\c@ sddlmZmZddlmZddlmZmZmZm Z ddl m Z ddl m Z ddlmZmZddlmZmZddlmZmZmZdd lmZdd lmZmZmZmZdd lm Z d eeefd YZ!de!fdYZ"deeefdYZ#deeefdYZ$defdYZ%defdYZ&e re&ee>> from sympy import S, Interval, pprint >>> 5 in S.Naturals True >>> iterable = iter(S.Naturals) >>> next(iterable) 1 >>> next(iterable) 2 >>> next(iterable) 3 >>> pprint(S.Naturals.intersect(Interval(0, 10))) {1, 2, ..., 10} See Also ======== Naturals0 : non-negative integers (i.e. includes 0, too) Integers : also includes negative integers cC sXt|tstjS|jr/|jr/tjS|jtksM|jtkrTtjSdS(N(t isinstanceRR tfalset is_positivet is_integerttruetFalse(tselftother((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyt _contains0s cc s)|j}xtr$|V|d}q WdS(Ni(t_inftTrue(Rti((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyt__iter__8s  cC s|S(N((R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyt _boundary>s(t__name__t __module__t__doc__R!t is_iterableR tOneR tInfinityt_supRR#tpropertyR$(((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyRs    t Naturals0cB s eZdZejZdZRS(sRepresents the whole numbers which are all the non-negative integers, inclusive of zero. See Also ======== Naturals : positive integers; does not include 0 Integers : also includes the negative integers cC sXt|tstjS|jr/|jr/tjS|jtksM|jtkrTtjSdS(N(RRR RRtis_nonnegativeRR(RR((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyROs (R%R&R'R tZeroR R(((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR-Cs  tIntegerscB sSeZdZeZdZdZedZedZ edZ RS(sE Represents all integers: positive, negative and zero. This set is also available as the Singleton, S.Integers. Examples ======== >>> from sympy import S, Interval, pprint >>> 5 in S.Naturals True >>> iterable = iter(S.Integers) >>> next(iterable) 0 >>> next(iterable) 1 >>> next(iterable) -1 >>> next(iterable) 2 >>> pprint(S.Integers.intersect(Interval(-4, 4))) {-4, -3, ..., 4} See Also ======== Naturals0 : non-negative integers Integers : positive and negative integers and zero cC s@t|tstjS|jr&tjS|jtkr<tjSdS(N(RRR RRRR(RR((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyRys  cc s7tjVtj}xtr2|V| V|d}qWdS(Ni(R R/R)R!(RR"((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR#s   cC stj S(N(R R*(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR scC stjS(N(R R*(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR+scC s|S(N((R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR$s( R%R&R'R!R(RR#R,R R+R$(((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR0Xs  tRealscB s#eZdZdZdZRS(cC stj|tj tjS(N(Rt__new__R R*(tcls((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR2scC s|ttj tjkS(N(RR R*(RR((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyt__eq__scC stttj tjS(N(thashRR R*(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyt__hash__s(R%R&R2R4R6(((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR1s  tImageSetcB sheZdZdZedZedZdZdZdZ edZ dZ RS( s Image of a set under a mathematical function. The transformation must be given as a Lambda function which has as many arguments as the elements of the set upon which it operates, e.g. 1 argument when acting on the set of integers or 2 arguments when acting on a complex region. This function is not normally called directly, but is called from `imageset`. Examples ======== >>> from sympy import Symbol, S, pi, Dummy, Lambda >>> from sympy.sets.sets import FiniteSet, Interval >>> from sympy.sets.fancysets import ImageSet >>> x = Symbol('x') >>> N = S.Naturals >>> squares = ImageSet(Lambda(x, x**2), N) # {x**2 for x in N} >>> 4 in squares True >>> 5 in squares False >>> FiniteSet(0, 1, 2, 3, 4, 5, 6, 7, 9, 10).intersect(squares) {1, 4, 9} >>> square_iterable = iter(squares) >>> for i in range(4): ... next(square_iterable) 1 4 9 16 If you want to get value for `x` = 2, 1/2 etc. (Please check whether the `x` value is in `base_set` or not before passing it as args) >>> squares.lamda(2) 4 >>> squares.lamda(S(1)/2) 1/4 >>> n = Dummy('n') >>> solutions = ImageSet(Lambda(n, n*pi), S.Integers) # solutions of sin(x) = 0 >>> dom = Interval(-1, 1) >>> dom.intersect(solutions) {0} See Also ======== sympy.sets.sets.imageset cG st|tstdn|tjkrGt|dkrG|dS|jj sa|jj rnt |jSt j |||S(Nsfirst argument must be a Lambdaii( RRt ValueErrorR tIdentityFunctiontlentexprt free_symbolstargsRRR2(R3tflambdatsets((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR2s! cC s |jdS(Ni(R=(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyttcC s |jdS(Ni(R=(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR@RAcc sTt}xD|jD]9}|j|}||kr:qq|j||VqWdS(N(tsettbase_settlamdatadd(Rt already_seenR"tval((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR#s   cC st|jjdkS(Ni(R:RDt variables(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyt_is_multivariatescC stddlm}ddlm}m}ddlm}m}m}|j }||r||j smt j St |j t |krttdqn!||rttdnd} |jr||j s|j|jt|j|j j|jkSgt||j D]\} } | | ^q)} |j} t| }tdt|| j| Drt|gt|j |D]\}} || ^q| } qg| D]}|j|@^q}i} xtt| ||D]\}\}}}|sJ||kr3t j S|g| t|||j ||}|j%r5t|} q|}nxt|j |D]\}}||||} | t j krt j Sx\| D]M}y||jkrPnWqt&k r|jj'|j(rPqqXqWt j SqQWt j)S| dkrt#td ||fnxO| D]G}y||jkrAt j)SWq"t&k rh|jj'|j(SXq"Wt j S( Ni(tMatrix(tsolvesettlinsolve(t is_sequencetiterabletcartess< Dimensions of other and output of Lambda are different.s6 `other` should be an ordered object like a Tuple.cs s|]}|jVqdS(N(t is_number(t.0R"((s3lib/python2.7/site-packages/sympy/sets/fancysets.pys siisU Determining whether %s contains %s has not been implemented.(*tsympy.matricesRJtsympy.solvers.solvesetRKRLtsympy.utilities.iterablesRMRNRORDR;R RR:R8RtNoneRItas_numer_denomtfuncRRHRCtzipRBtalltlisttjacobianR<t enumeratetvarstpoptEmptySetRRtNotImplementedErrorRt is_FiniteSett TypeErrortcontainstevalfR(RRRJRKRLRMRNROtLtsolnsRGR;teqsRHtfreetetsymsR"tstvtsytsoltxtsolnsSettmsgsettotsoln((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyRs    %/  + 8 .    &           cC s |jjS(N(RCR((R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR(MscK s8ddlm}|j}|j}||j|jS(Ni(tSetExpr(tsympy.sets.setexprRtRDRCt _eval_funcRB(RtkwargsRttfRC((s3lib/python2.7/site-packages/sympy/sets/fancysets.pytdoitQs  ( R%R&R'R2R,RDRCR#RIRR(Ry(((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR7s8   XtRangecB seZdZeZdZedZedZedZ edZ dZ dZ dZ ed Zd ZeZd Zed Zed ZedZRS(s9 Represents a range of integers. Can be called as Range(stop), Range(start, stop), or Range(start, stop, step); when stop is not given it defaults to 1. `Range(stop)` is the same as `Range(0, stop, 1)` and the stop value (juse as for Python ranges) is not included in the Range values. >>> from sympy import Range >>> list(Range(3)) [0, 1, 2] The step can also be negative: >>> list(Range(10, 0, -2)) [10, 8, 6, 4, 2] The stop value is made canonical so equivalent ranges always have the same args: >>> Range(0, 