGd d d eZGd d d eZGd ddeZGdddeZdS))print_functiondivision)S)Function)Add)get_integer_partPrecisionExhausted)Integer)GtLtGeLe)Symbolc@s4eZdZdZeddZddZddZdd Zd S) RoundFunctionz&The base class for rounding functions.c Csddlm}|js|jdkr |S|js2tj|jr`||}|tjsT||tjS||ddS| |}|dk rv|Stj }}}t |}xH|D]@} | js| jr|| jr|| 7}q| t r|| 7}q|| 7}qW|s|s|S|rt|r|jr|jstj|js|jrt|jrty:t||jidd\} }|t| t|tj7}tj }Wnttfk rrYnX||7}|s|S|jstj|jr||||ddtjS|||ddSdS)Nr)imF)evaluateT)Z return_ints)sympyr is_integer is_finite is_imaginaryr ImaginaryUnitis_realhas _eval_numberZeror make_argsrr_dirr rNotImplementedError) clsargrivZipartZnpartZsparttermstrr%Blib/python3.7/site-packages/sympy/functions/elementary/integers.pyevalsL           zRoundFunction.evalcCs |jdjS)Nr)argsr)selfr%r%r&_eval_is_finiteIszRoundFunction._eval_is_finitecCs |jdjS)Nr)r(r)r)r%r%r& _eval_is_realLszRoundFunction._eval_is_realcCs |jdjS)Nr)r(r)r)r%r%r&_eval_is_integerOszRoundFunction._eval_is_integerN) __name__ __module__ __qualname____doc__ classmethodr'r*r+r,r%r%r%r&rs  5rc@sPeZdZdZdZeddZddZddZd d Z d d Z d dZ ddZ dS)floora Floor is a univariate function which returns the largest integer value not greater than its argument. This implementation generalizes floor to complex numbers by taking the floor of the real and imaginary parts separately. Examples ======== >>> from sympy import floor, E, I, S, Float, Rational >>> floor(17) 17 >>> floor(Rational(23, 10)) 2 >>> floor(2*E) 5 >>> floor(-Float(0.567)) -1 >>> floor(-I/2) -I >>> floor(S(5)/2 + 5*I/2) 2 + 2*I See Also ======== sympy.functions.elementary.integers.ceiling References ========== .. [1] "Concrete mathematics" by Graham, pp. 87 .. [2] http://mathworld.wolfram.com/FloorFunction.html cCsB|jr|Stdd|| fDr*|S|jr>|tdSdS)Ncss&|]}ttfD]}t||VqqdS)N)r2ceiling isinstance).0r jr%r%r& }sz%floor._eval_number..r) is_Numberr2anyis_NumberSymbolapproximation_intervalr )rrr%r%r&ryszfloor._eval_numbercCsX||d}|jd}||d}||krP|||d}|jrF|S|dSn|SdS)Nr)subsr(leadterm is_positive)r)xnlogxr$r(args0 directionr%r%r& _eval_nseriess    zfloor._eval_nseriescCs t|  S)N)r4)r)rr%r%r&_eval_rewrite_as_ceilingszfloor._eval_rewrite_as_ceilingcCs |t|S)N)frac)r)rr%r%r&_eval_rewrite_as_fracszfloor._eval_rewrite_as_fraccCs0t|tr,|t|ks&|t|kr,tjSdS)N)r5r2rewriter4rHrtrue)r)otherr%r%r&_eval_Eqs zfloor._eval_EqcCs(|jd|kr|jrtjSt||ddS)NrF)r)r(rrrKr )r)rLr%r%r&__le__sz floor.__le__cCs(|jd|kr|jrtjSt||ddS)NrF)r)r(rrfalser )r)rLr%r%r&__gt__sz floor.