c419.java test cpoly to find zeros of polynomials machine constants eta=4.440892098500626E-16 infin=8.988465674311578E307 smalno=1.1125369292536007E-308 base=2.0 are=4.440892098500626E-16 mre=1.2560739669470201E-15 real part imaginary part modulus EXAMPLE 0. POLYNOMIAL WITH ZERO 0.5 COEFFICIENTS degree=1 +4.0000000000000000E+00 +4.0000000000000000E+00 -2.0000000000000000E+00 -2.0000000000000000E+00 ZEROS +5.0000000000000000E-01 +0.0000000000000000E+00 abs=5.00E-01 CHECK +0.0000000000000000E+00 +0.0000000000000000E+00 err=0.00E00 EXAMPLE 0a. POLYNOMIAL WITH ZEROS 0.0 -2.0 COEFFICIENTS degree=2 +1.0000000000000000E+00 +1.0000000000000000E+00 +2.0000000000000000E+00 +2.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 ZEROS +0.0000000000000000E+00 +0.0000000000000000E+00 abs=0.00E00 -2.0000000000000000E+00 +0.0000000000000000E+00 abs=2.00E00 CHECK +0.0000000000000000E+00 +0.0000000000000000E+00 err=0.00E00 +0.0000000000000000E+00 +0.0000000000000000E+00 err=0.00E00 EXAMPLE 0b. POLYNOMIAL WITH ZEROS (1+2i) (3-4i) COEFFICIENTS degree=2 +1.0000000000000000E+00 +0.0000000000000000E+00 -4.0000000000000000E+00 +2.0000000000000000E+00 +1.1000000000000000E+01 +2.0000000000000000E+00 ZEROS +1.0000000000000000E+00 +2.0000000000000000E+00 abs=2.24E00 +3.0000000000000000E+00 -4.0000000000000000E+00 abs=5.00E00 CHECK +0.0000000000000000E+00 +0.0000000000000000E+00 err=0.00E00 +0.0000000000000000E+00 +0.0000000000000000E+00 err=0.00E00 EXAMPLE 0c. POLYNOMIAL WITH ZEROS 10**15 and 10**(-15) COEFFICIENTS degree=2 +1.0000000000000000E+00 +0.0000000000000000E+00 -1.0000000000000000E+15 +0.0000000000000000E+00 +1.0000000000000000E+00 +0.0000000000000000E+00 ZEROS +1.0000000000000000E-15 +0.0000000000000000E+00 abs=1.00E-15 +1.0000000000000000E+15 -0.0000000000000000E+00 abs=1.00E15 CHECK +0.0000000000000000E+00 +0.0000000000000000E+00 err=0.00E00 +1.0000000000000000E+00 +0.0000000000000000E+00 err=1.00E-15 EXAMPLE 0d. POLYNOMIAL WITH ZEROS (1+2i) (3-4i) (-6+5i) COEFFICIENTS degree=3 +1.0000000000000000E+00 +0.0000000000000000E+00 +2.0000000000000000E+00 -3.0000000000000000E+00 -3.0000000000000000E+00 +3.4000000000000000E+01 +7.6000000000000000E+01 -4.3000000000000000E+01 ZEROS +1.0000000000000000E+00 +2.0000000000000000E+00 abs=2.24E00 -6.0000000000000000E+00 +5.0000000000000000E+00 abs=7.81E00 +3.0000000000000000E+00 -4.0000000000000000E+00 abs=5.00E00 CHECK +0.0000000000000000E+00 +0.0000000000000000E+00 err=0.00E00 +0.0000000000000000E+00 +0.0000000000000000E+00 err=0.00E00 +0.0000000000000000E+00 +0.0000000000000000E+00 err=0.00E00 EXAMPLE 1. POLYNOMIAL WITH ZEROS 1,2,3,4 COEFFICIENTS degree=4 +1.0000000000000000E+00 +0.0000000000000000E+00 -1.0000000000000000E+01 +0.0000000000000000E+00 +3.5000000000000000E+01 +0.0000000000000000E+00 -5.0000000000000000E+01 +0.0000000000000000E+00 +2.4000000000000000E+01 +0.0000000000000000E+00 ZEROS +9.9999999999999970E-01 +6.6174449004242214E-24 abs=1.00E00 +2.0000000000000004E+00 -6.9152299209433110E-22 abs=2.00E00 +3.0000000000000004E+00 +1.4657640454439650E-21 abs=3.00E00 +3.9999999999999996E+00 -7.8085849825005810E-22 abs=4.00E00 CHECK +3.5527136788005010E-15 -3.9704669402545350E-23 err=7.11E-17 -7.1054273576010020E-15 -1.3830459841886547E-21 err=1.42E-16 -2.4868995751603507E-14 -2.9315280908879570E-21 err=4.97E-16 +3.1974423109204510E-14 -4.6851509895003615E-21 err=6.39E-16 EXAMPLE 1a. POLYNOMIAL WITH ZEROS 1,2,...,10. COEFFICIENTS degree=10 +1.0000000000000000E+00 +0.0000000000000000E+00 -5.5000000000000000E+01 +0.0000000000000000E+00 +1.3200000000000000E+03 +0.0000000000000000E+00 -1.8150000000000000E+04 +0.0000000000000000E+00 +1.5777300000000000E+05 +0.0000000000000000E+00 -9.0205500000000000E+05 +0.0000000000000000E+00 +3.4169300000000000E+06 +0.0000000000000000E+00 -8.4095000000000000E+06 +0.0000000000000000E+00 +1.2753576000000000E+07 +0.0000000000000000E+00 -1.0628640000000000E+07 +0.0000000000000000E+00 +3.6288000000000000E+06 +0.0000000000000000E+00 ZEROS +9.9999999999999970E-01 +5.0849928922517410E-16 abs=1.00E00 +2.0000000000001110E+00 -4.5764936034401574E-15 abs=2.00E00 +2.9999999999945453E+00 -5.0283798358594000E-12 abs=3.00E00 +4.0000000000369470E+00 +3.5284086867594124E-11 abs=4.00E00 +4.9999999998809150E+00 -1.0595667244020035E-10 abs=5.00E00 +6.9999999997276800E+00 -1.7680661827597670E-10 abs=7.00E00 +6.0000000002274020E+00 +1.7677126582448747E-10 abs=6.00E00 +8.0000000002001310E+00 +1.0580349402751989E-10 abs=8.00E00 +8.9999999999181120E+00 -3.4966320042342220E-11 abs=9.00E00 +1.0000000000014160E+01 +4.9032118690914010E-12 abs=1.00E01 CHECK -4.6566128730774010E-10 -1.8452422207403243E-10 err=3.93E-17 +6.9849193096160700E-09 -1.8452422209063766E-10 err=5.48E-16 +6.0070306052588560E-08 +5.0686068745966740E-08 err=6.16E-15 +1.8766149850131590E-07 +1.5242725526252928E-07 err=1.90E-14 +4.1956081824114486E-07 +3.0515521662791254E-07 err=4.07E-14 +2.4540349818160090E-06 +7.6380459045791800E-07 err=2.02E-13 +6.3469633143564300E-07 +5.0910124562072450E-07 err=6.38E-14 +3.1720846884914934E-06 +1.0664992203568930E-06 err=2.62E-13 +8.9779496188002430E-07 +1.4098420237735936E-06 err=1.31E-13 +8.9062377810460760E-06 +1.7792775232195727E-06 err=7.12E-13 EXAMPLE 2. ZEROS ON IMAGINARY AXIS DEGREE 3. COEFFICIENTS degree=3 +1.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 -1.0001000100000000E+04 -1.0001000100000000E+04 +0.0000000000000000E+00 +0.0000000000000000E+00 +1.0000000000000000E+00 ZEROS +0.0000000000000000E+00 +1.0000000000000000E-04 abs=1.00E-04 +0.0000000000000000E+00 +1.0000000000000000E+00 abs=1.00E00 +0.0000000000000000E+00 +1.0000000000000000E+04 abs=1.00E04 CHECK +0.0000000000000000E+00 +0.0000000000000000E+00 err=0.00E00 +0.0000000000000000E+00 +0.0000000000000000E+00 err=0.00E00 +0.0000000000000000E+00 -7.0715235779061910E-05 err=7.07E-09 EXAMPLE 3. ZEROS AT 1+I,1/2*(1+I) . 1/(2**-9)*(1+I) COEFFICIENTS degree=10 +1.0000000000000000E+00 +0.0000000000000000E+00 -1.9980468750000000E+00 -1.9980468750000000E+00 +0.0000000000000000E+00 +2.6588592529296880E+00 +7.5670659542083740E-01 -7.5670659542083740E-01 -2.0021195337176320E-01 +0.0000000000000000E+00 +1.2715073651634160E-02 +1.2715073651634160E-02 +0.0000000000000000E+00 -7.8207794285845010E-04 -1.1546426321729090E-05 +1.1546426321729090E-05 +1.5848036127863450E-07 +0.0000000000000000E+00 -4.6520653995685280E-10 -4.6520653995685280E-10 +0.0000000000000000E+00 +9.0949470177292820E-13 ZEROS +1.9531249999999993E-03 +1.9531249999999985E-03 abs=2.76E-03 +3.9062500000000200E-03 +3.9062500000000250E-03 abs=5.52E-03 +7.8124999999998920E-03 +7.8124999999998750E-03 abs=1.10E-02 +1.5625000000000305E-02 +1.5625000000000310E-02 abs=2.21E-02 +3.1249999999999380E-02 +3.1249999999999445E-02 abs=4.42E-02 +6.2500000000000870E-02 +6.2500000000000720E-02 abs=8.84E-02 +1.2499999999999947E-01 +1.2499999999999951E-01 abs=1.77E-01 +2.4999999999999958E-01 +2.4999999999999994E-01 abs=3.54E-01 +5.0000000000000090E-01 +5.0000000000000040E-01 abs=7.07E-01 +9.9999999999999960E-01 +9.9999999999999980E-01 abs=1.41E00 CHECK +0.0000000000000000E+00 +0.0000000000000000E+00 err=0.00E00 -2.0194839173657902E-28 -2.0194839173657902E-28 err=1.01E-28 -2.1204581132340797E-27 +2.5243548967072380E-28 err=7.56E-28 -7.9769614735948710E-27 +2.4132832812521193E-26 err=9.00E-27 -5.3970707691600740E-26 +8.1738611555380360E-26 err=3.47E-26 +4.4126733336401200E-24 +4.4409461084832410E-24 err=2.22E-24 -1.1830611366649380E-22 -1.4026153891931120E-22 err=6.49E-23 -3.3548958598168250E-20 -1.6925988555629597E-20 err=1.33E-20 -7.4513883352742260E-18 +1.1471248709830551E-17 err=4.84E-18 -1.6720599257026714E-15 +3.8243843026689366E-15 err=1.48E-15 EXAMPLE 4. MULTIPLE ZEROS COEFFICIENTS degree=10 +1.0000000000000000E+00 +0.0000000000000000E+00 -1.0000000000000000E+01 -1.0000000000000000E+01 +3.0000000000000000E+00 +1.0000000000000000E+02 +2.8400000000000000E+02 -3.3400000000000000E+02 -1.2930000000000000E+03 +2.0000000000000000E+02 +2.3740000000000000E+03 +1.3940000000000000E+03 -1.5870000000000000E+03 -3.8360000000000000E+03 -9.2000000000000000E+02 +4.3340000000000000E+03 +2.2040000000000000E+03 -2.3520000000000000E+03 -1.3440000000000000E+03 +5.0400000000000000E+02 +2.8800000000000000E+02 +0.0000000000000000E+00 ZEROS +1.0007808739466801E+00 +9.6741546322255010E-05 abs=1.00E00 +9.9921933751876850E-01 -9.7140350877906480E-05 abs=9.99E-01 +9.9990295324051550E-01 +7.8096776100819350E-04 abs=1.00E00 +1.0000968352940323E+00 -7.8056895624728160E-04 abs=1.00E00 -7.7937557047770250E-05 +1.9999309477114995E+00 abs=2.00E00 +9.8772925194045530E-05 +1.9999670276042942E+00 abs=2.00E00 -2.0835368152908695E-05 +2.0001020246839434E+00 abs=2.00E00 +2.9999995964259223E+00 +2.6080932786568325E-07 abs=3.00E00 +1.7649770533978426E-13 +3.9999999999999627E+00 abs=4.00E00 +3.0000004035739103E+00 -2.6080923198890105E-07 abs=3.00E00 CHECK -3.7616606958902030E-11 +5.9268204927187540E-11 err=1.58E-14 -3.7394276021265440E-11 +5.9653424561156850E-11 err=1.59E-14 -3.7326625189175455E-11 +5.8972132732648670E-11 err=1.58E-14 -3.7887888816980420E-11 +5.9856147816006460E-11 err=1.60E-14 -2.0452262106118724E-10 -7.0224098584759090E-10 err=1.65E-13 -2.0156676328042522E-10 -6.9801331208096950E-10 err=1.64E-13 -2.0389734345371835E-10 -7.1234934227379370E-10 err=1.67E-13 -7.2312181191428600E-10 +4.8013184010873120E-10 err=1.96E-13 -8.8566594058647750E-09 -5.3442159586576420E-09 err=2.33E-12 -6.5155585740149670E-10 +5.2514762743721080E-10 err=1.89E-13 EXAMPLE 5. 12 ZEROS EVENLY DISTRIBUTE ON A CIRCLE OF RADIUS 1. CENTERED AT 0+2I. COEFFICIENTS degree=12 +1.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 -2.4000000000000000E+01 -2.6400000000000000E+02 +0.0000000000000000E+00 +0.0000000000000000E+00 +1.7600000000000000E+03 +7.9200000000000000E+03 +0.0000000000000000E+00 +0.0000000000000000E+00 -2.5344000000000000E+04 -5.9136000000000000E+04 +0.0000000000000000E+00 +0.0000000000000000E+00 +1.0137600000000000E+05 +1.2672000000000000E+05 +0.0000000000000000E+00 +0.0000000000000000E+00 -1.1264000000000000E+05 -6.7584000000000000E+04 +0.0000000000000000E+00 +0.0000000000000000E+00 +2.4576000000000000E+04 +4.0950000000000000E+03 +0.0000000000000000E+00 ZEROS +3.8338049504786295E-14 +1.0000000000000635E+00 abs=1.00E00 -4.9999999999940390E-01 +1.1339745962124460E+00 abs=1.24E00 +4.9999999999582780E-01 +1.1339745962160759E+00 abs=1.24E00 +8.6602540377551230E-01 +1.4999999999994830E+00 abs=1.73E00 -9.9999999997713560E-01 +2.0000000000083930E+00 abs=2.24E00 -5.0000000028748130E-01 +2.8660254036900907E+00 abs=2.91E00 -8.6602540378602410E-01 +1.5000000000004263E+00 abs=1.73E00 +5.0000000029491730E-01 +2.8660254036842550E+00 abs=2.91E00 +8.6602540373478520E-01 +2.4999999998853130E+00 abs=2.65E00 +5.6382453585411080E-12 +3.0000000004140635E+00 abs=3.00E00 +9.9999999997073790E-01 +1.9999999999945117E+00 abs=2.24E00 -8.6602540372741220E-01 +2.4999999998948780E+00 abs=2.65E00 CHECK +1.8189894035458565E-12 +4.6005659405709950E-13 