10, 3) Range(0, 12, 3) Infinite ranges are allowed. ``oo`` and ``-oo`` are never included in the set (``Range`` is always a subset of ``Integers``). If the starting point is infinite, then the final value is ``stop - step``. To iterate such a range, it needs to be reversed: >>> from sympy import oo >>> r = Range(-oo, 1) >>> r[-1] 0 >>> next(iter(r)) Traceback (most recent call last): ... ValueError: Cannot iterate over Range with infinite start >>> next(iter(r.reversed)) 0 Although Range is a set (and supports the normal set operations) it maintains the order of the elements and can be used in contexts where `range` would be used. >>> from sympy import Interval >>> Range(0, 10, 2).intersect(Interval(3, 7)) Range(4, 8, 2) >>> list(_) [4, 6] Although slicing of a Range will always return a Range -- possibly empty -- an empty set will be returned from any intersection that is empty: >>> Range(3)[:0] Range(0, 0, 1) >>> Range(3).intersect(Interval(4, oo)) EmptySet() >>> Range(3).intersect(Range(4, oo)) EmptySet() c G sddlm}t|dkr[t|dtr8tntr[|djd}q[nt|}|j dkrt dn|j pd|j |j pd}}}yYg|||fD]6}|t jt jgkr|ntt|^q\}}}Wn#t k r,t tdnX|jsKt tdntd||fDr||krt j}}qt td n|jr|}nV|jr|n|} ||| |} | dkrd}}d}n| | |}tj||||S( Ni(tceilingiisstep cannot be 0s Finite arguments to Range must be integers; `imageset` can define other cases, e.g. use `imageset(i, i/10, Range(3))` to give [0, 1/10, 1/5].s- Ranges must have a literal integer step.cs s|]}|jVqdS(N(t is_infinite(RQR"((s3lib/python2.7/site-packages/sympy/sets/fancysets.pys ss? Either the start or end value of the Range must be finite.(t#sympy.functions.elementary.integersR{R:RRRtxranget __reduce__tslicetstepR8tstarttstopR tNegativeInfinityR*RRRt is_IntegerRYR)R|t is_finiteRR2( R3R=R{tslcRRRtwtendtreftn((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR2s> )V        cC s |jdS(Ni(R=(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR@RAcC s |jdS(Ni(R=(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR@RAcC s |jdS(Ni(R=(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR@RAcC s5|s |S|j|j|j|j|j|j S(sReturn an equivalent Range in the opposite order. Examples ======== >>> from sympy import Range >>> Range(10).reversed Range(9, -1, -1) (RWRRR(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pytreverseds cC s|s tjS|jrtjS|js-|jS|jjrB|jn|j}|||jrctjSt||j ko||j kS(N( R RR|RRRRRR tinftsup(RRR((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyRs  cc s|jtjtjgkr*tdn|r|j}|j}x~tr|dkrz|j|kot|jkn s|dkr|j|ko|jkn rPn|V||7}qEWndS(Ns-Cannot iterate over Range with infinite starti(RR RR*R8RR!R(RR"R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR#s   //cC sC|s dS|j|j}|jr2tdnt||jS(Nis0Use .size to get the length of an infinite Range(RRR|R8tabsR(Rtdif((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyt__len__s  cC s0ytt|SWntk r+tjSXdS(N(R R:R8R R*(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pytsizes cC s|j|jkS(N(RR(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyt __nonzero__scC sddlm}d}d}dd}t|tr!