__gt__N) r-r.r/r0rr1rrFrGrIrMrNrPr%r%r%r&r2Ss#  r2c@sPeZdZdZdZeddZddZddZd d Z d d Z d dZ ddZ dS)r4a Ceiling is a univariate function which returns the smallest integer value not less than its argument. This implementation generalizes ceiling to complex numbers by taking the ceiling of the real and imaginary parts separately. Examples ======== >>> from sympy import ceiling, E, I, S, Float, Rational >>> ceiling(17) 17 >>> ceiling(Rational(23, 10)) 3 >>> ceiling(2*E) 6 >>> ceiling(-Float(0.567)) 0 >>> ceiling(I/2) I >>> ceiling(S(5)/2 + 5*I/2) 3 + 3*I See Also ======== sympy.functions.elementary.integers.floor References ========== .. [1] "Concrete mathematics" by Graham, pp. 87 .. [2] http://mathworld.wolfram.com/CeilingFunction.html r=cCsB|jr|Stdd|| fDr*|S|jr>|tdSdS)Ncss&|]}ttfD]}t||VqqdS)N)r2r4r5)r6r r7r%r%r&r8sz'ceiling._eval_number..r=)r9r4r:r;r<r )rrr%r%r&rszceiling._eval_numbercCsX||d}|jd}||d}||krP|||d}|jrJ|dS|Sn|SdS)Nrr=)r>r(r?r@)r)rArBrCr$r(rDrEr%r%r&rFs   zceiling._eval_nseriescCs t|  S)N)r2)r)rr%r%r&_eval_rewrite_as_floorszceiling._eval_rewrite_as_floorcCs|t| S)N)rH)r)rr%r%r&rIszceiling._eval_rewrite_as_fraccCs0t|tr,|t|ks&|t|kr,tjSdS)N)r5r4rJr2rHrrK)r)rLr%r%r&rMs zceiling._eval_EqcCs(|jd|kr|jrtjSt||ddS)NrF)r)r(rrrOr )r)rLr%r%r&__lt__szceiling.__lt__cCs(|jd|kr|jrtjSt||ddS)NrF)r)r(rrrKr )r)rLr%r%r&__ge__szceiling.__ge__N) r-r.r/r0rr1rrFrQrIrMrRrSr%r%r%r&r4s#  r4c@s4eZdZdZeddZddZddZdd Zd S) rHaRepresents the fractional part of x For real numbers it is defined [1]_ as .. math:: x - \lfloor{x}\rfloor Examples ======== >>> from sympy import Symbol, frac, Rational, floor, ceiling, I >>> frac(Rational(4, 3)) 1/3 >>> frac(-Rational(4, 3)) 2/3 returns zero for integer arguments >>> n = Symbol('n', integer=True) >>> frac(n) 0 rewrite as floor >>> x = Symbol('x') >>> frac(x).rewrite(floor) x - floor(x) for complex arguments >>> r = Symbol('r', real=True) >>> t = Symbol('t', real=True) >>> frac(t + I*r) I*frac(r) + frac(t) See Also ======== sympy.functions.elementary.integers.floor sympy.functions.elementary.integers.ceiling References =========== .. [1] http://en.wikipedia.org/wiki/Fractional_part .. [2] http://mathworld.wolfram.com/FractionalPart.html c sddlmm}fdd}t|}tjtj}}xN|D]F}|jsRtj|j rz||}| tjsp||7}q||7}q<||7}q._eval) rrTrrrrrrrrr) rrrrUr"realimagr#r r%)rTrr&r',s      z frac.evalcCs |t|S)N)r2)r)rr%r%r&rQPszfrac._eval_rewrite_as_floorcCs|t| S)N)r4)r)rr%r%r&rGSszfrac._eval_rewrite_as_ceilingcCs0t|tr,|t|ks&|t|kr,tjSdS)N)r5rHrJr2r4rrK)r)rLr%r%r&rMVs z frac._eval_EqN) r-r.r/r0r1r'rQrGrMr%r%r%r&rHs 0 $rHN)Z __future__rrZsympy.core.singletonrZsympy.core.functionrZ sympy.corerZsympy.core.evalfrrZsympy.core.numbersr Zsympy.core.relationalr r r r Zsympy.core.symbolrrr2r4rHr%r%r%r&s     BTT