err=1.48E-17 +5.9117155615240335E-12 +4.3428372009657323E-11 err=3.46E-16 -6.5938365878537300E-11 -5.2750692702829840E-11 err=6.66E-16 +6.8212102632969620E-12 -9.5496943686157460E-11 err=7.56E-16 +1.4551915228366852E-10 -1.1868905858136714E-10 err=1.48E-15 +1.4765646483283490E-09 +1.9201706891180947E-09 err=1.91E-14 -1.0868461686186492E-10 +1.2300915841478854E-10 err=1.30E-15 +1.6866579244378954E-09 -9.6893018053378910E-09 err=7.76E-14 +4.2700776248238980E-10 -8.3832674135919660E-10 err=7.42E-15 +1.0393705451861024E-08 -6.7658944693359090E-11 err=8.20E-14 -5.9026206145063040E-10 -2.8830982046201825E-10 err=5.18E-15 -1.0891199053730816E-09 -1.1207248462596908E-09 err=1.23E-14 EXAMPLE 6. 16 ZEROS EVENLY DISTRIBUTE ON A CIRCLE OF RADIUS 5. CENTERED AT 0,0 COEFFICIENTS degree=16 +1.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 -1.5258789062500000E+11 +0.0000000000000000E+00 ZEROS +3.5355339059327378E+00 +3.5355339059327378E+00 abs=5.00E00 -3.5355339059327378E+00 +3.5355339059327386E+00 abs=5.00E00 -3.5355339059327386E+00 -3.5355339059327380E+00 abs=5.00E00 +3.5355339059327386E+00 -3.5355339059327380E+00 abs=5.00E00 +1.9134171618254459E+00 +4.6193976625564360E+00 abs=5.00E00 -4.6193976625564370E+00 +1.9134171618254465E+00 abs=5.00E00 -1.9134171618254452E+00 -4.6193976625564370E+00 abs=5.00E00 +4.6193976625564360E+00 -1.9134171618254450E+00 abs=5.00E00 -3.9732399358723025E-15 +4.9999999999999970E+00 abs=5.00E00 -4.6193976625563600E+00 -1.9134171618254645E+00 abs=5.00E00 +9.0727073448859630E-14 -4.9999999999999990E+00 abs=5.00E00 +4.9999999999999560E+00 +4.7703222592423310E-14 abs=5.00E00 -1.9134171618254620E+00 +4.6193976625564215E+00 abs=5.00E00 -5.0000000000000430E+00 -4.6639674076713466E-14 abs=5.00E00 +1.9134171618254021E+00 -4.6193976625563540E+00 abs=5.00E00 +4.6193976625564210E+00 +1.9134171618253970E+00 abs=5.00E00 CHECK +1.2207031250000000E-04 +0.0000000000000000E+00 err=8.00E-16 +3.8146972656250000E-04 -2.7465820312500000E-04 err=3.08E-15 +5.6457519531250000E-04 -1.2207031250000000E-04 err=3.79E-15 +5.6457519531250000E-04 +1.2207031250000000E-04 err=3.79E-15 +3.3569335937500000E-04 +1.7242431640625000E-03 err=1.15E-14 +8.3160400390625000E-04 +1.5869140625000000E-03 err=1.17E-14 +5.4931640625000000E-04 +2.1667480468750000E-03 err=1.46E-14 +1.0681152343750000E-04 +2.1057128906250000E-03 err=1.38E-14 -1.2817382812500000E-03 +1.9400585624376324E-03 err=1.52E-14 -3.0323028564453125E-02 +2.0797729492187500E-02 err=2.41E-13 -3.9672851562500000E-04 +4.4300328832450886E-02 err=2.90E-13 -2.1697998046875208E-02 +2.3292589156453592E-02 err=2.09E-13 -3.0975341796875000E-03 +8.2550048828125000E-03 err=5.78E-14 +2.0843505859374802E-02 +2.2773278357773160E-02 err=2.02E-13 -4.4769287109375000E-02 -6.1950683593750000E-03 err=2.96E-13 -1.5632629394531250E-02 -2.0919799804687500E-02 err=1.71E-13 EXAMPLE 7a. 12 ZEROS ON A CIRCLE OF RADIUS 1. CENTERED AT 0,0 COEFFICIENTS degree=12 +1.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +1.0000000000000000E+00 +0.0000000000000000E+00 ZEROS +7.0710678118654750E-01 +7.0710678118654750E-01 abs=1.00E00 -7.0710678118654750E-01 +7.0710678118654750E-01 abs=1.00E00 -7.0710678118654750E-01 -7.0710678118654750E-01 abs=1.00E00 +7.0710678118654750E-01 -7.0710678118654750E-01 abs=1.00E00 +2.5881904510252074E-01 +9.6592582628906820E-01 abs=1.00E00 -9.6592582628906820E-01 +2.5881904510252080E-01 abs=1.00E00 -2.5881904510252080E-01 -9.6592582628906820E-01 abs=1.00E00 +9.6592582628906830E-01 -2.5881904510252080E-01 abs=1.00E00 -2.5881904510252424E-01 +9.6592582628906780E-01 abs=1.00E00 -9.6592582628906790E-01 -2.5881904510252440E-01 abs=1.00E00 +2.5881904510252307E-01 -9.6592582628906850E-01 abs=1.00E00 +9.6592582628906900E-01 +2.5881904510252520E-01 abs=1.00E00 CHECK +9.4368957093138300E-16 +0.0000000000000000E+00 err=9.44E-16 +9.4368957093138300E-16 +0.0000000000000000E+00 err=9.44E-16 +9.4368957093138300E-16 +0.0000000000000000E+00 err=9.44E-16 +9.4368957093138300E-16 +0.0000000000000000E+00 err=9.44E-16 +9.9920072216264090E-16 -1.1102230246251565E-16 err=1.01E-15 +7.3552275381416620E-16 +5.2735593669694940E-16 err=9.05E-16 +7.7715611723760960E-16 +5.2735593669694940E-16 err=9.39E-16 -4.7184478546569150E-16 +3.8857805861880480E-16 err=6.11E-16 -4.8849813083506890E-15 -4.2049697057677804E-14 err=4.23E-14 -6.5503158452884236E-15 -4.3548498140921765E-14 err=4.40E-14 -1.0103029524088925E-14 -2.6117996654306808E-14 err=2.80E-14 -2.1954660311962470E-14 -4.9155124415278806E-14 err=5.38E-14 EXAMPLE 7b. 24 ZEROS ON A CIRCLE OF RADIUS 1. CENTERED AT 0,0 COEFFICIENTS degree=24 +1.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +1.0000000000000000E+00 +0.0000000000000000E+00 ZEROS +6.0876142900871600E-01 +7.9335334029123760E-01 abs=1.00E00 +6.0876142900872420E-01 -7.9335334029123130E-01 abs=1.00E00 -6.0876142900871600E-01 -7.9335334029123760E-01 abs=1.00E00 +9.2387953251128780E-01 -3.8268343236508460E-01 abs=1.00E00 +3.8268343236508420E-01 +9.2387953251128470E-01 abs=1.00E00 +3.8268343236509494E-01 -9.2387953251128340E-01 abs=1.00E00 +7.9335334029123330E-01 +6.0876142900872390E-01 abs=1.00E00 -6.0876142900872100E-01 +7.9335334029124740E-01 abs=1.00E00 -9.9144486137382120E-01 +1.3052619222004105E-01 abs=1.00E00 +1.3052619222005870E-01 -9.9144486137380920E-01 abs=1.00E00 +9.9144486137380840E-01 +1.3052619222005474E-01 abs=1.00E00 +1.3052619222005088E-01 +9.9144486137380450E-01 abs=1.00E00 -9.9144486137381500E-01 -1.3052619222006556E-01 abs=1.00E00 +7.9335334029123770E-01 -6.0876142900871620E-01 abs=1.00E00 +9.2387953251128770E-01 +3.8268343236510200E-01 abs=1.00E00 -7.9335334029148050E-01 +6.0876142900895260E-01 abs=1.00E00 -9.2387953251135000E-01 -3.8268343236537455E-01 abs=1.00E00 +9.9144486137381760E-01 -1.3052619222004436E-01 abs=1.00E00 -1.3052619221998019E-01 +9.9144486137374250E-01 abs=1.00E00 -9.2387953251137490E-01 +3.8268343236480185E-01 abs=1.00E00 -7.9335334029094310E-01 -6.0876142900864570E-01 abs=1.00E00 -1.3052619222011438E-01 -9.9144486137383100E-01 abs=1.00E00 -3.8268343236503644E-01 +9.2387953251147280E-01 abs=1.00E00 -3.8268343236504854E-01 -9.2387953251114200E-01 abs=1.00E00 CHECK +2.1316282072803006E-14 -1.2395640069939873E-13 err=1.26E-13 +2.1760371282653068E-14 -1.2473355681663634E-13 err=1.27E-13 +2.1316282072803006E-14 -1.2395640069939873E-13 err=1.26E-13 +2.3148150063434514E-14 -1.2445600106048005E-13 err=1.27E-13 +9.6034291630076040E-14 -1.0547118733938987E-13 err=1.43E-13 +2.6645352591003757E-14 -1.4538370507466425E-13 err=1.48E-13 -1.1213252548714081E-14 -8.8873353121243780E-14 err=8.96E-14 -2.3725466036239595E-13 +1.7164047960704920E-13 err=2.93E-13 -2.2246093855926574E-13 -2.8449465006019636E-13 err=3.61E-13 +7.5495165674510640E-15 -1.7344459202206508E-13 err=1.74E-13 +3.8302694349567900E-14 -8.1185058675714570E-14 err=8.98E-14 +1.4288570326925765E-13 +1.4710455076283324E-15 err=1.43E-13 -1.5406079190150024E-13 -3.1782909637456670E-13 err=3.53E-13 +1.6320278461989800E-14 -1.2151391004522338E-13 err=1.23E-13 -1.3397616349664077E-13 -2.6195712266030570E-13 err=2.94E-13 -8.0599971141737110E-12 +8.3155704544424220E-13 err=8.10E-12 -4.0183134597526760E-12 -5.7333027214667710E-12 err=7.00E-12 -1.4790599300873453E-13 -1.9459434064117431E-13 err=2.44E-13 +1.8383072841743340E-12 +1.4863943409437752E-12 err=2.36E-12 +6.9064198804369430E-13 -7.1938011103611640E-12 err=7.23E-12 +6.6561200995352010E-12 -2.8412272534694694E-12 err=7.24E-12 -6.8767214145282200E-13 +1.4295231665073516E-12 err=1.59E-12 -3.6356473387400000E-12 +2.8914648453337577E-12 err=4.65E-12 +3.5889069494032810E-12 +4.1516790005857730E-13 err=3.61E-12 EXAMPLE 7c. 36 ZEROS ON A CIRCLE OF RADIUS 1. CENTERED AT 0,0 COEFFICIENTS degree=36 +1.