|jjr|j|j\}}}||||} | dkrtdS|| |} | |} ||j} t|||| | | S|j }|j }|jdkrt |n|jpd}||j} |j j r`|j |dkr7|n| d|dkrQ|n| |j S|dkr}|dkr|dkrt|d|j | S|dkrt |qz|Sq|dkr|dkrt|d||| St|j ||| Sq|dkr8|dkr)tdSt |q|dkrn|dkr_t |qzt |qt |q|dkrH|dkr|dkrt|||j | St|||j | Sq|dkrt||||| S|dkr*|dkrt |qEtdSq|dkrt |qq|dkr|dkr|dkr{t |q|dkrt |q|Sq|dkr|dkrt |q|dkrt|j ||| StdSqt |q|dkrt |qn|s6td n|dkrI|j S|dksd|tjkrr|j |jS|dkr|j n|j ||j} | j rt |n| |jks| |jkrtd n| SdS( Ni(R{s0cannot slice from the end with an infinite valuesslice step cannot be zeros,cannot unambiguously re-stride from the end swith an infinite valueiisRange index out of range(R}R{RRRRtindicesRzRRRR8R|RRUt IndexErrorR R*RR(RR"R{tooslicetzerostept ambiguousRRRRtcanonical_stopRtsstrv((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyt __getitem__ s                                       ) cC s7|stn|jdkr%|jS|j|jSdS(Ni(R`RRR(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR s  cC s7|stn|jdkr,|j|jS|jSdS(Ni(R`RRR(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR+s  cC s|S(N((R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR$s(R%R&R'R!R(R2R,RRRRRR#RRRt__bool__RR R+R$(((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyRzXs"= 1    v  c C sYddlm}|jr|j}|dtjkr|dtjkr|jr|jr||j}t t d|tjt t t |tjdtjt t St ddtjt t S||j||j }}|d ks|d kr tdn|tj}|tj}||krjt t tj|t |jt |dtj|jt St |||j|jSn|jrg}xI|D]A} || }|d krtdq|j|tjqWt|S|jrt g|jD]} t| ^qS|jtjrEtdt|ntd|d S( s Normalize a Real Set `theta` in the Interval [0, 2*pi). It returns a normalized value of theta in the Set. For Interval, a maximum of one cycle [0, 2*pi], is returned i.e. for theta equal to [0, 10*pi], returned normalized value would be [0, 2*pi). As of now intervals with end points as non-multiples of `pi` is not supported. Raises ====== NotImplementedError The algorithms for Normalizing theta Set are not yet implemented. ValueError The input is not valid, i.e. the input is not a real set. RuntimeError It is a bug, please report to the github issue tracker. Examples ======== >>> from sympy.sets.fancysets import normalize_theta_set >>> from sympy import Interval, FiniteSet, pi >>> normalize_theta_set(Interval(9*pi/2, 5*pi)) Interval(pi/2, pi) >>> normalize_theta_set(Interval(-3*pi/2, pi/2)) Interval.Ropen(0, 2*pi) >>> normalize_theta_set(Interval(-pi/2, pi/2)) Union(Interval(0, pi/2), Interval.Ropen(3*pi/2, 2*pi)) >>> normalize_theta_set(Interval(-4*pi, 3*pi)) Interval.Ropen(0, 2*pi) >>> normalize_theta_set(Interval(-3*pi/2, -pi/2)) Interval(pi/2, 3*pi/2) >>> normalize_theta_set(FiniteSet(0, pi, 3*pi)) {0, pi} i(t _pi_coeffiisBNormalizing theta without pi as coefficient is not yet implementeds@Normalizing theta without pi as coefficient, is not Implemented.s;Normalizing theta when, it is of type %s is not implementeds %s is not a real setN(t(sympy.functions.elementary.trigonometricRt is_IntervaltmeasureR tPit left_opent right_openRRRRR!RRUR`R/RatappendRtis_UnionR=tnormalize_theta_sett is_subsetR1ttypeR8( tthetatcoefft interval_lentktk_starttk_endt new_starttnew_endt new_thetatelementtinterval((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyRs@&  %$          &t ComplexRegioncB seZdZeZedZedZedZ edZ edZ edZ edZ edZed Zed Zed Zd ZRS( s Represents the Set of all Complex Numbers. It can represent a region of Complex Plane in both the standard forms Polar and Rectangular coordinates. * Polar Form Input is in the form of the ProductSet or Union of ProductSets of the intervals of r and theta, & use the flag polar=True. Z = {z in C | z = r*[cos(theta) + I*sin(theta)], r in [r], theta in [theta]} * Rectangular Form Input is in the form of the ProductSet or Union of ProductSets of interval of x and y the of the Complex numbers in a Plane. Default input type is in rectangular form. Z = {z in C | z = x + I*y, x in [Re(z)], y in [Im(z)]} Examples ======== >>> from sympy.sets.fancysets import ComplexRegion >>> from sympy.sets import Interval >>> from sympy import S, I, Union >>> a = Interval(2, 3) >>> b = Interval(4, 6) >>> c = Interval(1, 8) >>> c1 = ComplexRegion(a*b) # Rectangular Form >>> c1 ComplexRegion(Interval(2, 3) x Interval(4, 6), False) * c1 represents the rectangular region in complex plane surrounded by the coordinates (2, 4), (3, 4), (3, 6) and (2, 6), of the four vertices. >>> c2 = ComplexRegion(Union(a*b, b*c)) >>> c2 ComplexRegion(Union(Interval(2, 3) x Interval(4, 6), Interval(4, 6) x Interval(1, 8)), False) * c2 represents the Union of two rectangular regions in complex plane. One of them surrounded by the coordinates of c1 and other surrounded by the coordinates (4, 1), (6, 1), (6, 8) and (4, 8). >>> 2.5 + 4.5*I in c1 True >>> 2.5 + 6.5*I in c1 False >>> r = Interval(0, 1) >>> theta = Interval(0, 2*S.Pi) >>> c2 = ComplexRegion(r*theta, polar=True) # Polar Form >>> c2 # unit Disk ComplexRegion(Interval(0, 1) x Interval.Ropen(0, 2*pi), True) * c2 represents the region in complex plane inside the Unit Disk centered at the origin. >>> 0.5 + 0.5*I in c2 True >>> 1 + 2*I in c2 False >>> unit_disk = ComplexRegion(Interval(0, 1)*Interval(0, 2*S.Pi), polar=True) >>> upper_half_unit_disk = ComplexRegion(Interval(0, 1)*Interval(0, S.Pi), polar=True) >>> intersection = unit_disk.intersect(upper_half_unit_disk) >>> intersection ComplexRegion(Interval(0, 1) x Interval(0, pi), True) >>> intersection == upper_half_unit_disk True See Also ======== Reals c C siddlm}m}tddt\}}}}tj} t|}|tkr,t d|j Drt |j dkrg} xB|j dD]3}x*|j dD]}| j || |qWqWt | } n,tj|t||f|| ||} ||f| _|| || _n'|tkrGg} |jskx.|j D]} | j | qQWn | j |xQt| D]C\} }dd lm}||j dt|j d| | Msiii(t ProductSets$polar should be either True or False(tsympyRRR R R t ImaginaryUnitRRRYR=R:RRR7R2Rt _variablest_exprR!t is_ProductSetR\t sympy.setsRRRR8t_setst_polar(R3R?tpolarRRRotytrRtIt complex_numtobjtnew_setsRRlR((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR2DsD   .,      $   cC s|jS(s Return raw input sets to the self. Examples ======== >>> from sympy import Interval, ComplexRegion, Union >>> a = Interval(2, 3) >>> b = Interval(4, 5) >>> c = Interval(1, 7) >>> C1 = ComplexRegion(a*b) >>> C1.sets Interval(2, 3) x Interval(4, 5) >>> C2 = ComplexRegion(Union(a*b, b*c)) >>> C2.sets Union(Interval(2, 3) x Interval(4, 5), Interval(4, 5) x Interval(1, 7)) (R(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR?yscC s|j|jfS(N(RR(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR=scC s|jS(N(R(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyRHscC s|jS(N(R(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR;scC s5|jjr%d}||jf}n |jj}|S(s Return a tuple of sets (ProductSets) input of the self. Examples ======== >>> from sympy import Interval, ComplexRegion, Union >>> a = Interval(2, 3) >>> b = Interval(4, 5) >>> c = Interval(1, 7) >>> C1 = ComplexRegion(a*b) >>> C1.psets (Interval(2, 3) x Interval(4, 5),) >>> C2 = ComplexRegion(Union(a*b, b*c)) >>> C2.psets (Interval(2, 3) x Interval(4, 5), Interval(4, 5) x Interval(1, 7)) ((R?RR=(Rtpsets((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyRs   cC s>g}x%|jD]}|j|jdqWt|}|S(s2 Return the union of intervals of `x` when, self is in rectangular form, or the union of intervals of `r` when self is