ó ¡¼™\c@ sðddlmZmZddlmZmZddlmZmZddl m Z ddl m Z ddl mZmZmZmZddlmZde fd „ƒYZd efd „ƒYZd efd „ƒYZde fd„ƒYZdS(iÿÿÿÿ(tprint_functiontdivision(tAddtS(tget_integer_parttPrecisionExhausted(tFunction(tInteger(tGttLttGetLe(tSymbolt RoundFunctioncB s8eZdZed„ƒZd„Zd„Zd„ZRS(s&The base class for rounding functions.c C sKddlm}|js(|jtkr,|S|jsEtj|jr„||ƒ}|j tjƒst||ƒtjS||dtƒS|j |ƒ}|dk r£|Stj }}}t j|ƒ}xb|D]Z} | jsñ| jrþ|| ƒjrþ|| 7}qÊ| j tƒr|| 7}qÊ|| 7}qÊW|p1|s8|S|rå| sy|jrg|jsytj|jsy|jrå|jråyOt||jidtƒ\} }|t| ƒt|ƒtj7}tj }Wqåttfk ráqåXn||7}|sù|S|jstj|jr3||||ƒdtƒtjS|||dtƒSdS(Niÿÿÿÿ(timtevaluatet return_ints(tsympyRt is_integert is_finitetFalset is_imaginaryRt ImaginaryUnittis_realthast _eval_numbertNonetZeroRt make_argsR Rt_dirtTrueRRtNotImplementedError( tclstargRtitvtiparttnparttspartttermstttr((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pytevalsL   !   "!  !cC s|jdjS(Ni(targsR(tself((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyt_eval_is_finiteHscC s|jdjS(Ni(R+R(R,((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyt _eval_is_realKscC s|jdjS(Ni(R+R(R,((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyt_eval_is_integerNs(t__name__t __module__t__doc__t classmethodR*R-R.R/(((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyR s 5  tfloorcB sYeZdZdZed„ƒZd„Zd„Zd„Zd„Z d„Z d„Z RS( sç 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 iÿÿÿÿcC sR|jr|jƒStd„|| fDƒƒr4|S|jrN|jtƒdSdS(Ncs s1|]'}ttfD]}t||ƒVqqdS(N(R4tceilingt isinstance(t.0R"tj((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pys |si(t is_NumberR4tanytis_NumberSymboltapproximation_intervalR(R R!((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyRxs    cC st|j|dƒ}|jd}|j|dƒ}||krl||j|ƒd}|jra|S|dSn|SdS(Nii(tsubsR+tleadtermt is_positive(R,txtntlogxR)R+targs0t direction((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyt _eval_nseries‚s    cK s t| ƒ S(N(R5(R,R!tkwargs((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyt_eval_rewrite_as_ceilingscK s|t|ƒS(N(tfrac(R,R!RF((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyt_eval_rewrite_as_frac’scC sGt|tƒrC|jtƒ|ks9|jtƒ|krCtjSndS(N(R6R4trewriteR5RHRttrue(R,tother((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyt_eval_Eq•scC s6|jd|kr#|jr#tjSt||dtƒS(NiR(R+RRRKR R(R,RL((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyt__le__›scC s6|jd|kr#|jr#tjSt||dtƒS(NiR(R+RRtfalseRR(R,RL((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyt__gt__ s( R0R1R2RR3RRERGRIRMRNRP(((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyR4Rs#    R5cB sYeZdZdZed„ƒZd„Zd„Zd„Zd„Z d„Z d„Z RS( sö 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 icC sR|jr|jƒStd„|| fDƒƒr4|S|jrN|jtƒdSdS(Ncs s1|]'}ttfD]}t||ƒVqqdS(N(R4R5R6(R7R"R8((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pys Ðsi(R9R5R:R;R<R(R R!((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyRÌs    cC st|j|dƒ}|jd}|j|dƒ}||krl||j|ƒd}|jre|dS|Sn|SdS(Nii(R=R+R>R?(R,R@RARBR)R+RCRD((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyREÖs   cK s t| ƒ S(N(R4(R,R!RF((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyt_eval_rewrite_as_floorãscK s|t| ƒS(N(RH(R,R!RF((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyRIæscC sGt|tƒrC|jtƒ|ks9|jtƒ|krCtjSndS(N(R6R5RJR4RHRRK(R,RL((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyRMéscC s6|jd|kr#|jr#tjSt||dtƒS(NiR(R+RRROR R(R,RL((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyt__lt__ïscC s6|jd|kr#|jr#tjSt||dtƒS(NiR(R+RRRKR R(R,RL((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyt__ge__ôs( R0R1R2RR3RRERQRIRMRRRS(((sBlib/python2.7/site-packages/sympy/functions/elementary/integers.pyR5¦s#    RHcB s8eZdZed„ƒZd„Zd„Zd„ZRS(sœRepresents the fractional part of x For real numbers it is defined [1]_ as .. math:: x - \left\lfloor{x}\right\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 =========== .. 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