419.for test cpoly to find zeros of polynomials machine constants ETA = 4.4408920985006262D-16 INFIN = 8.9884656743115775+307 SMALNO = 1.1125369292536007-308 BASE = 2.0000000000000000D+00 ARE = 4.4408920985006262D-16 MRE = 1.2560739669470201D-15 real part imaginary part modulus EXAMPLE 0. POLYNOMIAL WITH ZERO 0.5 COEFFICIENTS degree= 1 4.0000000000000000D+00 4.0000000000000000D+00 -2.0000000000000000D+00 -2.0000000000000000D+00 ZEROS 5.0000000000000000D-01 0.0000000000000000D+00 abs= 5.000D-01 CHECK 0.0000000000000000D+00 0.0000000000000000D+00 err= 0.000D+00 EXAMPLE 0a. POLYNOMIAL WITH ZEROS 0.0 -2.0 COEFFICIENTS degree= 2 1.0000000000000000D+00 1.0000000000000000D+00 2.0000000000000000D+00 2.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 ZEROS 0.0000000000000000D+00 0.0000000000000000D+00 abs= 0.000D+00 -2.0000000000000000D+00 0.0000000000000000D+00 abs= 2.000D+00 CHECK 0.0000000000000000D+00 0.0000000000000000D+00 err= 0.000D+00 0.0000000000000000D+00 0.0000000000000000D+00 err= 0.000D+00 EXAMPLE 0b. POLYNOMIAL WITH ZEROS (1+2i) (3-4i) COEFFICIENTS degree= 2 1.0000000000000000D+00 0.0000000000000000D+00 -4.0000000000000000D+00 2.0000000000000000D+00 1.1000000000000000D+01 2.0000000000000000D+00 ZEROS 9.9999999999999989D-01 2.0000000000000000D+00 abs= 2.236D+00 3.0000000000000000D+00 -4.0000000000000000D+00 abs= 5.000D+00 CHECK 3.3306690738754696D-16 -4.4408920985006262D-16 err= 5.551D-16 0.0000000000000000D+00 0.0000000000000000D+00 err= 0.000D+00 EXAMPLE 0c. POLYNOMIAL WITH ZEROS 10**15 and 10**(-15) COEFFICIENTS degree= 2 1.0000000000000000D+00 0.0000000000000000D+00 -1.0000000000000000D+15 0.0000000000000000D+00 1.0000000000000000D+00 0.0000000000000000D+00 ZEROS 1.0000000000000001D-15 0.0000000000000000D+00 abs= 1.000D-15 1.0000000000000000D+15 -0.0000000000000000D+00 abs= 1.000D+15 CHECK -7.7737295767210668D-17 0.0000000000000000D+00 err= 7.774D-17 1.0000000000000000D+00 0.0000000000000000D+00 err= 1.000D+00 EXAMPLE 0d. POLYNOMIAL WITH ZEROS (1+2i) (3-4i) (-6+5i) COEFFICIENTS degree= 3 1.0000000000000000D+00 0.0000000000000000D+00 2.0000000000000000D+00 -3.0000000000000000D+00 -3.0000000000000000D+00 3.4000000000000000D+01 7.6000000000000000D+01 -4.3000000000000000D+01 ZEROS 9.9999999999999989D-01 1.9999999999999998D+00 abs= 2.236D+00 -6.0000000000000000D+00 5.0000000000000000D+00 abs= 7.810D+00 3.0000000000000000D+00 -4.0000000000000000D+00 abs= 5.000D+00 CHECK 8.4376949871511897D-15 -4.7739590058881731D-15 err= 9.695D-15 0.0000000000000000D+00 0.0000000000000000D+00 err= 0.000D+00 0.0000000000000000D+00 0.0000000000000000D+00 err= 0.000D+00 EXAMPLE 1. POLYNOMIAL WITH ZEROS 1,2,3,4 COEFFICIENTS degree= 4 1.0000000000000000D+00 0.0000000000000000D+00 -1.0000000000000000D+01 0.0000000000000000D+00 3.5000000000000000D+01 0.0000000000000000D+00 -5.0000000000000000D+01 0.0000000000000000D+00 