in polar form. Examples ======== >>> from sympy import Interval, ComplexRegion, Union >>> a = Interval(2, 3) >>> b = Interval(4, 5) >>> c = Interval(1, 7) >>> C1 = ComplexRegion(a*b) >>> C1.a_interval Interval(2, 3) >>> C2 = ComplexRegion(Union(a*b, b*c)) >>> C2.a_interval Union(Interval(2, 3), Interval(4, 5)) i(RRR=R(Rt a_intervalR((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyRs  cC s>g}x%|jD]}|j|jdqWt|}|S(s Return the union of intervals of `y` when, self is in rectangular form, or the union of intervals of `theta` when self is in polar form. Examples ======== >>> from sympy import Interval, ComplexRegion, Union >>> a = Interval(2, 3) >>> b = Interval(4, 5) >>> c = Interval(1, 7) >>> C1 = ComplexRegion(a*b) >>> C1.b_interval Interval(4, 5) >>> C2 = ComplexRegion(Union(a*b, b*c)) >>> C2.b_interval Interval(1, 7) i(RRR=R(Rt b_intervalR((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyRs  cC s|jS(s Returns True if self is in polar form. Examples ======== >>> from sympy import Interval, ComplexRegion, Union, S >>> a = Interval(2, 3) >>> b = Interval(4, 5) >>> theta = Interval(0, 2*S.Pi) >>> C1 = ComplexRegion(a*b) >>> C1.polar False >>> C2 = ComplexRegion(a*theta, polar=True) >>> C2.polar True (R(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyRscC s |jjS(sy The measure of self.sets. Examples ======== >>> from sympy import Interval, ComplexRegion, S >>> a, b = Interval(2, 5), Interval(4, 8) >>> c = Interval(0, 2*S.Pi) >>> c1 = ComplexRegion(a*b) >>> c1.measure 12 >>> c2 = ComplexRegion(a*c, polar=True) >>> c2.measure 6*pi (R?t_measure(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyRscC s5|jtjs!tdn||tdS(s% Converts given subset of real numbers to a complex region. Examples ======== >>> from sympy import Interval, ComplexRegion >>> unit = Interval(0,1) >>> ComplexRegion.from_real(unit) ComplexRegion(Interval(0, 1) x {0}, False) s&sets must be a subset of the real linei(RR R1R8R(R3R?((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyt from_realsc C sddlm}m}ddlm}t|}t||}|rht|dkrhtdnt|t  rt|| rt j S|j s|r|n |j \}}xD|jD]9}t|jdj||jdj|rtSqWtS|j r|r|\} } n8|jr>t jt j} } n||||} } xD|jD]9}t|jdj| |jdj| ratSqaWtSdS(Ni(targtAbs(tTupleisexpecting Tuple of length 2ii(tsympy.functionsRRtsympy.core.containersRRRR:R8RR RRt as_real_imagRRR=RR!Rtis_zeroR/( RRRRRtisTupletretimRRR((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR-s4     (R%R&R'R!tis_ComplexRegionRR2R,R?R=RHR;RRRRRt classmethodRR(((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyRsM 5t ComplexescB s5eZdZdZdZdZdZRS(cC stj|tjtjS(N(RR2R R1(R3((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR2RscC s|ttjtjkS(N(RR R1(RR((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR4UscC stttjtjS(N(R5RR R1(R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyR6XscC sdS(Ns S.Complexes((R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyt__str__[scC sdS(Ns S.Complexes((R((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyt__repr__^s(R%R&R2R4R6RR(((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyRPs     N(+t __future__RRtsympy.core.basicRtsympy.core.compatibilityRRRRtsympy.core.exprRtsympy.core.functionRtsympy.core.singletonR R tsympy.core.symbolR R tsympy.core.sympifyR RRtsympy.logic.boolalgRtsympy.sets.setsRRRRtsympy.utilities.miscRRR-R0R1R7RzR~RRR(((s3lib/python2.7/site-packages/sympy/sets/fancysets.pyts0""4> C   U]