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +1.0000000000000000E+00 +0.0000000000000000E+00 ZEROS +7.0710678118654760E-01 +7.0710678118654760E-01 abs=1.00E00 +7.0710678118654760E-01 -7.0710678118654750E-01 abs=1.00E00 -7.0710678118654750E-01 -7.0710678118654760E-01 abs=1.00E00 +9.0630778703664990E-01 -4.2261826174069940E-01 abs=1.00E00 +9.0630778703664990E-01 +4.2261826174069940E-01 abs=1.00E00 -7.0710678118654790E-01 +7.0710678118654880E-01 abs=1.00E00 -8.1915204428899170E-01 -5.7357643635104620E-01 abs=1.00E00 +9.6592582628906820E-01 -2.5881904510252080E-01 abs=1.00E00 -8.1915204428898840E-01 +5.7357643635105230E-01 abs=1.00E00 -9.9619469809174730E-01 -8.7155742747667580E-02 abs=1.00E00 +9.6592582628906220E-01 +2.5881904510251950E-01 abs=1.00E00 -9.9619469809175430E-01 +8.7155742747659600E-02 abs=1.00E00 -9.6592582628906020E-01 -2.5881904510252400E-01 abs=1.00E00 +5.7357643635105360E-01 -8.1915204428900070E-01 abs=1.00E00 +5.7357643635105290E-01 +8.1915204428901290E-01 abs=1.00E00 -8.7155742747653490E-02 +9.9619469809182750E-01 abs=1.00E00 -2.5881904510255830E-01 -9.6592582628912630E-01 abs=1.00E00 +2.5881904510244310E-01 -9.6592582628901620E-01 abs=1.00E00 +2.5881904510247150E-01 +9.6592582628898340E-01 abs=1.00E00 -2.5881904510257590E-01 +9.6592582628903480E-01 abs=1.00E00 -4.2261826174071904E-01 -9.0630778703662950E-01 abs=1.00E00 +8.1915204428899110E-01 -5.7357643635104630E-01 abs=1.00E00 +8.1915204428898980E-01 +5.7357643635104900E-01 abs=1.00E00 -5.7357643635103170E-01 +8.1915204428901400E-01 abs=1.00E00 -8.7155742747560260E-02 -9.9619469809180200E-01 abs=1.00E00 +9.9619469809174890E-01 -8.7155742747655520E-02 abs=1.00E00 +4.2261826174064326E-01 +9.0630778703667920E-01 abs=1.00E00 -9.0630778703664690E-01 +4.2261826174070610E-01 abs=1.00E00 +4.2261826174066913E-01 -9.0630778703668500E-01 abs=1.00E00 +9.9619469809174180E-01 +8.7155742747665900E-02 abs=1.00E00 -4.2261826174065686E-01 +9.0630778703661230E-01 abs=1.00E00 -9.0630778703665060E-01 -4.2261826174069295E-01 abs=1.00E00 +8.7155742747721200E-02 -9.9619469809163670E-01 abs=1.00E00 +8.7155742747748150E-02 +9.9619469809170120E-01 abs=1.00E00 -9.6592582628907050E-01 +2.5881904510252310E-01 abs=1.00E00 -5.7357643635103950E-01 -8.1915204428899260E-01 abs=1.00E00 CHECK -2.2204460492503130E-16 +0.0000000000000000E+00 err=2.22E-16 +0.0000000000000000E+00 -2.8865798640254070E-15 err=2.89E-15 +0.0000000000000000E+00 -2.8865798640254070E-15 err=2.89E-15 +1.5265566588595902E-15 -1.4988010832439613E-15 err=2.14E-15 +1.5265566588595902E-15 +1.4988010832439613E-15 err=2.14E-15 -4.1411318818518340E-14 +2.2537527399890678E-14 err=4.71E-14 +1.4432899320127035E-15 -4.3298697960381105E-15 err=4.56E-15 +2.9559688030644793E-15 +1.7486012637846216E-15 err=3.43E-15 -2.6423307986078726E-14 +2.5252022695099186E-13 err=2.54E-13 -9.3697619107935280E-14 -3.3142932842622486E-13 err=3.44E-13 +2.2311319458623302E-13 -1.3516965324811281E-14 err=2.24E-13 -3.1964708657739040E-13 +2.3120394487818885E-14 err=3.20E-13 +2.5035529205297280E-13 -1.8843260285450470E-13 err=3.13E-13 -4.1766590186398390E-13 -3.7969627442180354E-14 err=4.19E-13 -7.6350037403472020E-13 -2.3453461395206430E-13 err=7.99E-13 -2.9236613130478872E-12 +4.2520154064362714E-13 err=2.95E-12 -2.3664403769885210E-12 +7.6594286468889550E-13 err=2.49E-12 +2.5337509867995323E-12 +2.2157831125468874E-12 err=3.37E-12 +3.4119373992780310E-12 -9.2198471079996120E-13 err=3.53E-12 +6.5092375933772930E-13 -2.2300217228377050E-12 err=2.32E-12 +3.6948222259525210E-13 +9.5079499828898400E-13 err=1.02E-12 +1.5543122344752190E-14 +1.8429702208777600E-14 err=2.41E-14 -2.9420910152566650E-15 -1.2800871473928055E-13 err=1.28E-13 -3.5826897004653800E-13 +8.8246077112330570E-13 err=9.52E-13 -1.7159607068606420E-12 -3.6886327325902360E-12 err=4.07E-12 -1.1151843337664502E-13 -1.0626222124443530E-13 err=1.54E-13 -1.0103029524088925E-13 -2.2781776465308212E-12 err=2.28E-12 -2.6090241078691180E-15 +2.6373347949970594E-13 err=2.64E-13 -6.8256511553954620E-13 +1.5222823002147834E-12 err=1.67E-12 +1.1048627290843882E-13 -2.8831104170734534E-13 err=3.09E-13 +1.8759438447091270E-12 +8.1612494540195260E-13 err=2.05E-12 +7.7798878450607840E-14 +2.2154500456395000E-13 err=2.35E-13 +3.7040370770569100E-12 -2.6016966359065920E-12 err=4.53E-12 +1.3056222769591840E-12 +3.3656549769389700E-12 err=3.61E-12 -1.0021150576022819E-13 +6.1395333261771160E-14 err=1.18E-13 +1.1335377081422848E-13 -2.1094237467877974E-13 err=2.39E-13 EXAMPLE 7d. 48 ZEROS ON A CIRCLE OF RADIUS 1. CENTERED AT 0,0 COEFFICIENTS degree=48 +1.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +0.0000000000000000E+00 +1.0000000000000000E+00 +0.0000000000000000E+00 ZEROS +6.5934581510006880E-01 +7.5183980747897740E-01 abs=1.00E00 +6.5934581510006880E-01 -7.5183980747897740E-01 abs=1.00E00 +7.5183980747897800E-01 -6.5934581510006500E-01 abs=1.00E00 +7.5183980747897560E-01 +6.5934581510006520E-01 abs=1.00E00 +8.3146961230254020E-01 +5.5557023301959650E-01 abs=1.00E00 +8.3146961230254460E-01 -5.5557023301959500E-01 abs=1.00E00 -8.9687274153232970E-01 -4.4228869021906864E-01 abs=1.00E00 -9.4693012949539710E-01 +3.2143946530326545E-01 abs=1.00E00 -8.9687274153285410E-01 +4.4228869021919990E-01 abs=1.00E00 -9.4693012949483560E-01 -3.2143946530344797E-01 abs=1.00E00 -8.3146961230222040E-01 -5.5557023301952060E-01 abs=1.00E00 +8.9687274153268170E-01 +4.4228869021898604E-01 abs=1.00E00 -3.2143946530307255E-01 +9.4693012949456580E-01 abs=1.00E00 -8.3146961230259600E-01 +5.5557023301982480E-01 abs=1.00E00 +6.5403129230122880E-02 -9.9785892323840620E-01 abs=1.00E00 +9.9785892323854210E-01 +6.5403129230190610E-02 abs=1.00E00 -5.5557023301966700E-01 -8.3146961230240800E-01 abs=1.00E00 +8.9687274153268640E-01 -4.4228869021900120E-01 abs=1.00E00 +6.5403129229966060E-02 +9.9785892323893650E-01 abs=1.00E00 -5.5557023301923460E-01 +8.3146961230258340E-01 abs=1.00E00 -3.2143946530319260E-01 -9.4693012949513730E-01 abs=1.00E00 +4.4228869021898650E-01 -8.9687274153272580E-01 abs=1.00E00 +4.4228869021902917E-01 +8.9687274153268700E-01 abs=1.00E00 -9.8078528040356160E-01 +1.9509032201603307E-01 abs=1.00E00 -4.4228869021908507E-01 -8.9687274153266300E-01 abs=1.00E00 +9.8078528040326640E-01 -1.9509032201608725E-01 abs=1.00E00 +1.9509032201620882E-01 +9.8078528040341450E-01 abs=1.00E00 -9.9785892323867610E-01 -6.5403129230512430E-02 abs=1.00E00 -6.5403129230024250E-02 -9.9785892323850000E-01 abs=1.00E00 +9.8078528040316960E-01 +1.9509032201611815E-01 abs=1.00E00 -1.9509032201651935E-01 +9.8078528040281780E-01 abs=1.00E00 -9.9785892323884530E-01 +6.5403129229871570E-02 abs=1.00E00 +1.9509032201596996E-01 -9.8078528040315020E-01 abs=1.00E00 +9.4693012949507960E-01 +3.2143946530313827E-01 abs=1.00E00 -4.4228869021863876E-01 +8.9687274153243820E-01 abs=1.00E00 -9.8078528040312050E-01 -1.9509032201648402E-01 abs=1.00E00 +3.2143946530307390E-01 -9.4693012949515690E-01 