2.4000000000000000D+01 0.0000000000000000D+00 ZEROS 1.0000000000000000D+00 -7.2672779896458799D-20 abs= 1.000D+00 2.0000000000000009D+00 2.1801813289422326D-19 abs= 2.000D+00 2.9999999999999991D+00 -2.8322664173815668D-19 abs= 3.000D+00 4.0000000000000000D+00 1.3788128874039222D-19 abs= 4.000D+00 CHECK -9.5063992881824632D-38 4.3603667937875280D-19 err= 4.360D-19 -3.5527136788005009D-15 4.3603626578844479D-19 err= 3.553D-15 1.7763568394002505D-15 5.6645328347631345D-19 err= 1.776D-15 -5.7033749354134227D-38 8.2728773244235329D-19 err= 8.273D-19 EXAMPLE 1a. POLYNOMIAL WITH ZEROS 1,2,...,10. COEFFICIENTS degree=10 1.0000000000000000D+00 0.0000000000000000D+00 -5.5000000000000000D+01 0.0000000000000000D+00 1.3200000000000000D+03 0.0000000000000000D+00 -1.8150000000000000D+04 0.0000000000000000D+00 1.5777300000000000D+05 0.0000000000000000D+00 -9.0205500000000000D+05 0.0000000000000000D+00 3.4169300000000000D+06 0.0000000000000000D+00 -8.4095000000000000D+06 0.0000000000000000D+00 1.2753576000000000D+07 0.0000000000000000D+00 -1.0628640000000000D+07 0.0000000000000000D+00 3.6288000000000000D+06 0.0000000000000000D+00 ZEROS 1.0000000000000000D+00 7.7900561367793934D-20 abs= 1.000D+00 2.0000000000000160D+00 -7.0110352719589101D-19 abs= 2.000D+00 2.9999999999994618D+00 4.1135943325168282D-17 abs= 3.000D+00 4.0000000000059366D+00 4.8392930118614907D-13 abs= 4.000D+00 4.9999999999635696D+00 -2.9044102237218120D-12 abs= 5.000D+00 6.9999999997345803D+00 -9.6827352469967460D-12 abs= 7.000D+00 6.0000000001296074D+00 7.2607966891981008D-12 abs= 6.000D+00 8.0000000003063558D+00 7.0970953926544587D-12 abs= 8.000D+00 8.9999999998150884D+00 -2.5709795146362086D-12 abs= 9.000D+00 1.0000000000045389D+01 3.1626308957569855D-13 abs= 1.000D+01 CHECK -1.9819227229192409D-32 -2.8268555709145063D-14 err= 2.827D-14 4.0547547541791573D-09 -2.8268494216541528D-14 err= 4.055D-09 1.5422756405314431D-08 -4.1465030871756441D-13 err= 1.542D-08 3.8353164200035571D-08 2.0905745811217238D-09 err= 3.841D-08 -1.0405756257879100D-08 8.3647014448350172D-09 err= 1.335D-08 1.3121434676508484D-06 4.1829416250914873D-08 err= 1.313D-06 4.6477998693638191D-07 2.0911094466274212D-08 err= 4.653D-07 8.0383415479153889D-07 7.1538721594262034D-08 err= 8.070D-07 3.2216630643230993D-06 1.0366189397107626D-07 err= 3.223D-06 7.7254117059055648D-06 1.1476554997267033D-07 err= 7.726D-06 EXAMPLE 2. ZEROS ON IMAGINARY AXIS DEGREE 3. COEFFICIENTS degree= 3 1.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 -1.0001000099999999D+04 -1.0001000099999999D+04 0.0000000000000000D+00 0.0000000000000000D+00 1.0000000000000000D+00 ZEROS 0.0000000000000000D+00 1.0000000000000000D-04 abs= 1.000D-04 0.0000000000000000D+00 1.0000000000000000D+00 abs= 1.000D+00 0.0000000000000000D+00 1.0000000000000000D+04 abs= 1.000D+04 CHECK 0.0000000000000000D+00 -4.7921736023859296D-17 err= 4.792D-17 0.0000000000000000D+00 0.0000000000000000D+00 err= 0.000D+00 0.0000000000000000D+00 -7.0715235779061913D-05 err= 7.072D-05 EXAMPLE 3. ZEROS AT 1+I,1/2*(1+I) . 