a ¬>> 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 éÿÿÿÿcCsB|jr| ¡Stdd„||fDƒƒr*|S|jr>| t¡dSdS)Ncss&|]}ttfD]}t||ƒVqqdSr5©r(r)r'©Ú.0r-Újr2r2r3Ú ‰sÿz%floor._eval_number..r)Ú is_Numberr(ÚanyÚis_NumberSymbolÚapproximation_intervalrr6r2r2r3r…sÿzfloor._eval_numberNrc Csž|jd}| |d¡}| |d¡}|jrŽ||krŠ|dkrj|j|dd}|j|dd}||krxtd|ƒ‚n|j||d}|jr†|dS|S|S|j|||dS©NrrE©Úcdiréz,Two sided limit of %s around 0does not exist)ÚlogxrQ©rÚsubsrÚdirÚ ValueErrorÚis_negativeZas_leading_term© r9ÚxrSrQr+Úarg0r1ZndirlÚndirr2r2r3Ú_eval_as_leading_terms ÿzfloor._eval_as_leading_termc Cs´|jd}| |d¡}|jrlddlm}ddlm}| ||||¡} |dkrZ|d|dfƒn|ddƒ} | | S| |d¡}||kr¬|j||dkr’|ndd}|j r¨|dS|S|SdS)Nr©ÚAccumBounds©ÚOrderrRrErP© rrUÚis_infiniteÚ!sympy.calculus.accumulationboundsr_Zsympy.series.orderraÚ _eval_nseriesrVrX© r9rZÚnrSrQr+r[r_raÚsÚor1r\r2r2r3re¢s zfloor._eval_nseriescCs|jdjSr7)rrXr8r2r2r3Ú_eval_is_negative²szfloor._eval_is_negativecCs|jdjSr7)rZis_nonnegativer8r2r2r3Ú_eval_is_nonnegativeµszfloor._eval_is_nonnegativecKst|ƒSr5©r)©r9r+Úkwargsr2r2r3Ú_eval_rewrite_as_ceiling¸szfloor._eval_rewrite_as_ceilingcKs|t|ƒSr5©Úfracrmr2r2r3Ú_eval_rewrite_as_frac»szfloor._eval_rewrite_as_fraccCsˆt|ƒ}|jdjrJ|jr,|jd|dkS|jrJ|jrJ|jdt|ƒkS|jd|krd|jrdtjS|tjurz|jrztjSt ||ddS©NrrRFr) rrr!rÚ is_numberr)ÚtrueÚInfinityrr©r9Úotherr2r2r3Ú__le__¾szfloor.__le__cCs„t|ƒ}|jdjrF|jr(|jd|kS|jrF|jrF|jdt|ƒkS|jd|kr`|jr`tjS|tjurv|jrvtj St ||ddS©NrFr)rrr!rrtr)ÚfalseÚNegativeInfinityrrurrwr2r2r3Ú__ge__Ìszfloor.__ge__cCsˆt|ƒ}|jdjrJ|jr,|jd|dkS|jrJ|jrJ|jdt|ƒkS|jd|krd|jrdtjS|tjurz|jrztj St ||ddSrs)rrr!rrtr)r{r|rrurrwr2r2r3Ú__gt__Úszfloor.__gt__cCs„t|ƒ}|jdjrF|jr(|jd|kS|jrF|jrF|jdt|ƒkS|jd|kr`|jr`tjS|tjurv|jrvtj St ||ddSrz)rrr!rrtr)r{rvrrur rwr2r2r3Ú__lt__èszfloor.__lt__)Nr)r)r>r?r@rAr%rDrr]rerjrkrorrryr}r~rr2r2r2r3r(_s# r(cCs t| t¡|ƒpt| t¡|ƒSr5)rÚrewriter)rq©ÚlhsÚrhsr2r2r3Ú_eval_is_eq÷sÿr„c@steZdZdZdZedd„ƒZddd„Zdd d „Zdd„Z d d„Z dd„Zdd„Zdd„Z dd„Zdd„Zdd„ZdS)r)aö 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 .. 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