abs=1.00E00 +9.9785892323859300E-01 -6.5403129230071040E-02 abs=1.00E00 -6.5403129230648320E-02 +9.9785892323864960E-01 abs=1.00E00 -7.5183980747875960E-01 -6.5934581509986080E-01 abs=1.00E00 +5.5557023301960560E-01 -8.3146961230255460E-01 abs=1.00E00 +5.5557023301960750E-01 +8.3146961230253910E-01 abs=1.00E00 -7.5183980747891920E-01 +6.5934581510031580E-01 abs=1.00E00 -6.5934581510004280E-01 -7.5183980747871190E-01 abs=1.00E00 +9.4693012949512780E-01 -3.2143946530316480E-01 abs=1.00E00 +3.2143946530324090E-01 +9.4693012949514040E-01 abs=1.00E00 -6.5934581509985300E-01 +7.5183980747917210E-01 abs=1.00E00 -1.9509032201604093E-01 -9.8078528040325730E-01 abs=1.00E00 CHECK +8.8817841970012520E-16 -3.3306690738754696E-16 err=9.49E-16 +8.8817841970012520E-16 +3.3306690738754696E-16 err=9.49E-16 +1.0008660566995786E-13 -1.6175949468788530E-13 err=1.90E-13 +1.8085533071143800E-13 +7.6272321791748250E-14 err=1.96E-13 +3.5216274341109965E-13 +9.5201624361607170E-14 err=3.65E-13 +2.1999069232947477E-13 -2.7222668563808840E-13 err=3.50E-13 +1.4009821081018003E-11 -1.0513589998595307E-11 err=1.75E-11 -1.4850370932961710E-11 +2.2426505097428162E-13 err=1.49E-11 -1.1355000273383098E-11 +5.0310866583913590E-12 err=1.24E-11 +7.8577283568748160E-12 -1.7184142997450635E-11 err=1.89E-11 +1.5142331832862510E-11 -5.4042881281191060E-12 err=1.61E-11 +6.0759730580173250E-13 +5.1630921760192900E-13 err=7.97E-13 +2.5912383350146230E-11 -4.2832404290038540E-12 err=2.63E-11 -7.9600215308062160E-12 +7.5293660195541180E-12 err=1.10E-11 +9.5140562095252790E-12 +3.4756919564671307E-13 err=9.52E-12 +2.7921397832697537E-12 -2.4694551958859280E-12 err=3.73E-12 +3.7487790649493036E-12 +6.2452820692726620E-12 err=7.28E-12 +8.4932061383824480E-14 +3.7247982476174000E-14 err=9.27E-14 -1.5396239838594283E-11 -9.5232016716906290E-12 err=1.81E-11 +8.2798212730494920E-12 +1.5691281607388420E-11 err=1.77E-11 -1.9181323196448830E-12 +9.2198471079996120E-13 err=2.13E-12 -1.2991829834163582E-12 +1.4332979247910770E-12 err=1.93E-12 -5.3734794391857580E-13 +1.2272405314206480E-12 err=1.34E-12 -1.4698992023554070E-11 -7.5826289691605100E-12 err=1.65E-11 -6.9200201124886010E-13 +4.1427417052375400E-12 err=4.20E-12 -1.3084602845658821E-12 -2.2674917499188040E-12 err=2.62E-12 -9.4200203193395280E-12 +2.0689561175402105E-12 err=9.64E-12 -4.6359539471185760E-12 -1.7463613888324403E-11 err=1.81E-11 +5.3301807412253766E-12 -5.3659715559817300E-12 err=7.56E-12 +2.9599725448470338E-12 -9.3369756370975670E-14 err=2.96E-12 +1.5766166150399386E-11 -2.2275403743776678E-11 err=2.73E-11 -1.0728659280423436E-11 -1.3763212791673140E-11 err=1.75E-11 +5.2623461144207795E-12 +6.7008898430032104E-12 err=8.52E-12 +1.5448337054024819E-12 +6.5730754172932390E-13 err=1.68E-12 +1.8461565609584340E-11 +1.0297818153759408E-11 err=2.11E-11 +1.8439277882364990E-12 -1.7777668226415244E-11 err=1.79E-11 -9.7366559259626230E-13 +4.7761794519374234E-12 err=4.87E-12 +7.2692372954374920E-13 -3.4172525920084240E-12 err=3.49E-12 -3.7920777629096850E-12 -2.4055993308458312E-11 err=2.44E-11 +1.4446721596783618E-11 +6.1517457794479920E-13 err=1.45E-11 -4.6218584515145270E-13 +1.1307621505807219E-13 err=4.76E-13 +1.0247358517290195E-13 +3.7342351433267140E-13 err=3.87E-13 -5.7132631958722870E-12 +1.0751344259318785E-11 err=1.22E-11 +1.0407230632836217E-11 +7.4586448128854950E-12 err=1.28E-11 -1.0553224960574425E-12 -1.9423351815817114E-13 err=1.07E-12 -2.8044233602031454E-12 +3.0688229735176265E-12 err=4.16E-12 -1.9650947535865270E-13 +1.3952783373127886E-11 err=1.40E-11 -4.4619863359685040E-13 -4.3631209756256340E-12 err=4.39E-12 end of c419,java test driver for cpoly