1/(2**-9)*(1+I) COEFFICIENTS degree=10 1.0000000000000000D+00 0.0000000000000000D+00 -1.9980468750000000D+00 -1.9980468750000000D+00 0.0000000000000000D+00 2.6588592529296879D+00 7.5670659542083740D-01 -7.5670659542083740D-01 -2.0021195337176320D-01 0.0000000000000000D+00 1.2715073651634160D-02 1.2715073651634160D-02 0.0000000000000000D+00 -7.8207794285845011D-04 -1.1546426321729090D-05 1.1546426321729090D-05 1.5848036127863449D-07 0.0000000000000000D+00 -4.6520653995685279D-10 -4.6520653995685279D-10 0.0000000000000000D+00 9.0949470177292824D-13 ZEROS 1.9531249999999976D-03 1.9531249999999976D-03 abs= 2.762D-03 3.9062500000000243D-03 3.9062500000000234D-03 abs= 5.524D-03 7.8124999999998950D-03 7.8124999999998916D-03 abs= 1.105D-02 1.5625000000000271D-02 1.5625000000000295D-02 abs= 2.210D-02 3.1249999999999462D-02 3.1249999999999389D-02 abs= 4.419D-02 6.2500000000000805D-02 6.2500000000000944D-02 abs= 8.839D-02 1.2499999999999983D-01 1.2499999999999965D-01 abs= 1.768D-01 2.4999999999999795D-01 2.4999999999999833D-01 abs= 3.536D-01 5.0000000000000377D-01 5.0000000000000233D-01 abs= 7.071D-01 9.9999999999999778D-01 9.9999999999999944D-01 abs= 1.414D+00 CHECK 0.0000000000000000D+00 1.0097419586828951D-28 err= 1.010D-28 1.5146129380243427D-28 1.5146129380243427D-28 err= 2.142D-28 0.0000000000000000D+00 1.5146129380243427D-27 err= 1.515D-27 -5.6040678706900679D-27 7.5730646901217133D-28 err= 5.655D-27 -1.9281022701049882D-25 1.6206358436860467D-26 err= 1.935D-25 -4.5418193301556622D-24 -3.7356413503432388D-24 err= 5.881D-24 -1.1342305204140125D-22 -8.1499509708274043D-22 err= 8.228D-22 -1.4449044022621299D-20 -1.6612434738254022D-19 err= 1.668D-19 -8.6819889776967741D-18 -4.0116779121057823D-17 err= 4.105D-17 -7.7098349456882969D-15 -5.8502758966323063D-15 err= 9.678D-15 EXAMPLE 4. MULTIPLE ZEROS COEFFICIENTS degree=10 1.0000000000000000D+00 0.0000000000000000D+00 -1.0000000000000000D+01 -1.0000000000000000D+01 3.0000000000000000D+00 1.0000000000000000D+02 2.8400000000000000D+02 -3.3400000000000000D+02 -1.2930000000000000D+03 2.0000000000000000D+02 2.3740000000000000D+03 1.3940000000000000D+03 -1.5870000000000000D+03 -3.8360000000000000D+03 -9.2000000000000000D+02 4.3340000000000000D+03 2.2040000000000000D+03 -2.3520000000000000D+03 -1.3440000000000000D+03 5.0400000000000000D+02 2.8800000000000000D+02 0.0000000000000000D+00 ZEROS 9.9999995408258791D-01 6.1427072668013283D-08 abs= 1.000D+00 9.9999885055921289D-01 -3.4572848263067502D-07 abs= 1.000D+00 1.0000008148225012D+00 -9.2156523204936294D-07 abs= 1.000D+00 1.0000003805357924D+00 1.2058668868537030D-06 abs= 1.000D+00 3.4038956453458225D-05 1.9999863321856808D+00 abs= 2.000D+00 -5.1866421146691125D-06 2.0000363130505261D+00 abs= 2.000D+00 -2.8852314375525420D-05 1.9999773547635822D+00 abs= 2.000D+00 2.9999999937341291D+00 3.6608533627582097D-10 abs= 3.000D+00 2.0389917713774762D-14 4.0000000000000009D+00 abs= 4.000D+00 3.0000000062657945D+00 -3.6612268772273637D-10 abs= 3.000D+00 CHECK 2.0262349215277972D-13 1.3402690622295590D-13 err= 2.429D-13 -3.0152770445242722D-14 3.0020622058323704D-13 err= 3.017D-13 4.6271090792046118D-14 3.2592910103086686D-13 err= 3.292D-13 9.7308808855079484D-14 2.7861780386440185D-13 err= 2.951D-13 -1.4805379144888775D-11 -2.4174618969984604D-11 err= 2.835D-11 -1.3755607763954458D-11 -2.8882371540257469D-11 err= 3.199D-11 -9.2321150724217205D-12 -2.8156998287688889D-11 err= 2.963D-11 3.2487258586770290D-11 3.6819507644449418D-11 err= 4.910D-11 -1.0234160185973451D-09 -9.3292182471251615D-10 err= 1.385D-09 8.5277575344516797D-12 -5.0031792417927597D-11 err= 5.075D-11 EXAMPLE 5. 12 ZEROS EVENLY DISTRIBUTE ON A CIRCLE OF RADIUS 1. CENTERED AT 0+2I. COEFFICIENTS degree=12 1.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 -2.4000000000000000D+01 -2.6400000000000000D+02 0.0000000000000000D+00 0.0000000000000000D+00 1.7600000000000000D+03 7.9200000000000000D+03 0.0000000000000000D+00 0.0000000000000000D+00 -2.5344000000000000D+04 -5.9136000000000000D+04 0.0000000000000000D+00 0.0000000000000000D+00 1.0137600000000000D+05 1.2672000000000000D+05 0.0000000000000000D+00 0.0000000000000000D+00 -1.1264000000000000D+05 -6.7584000000000000D+04 0.0000000000000000D+00 0.0000000000000000D+00 2.4576000000000000D+04 4.0950000000000000D+03 0.0000000000000000D+00 ZEROS -4.9534982591578148D-12 1.0000000000055755D+00 abs= 1.000D+00 -5.0000000000044909D-01 1.1339745962224650D+00 abs= 1.239D+00 4.9999999999220868D-01 1.1339745962173262D+00 abs= 1.239D+00 8.6602540377739423D-01 1.4999999999956262D+00 abs= 1.732D+00 -8.6602540378028048D-01 1.5000000000034848D+00 abs= 1.732D+00 -8.6602540375632731D-01 2.5000000000051736D+00 abs= 2.646D+00 -1.0000000000031515D+00 2.0000000000025517D+00 abs= 2.236D+00 1.0000000000034184D+00 2.0000000000005786D+00 abs= 2.236D+00 8.6602540374057302D-01 2.5000000000011142D+00 abs= 2.646D+00 3.6283595900816015D-11 3.0000000001236864D+00 abs= 3.000D+00 5.0000000005407941D-01 2.8660254036882167D+00 abs= 2.909D+00 -5.0000000005879564D-01 2.8660254037342048D+00 abs= 2.909D+00 CHECK -6.9003025515712579D-11 -5.9441979106294714D-11 err= 9.108D-11 -5.9149796172164315D-11 -4.5150994054665716D-11 err= 7.441D-11 -7.1242789445591370D-11 -7.3351769103169318D-11 err= 1.023D-10 -4.1959768992683166D-11 -2.5406565740127007D-11 err= 4.905D-11 -7.4183770237823410D-11 -7.5219386275193756D-11 err= 1.056D-10 -6.4020566625799802D-11 -1.3179679569930158D-10 err= 1.465D-10 -1.4320877816942357D-10 4.1859404831257052D-11 err= 1.492D-10 -4.5169490370255971D-10 2.7891822185210913D-10 err= 5.309D-10 2.2895907392239678D-11 2.9106839161130438D-10 err= 2.920D-10 2.0571238046329654D-09 -4.3540315148393052D-10 err= 2.103D-09 -2.2441115632432229D-10 -3.7855818479926029D-10 err= 4.401D-10 -6.6040284352197887D-11 1.6245115252999653D-09 err= 1.626D-09 EXAMPLE 6. 