;ò …Rã?c@sodklZdkZdfd„ƒYZedjo5eddgƒZdeZeeƒZeeGHndS((s PolynomialNsRationalFunctioncBs°tZdZdgd„ZdZd„Zd„Zd„Zd„Zd„Z d „Z e Z d „Z d „Z d „ZeZd „Zd„Zdd„Zd„Zd„ZRS(sÌRational Function Instances of this class represent rational functions in a single variable. They can be evaluated like functions. Constructor: RationalFunction(|numerator|, |denominator|) Arguments: |numerator|, |denominator| -- polynomials or sequences of numbers that represent the polynomial coefficients Rational functions support addition, subtraction, multiplication, and division. f1.0cCsft|dƒo ||_nt|ƒ|_t|dƒo ||_nt|ƒ|_|iƒdS(Ns is_polynomial(shasattrs numeratorsselfs Polynomials denominators _normalize(sselfs numerators denominator((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/Rational.pys__init__s  icCs|i|ƒ|i|ƒSdS(N(sselfs numeratorsvalues denominator(sselfsvalue((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/Rational.pys__call__)scCs6dtt|iiƒƒtt|iiƒƒfSdS(NsRationalFunction(%s,%s)(sreprslistsselfs numeratorscoeffs denominator(sself((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/Rational.pys__repr__,scCs'|i|iƒ|_|i|iƒ|_d}xlnod|ii|djoPn|ii|djoPn|d}|t|iiƒjoPq3q:W|djo6t|ii|ƒ|_t|ii|ƒ|_n|iid}|djo$|i||_|i||_ndS(Niiiÿÿÿÿf1.0( sselfs _truncates numerators denominatorsnscoeffslens Polynomialsfactor(sselfsfactorsn((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/Rational.pys _normalize0s&    cCsi|iddjo|Sn|i}x3t|ƒdjo|ddjo|d }q(Wt|ƒSdS(Niÿÿÿÿf0.0i(spolyscoeffslens Polynomial(sselfspolyscoeff((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/Rational.pys _truncateDs $cCset|dƒo||fSnDt|dƒo|t|dgƒfSn|t|gdgƒfSdS(Nsis_rational_functions is_polynomialf1.0(shasattrsothersselfsRationalFunction(sselfsother((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/Rational.pys __coerce__Ls cCs%t|i|i|i|iƒSdS(N(sRationalFunctionsselfs numeratorsothers denominator(sselfsother((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/Rational.pys__mul__TscCs%t|i|i|i|iƒSdS(N(sRationalFunctionsselfs numeratorsothers denominator(sselfsother((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/Rational.pys__div__YscCs%t|i|i|i|iƒSdS(N(sRationalFunctionsothers numeratorsselfs denominator(sselfsother((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/Rational.pys__rdiv__]scCs3t|i|i|i|i|i|iƒSdS(N(sRationalFunctionsselfs numeratorsothers denominator(sselfsother((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/Rational.pys__add__ascCs3t|i|i|i|i|i|iƒSdS(N(sRationalFunctionsselfs numeratorsothers denominator(sselfsother((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/Rational.pys__sub__gscCs3t|i|i|i|i|i|iƒSdS(N(sRationalFunctionsothers numeratorsselfs denominator(sselfsother((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/Rational.pys__rsub__lsicCsti|iiddƒ}|djo ti|dg|fƒ}n|ii}t |ƒ}g}xYt |ƒ|joE|d|d}|i |ƒ|| |||| )|d }qiW| o dg}n|iƒt |ƒdjo dg}nt|ƒt||ƒfSdS(s›Returns a polynomial and a rational function such that the sum of the two is equal to the original rational function. The returned rational function's numerator is of lower order than its denominator. The argument |shift| (default: 0) specifies a positive integer power of the independent variable by which the numerator is multiplied prior to division. scopyiif0.0iÿÿÿÿN(sNumericsarraysselfs numeratorscoeffsnumsshifts concatenates denominatorsdenslens den_ordersqsappendsreverses PolynomialsRationalFunction(sselfsshiftsqs den_ordersnumsdenscoeff((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/Rational.pysdivideqs&         cCs|iiƒSdS(s&Returns an array containing the zeros.N(sselfs numeratorszeros(sself((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/Rational.pyszerosscCs|iiƒSdS(s&Returns an array containing the poles.N(sselfs denominatorszeros(sself((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/Rational.pyspoles‘s(s__name__s __module__s__doc__s__init__sis_rational_functions__call__s__repr__s _normalizes _truncates __coerce__s__mul__s__rmul__s__div__s__rdiv__s__add__s__radd__s__sub__s__rsub__sdivideszerosspoles(((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/Rational.pysRationalFunction s&               s__main__f1.0(s PolynomialsNumericsRationalFunctions__name__spsinvpspr(sprsNumericsinvpsps PolynomialsRationalFunction((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/Rational.pys?s  Ž