16 ZEROS EVENLY DISTRIBUTE ON A CIRCLE OF RADIUS 5. CENTERED AT 0,0 COEFFICIENTS degree=16 1.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 -1.5258789478400000D+11 0.0000000000000000D+00 ZEROS 3.5355339119556128D+00 3.5355339119556128D+00 abs= 5.000D+00 -3.5355339119556128D+00 3.5355339119556128D+00 abs= 5.000D+00 -3.5355339119556128D+00 -3.5355339119556124D+00 abs= 5.000D+00 4.6193976704257000D+00 -1.9134171650850056D+00 abs= 5.000D+00 1.9134171650850047D+00 4.6193976704256992D+00 abs= 5.000D+00 -4.6193976704256992D+00 1.9134171650850045D+00 abs= 5.000D+00 -1.9134171650850069D+00 -4.6193976704257009D+00 abs= 5.000D+00 5.0000000085176310D+00 1.1533993662376749D-15 abs= 5.000D+00 -2.6193432791719334D-16 5.0000000085176310D+00 abs= 5.000D+00 -4.6193976704257000D+00 -1.9134171650850047D+00 abs= 5.000D+00 3.2246139611869835D-15 -5.0000000085176328D+00 abs= 5.000D+00 4.6193976704256983D+00 1.9134171650850047D+00 abs= 5.000D+00 -1.9134171650850051D+00 4.6193976704256992D+00 abs= 5.000D+00 -5.0000000085176310D+00 5.1066744502993701D-16 abs= 5.000D+00 1.9134171650850080D+00 -4.6193976704257000D+00 abs= 5.000D+00 3.5355339119556106D+00 -3.5355339119556088D+00 abs= 5.000D+00 CHECK -6.6876411437988281D-05 0.0000000000000000D+00 err= 6.688D-05 -6.6876411437988281D-05 0.0000000000000000D+00 err= 6.688D-05 -1.8435716629028320D-04 -1.4445185661315918D-04 err= 2.342D-04 2.6279687881469727D-04 4.0307641029357910D-05 err= 2.659D-04 -3.4380704164505005D-04 2.7092918753623962D-04 err= 4.377D-04 -3.7007220089435577D-04 3.6957487463951111D-04 err= 5.230D-04 9.2191994190216064D-04 -3.8759782910346985D-04 err= 1.000D-03 -3.6582350730896007D-04 5.6318329868670219D-04 err= 6.716D-04 -3.6582350730895996D-04 1.2789762432147136D-04 err= 3.875D-04 7.2667375206947327D-05 -4.2884051799774170D-04 err= 4.350D-04 5.0854682922363281D-04 1.5745185759693447D-03 err= 1.655D-03 -7.2503834962844849D-04 -9.8418444395065308D-05 err= 7.317D-04 -2.6271492242813110D-04 -9.2774629592895508D-05 err= 2.786D-04 -3.6582350730895996D-04 -2.4934934476512102D-04 err= 4.427D-04 6.8232417106628418D-04 1.0782480239868164D-03 err= 1.276D-03 -2.1566525101661682D-03 6.1827152967453003D-04 err= 2.244D-03 EXAMPLE 7a. 12 ZEROS EVENLY DISTRIBUTE ON A CIRCLE OF' RADIUS 1. CENTERED AT 0,0 COEFFICIENTS degree=12 1.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 1.0000000000000000D+00 0.0000000000000000D+00 ZEROS 7.0710678118654757D-01 7.0710678118654757D-01 abs= 1.000D+00 -7.0710678118654757D-01 7.0710678118654757D-01 abs= 1.000D+00 -7.0710678118654746D-01 -7.0710678118654757D-01 abs= 1.000D+00 7.0710678118654802D-01 -7.0710678118655379D-01 abs= 1.000D+00 2.5881904510252202D-01 9.6592582628906920D-01 abs= 1.000D+00 -9.6592582628906787D-01 2.5881904510252030D-01 abs= 1.000D+00 -2.5881904510252063D-01 -9.6592582628906398D-01 abs= 1.000D+00 9.6592582628907164D-01 -2.5881904510252196D-01 abs= 1.000D+00 -2.5881904510252146D-01 9.6592582628906898D-01 abs= 1.000D+00 -9.6592582628906776D-01 -2.5881904510251924D-01 abs= 1.000D+00 2.5881904510251352D-01 -9.6592582628906909D-01 abs= 1.000D+00 9.6592582628906987D-01 2.5881904510252207D-01 abs= 1.000D+00 CHECK -2.9371036852632315D-16 0.0000000000000000D+00 err= 2.937D-16 -2.9371036852632315D-16 0.0000000000000000D+00 err= 2.937D-16 2.0274580625478933D-17 -9.4206326767265480D-16 err= 9.423D-16 -5.7288104381852945D-14 4.8986910448217680D-14 err= 7.538D-14 -1.4457673339768329D-14 1.1675068464084282D-14 err= 1.858D-14 6.1804538266721498D-15 -4.0181887765028401D-15 err= 7.372D-15 5.0285730440746690D-14 1.1817898547782091D-14 err= 5.166D-14 -4.2592956884992400D-14 3.5324390981750220D-15 err= 4.274D-14 -1.0079393916728741D-14 -6.0388028128369187D-15 err= 1.175D-14 1.0859944942018945D-14 1.5987469052618219D-14 err= 1.933D-14 1.3049511558144156D-14 8.6468443624872215D-14 err= 8.745D-14 -2.2383109905474430D-14 -1.0170426241636055D-14 err= 2.459D-14 EXAMPLE 7b. 24 ZEROS EVENLY DISTRIBUTE ON A CIRCLE OF' RADIUS 1. CENTERED AT 0,0 COEFFICIENTS degree=24 1.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 1.0000000000000000D+00 0.0000000000000000D+00 ZEROS 6.0876142900872066D-01 7.9335334029123517D-01 abs= 1.000D+00 7.9335334029123517D-01 6.0876142900872066D-01 abs= 1.000D+00 -6.0876142900872066D-01 -7.9335334029123528D-01 abs= 1.000D+00 7.9335334029123539D-01 -6.0876142900872054D-01 abs= 1.000D+00 3.8268343236511998D-01 9.2387953251130039D-01 abs= 1.000D+00 -9.2387953251107435D-01 3.8268343236461799D-01 abs= 1.000D+00 9.2387953251127042D-01 -3.8268343236505387D-01 abs= 1.000D+00 1.3052619222008802D-01 9.9144486137390708D-01 abs= 1.000D+00 -9.9144486137329235D-01 1.3052619221979539D-01 abs= 1.000D+00 -7.9335334029144022D-01 -6.0876142900858321D-01 abs= 1.000D+00 9.9144486137376586D-01 -1.3052619222004019D-01 abs= 1.000D+00 -1.3052619222013889D-01 9.9144486137400434D-01 abs= 1.000D+00 -9.9144486137325805D-01 -1.3052619221981043D-01 abs= 1.000D+00 1.3052619222007023D-01 -9.9144486137371579D-01 abs= 1.000D+00 9.9144486137377730D-01 1.3052619222003489D-01 abs= 1.000D+00 -3.8268343236542246D-01 9.2387953251139743D-01 abs= 1.000D+00 -9.2387953251122401D-01 -3.8268343236460856D-01 abs= 1.000D+00 3.8268343236500280D-01 -9.2387953251126587D-01 abs= 1.000D+00 9.2387953251128163D-01 3.8268343236507374D-01 abs= 1.000D+00 -6.0876142900911956D-01 7.9335334029099425D-01 abs= 1.000D+00 -1.3052619222007872D-01 -9.9144486137384835D-01 abs= 1.000D+00 6.0876142900869556D-01 -7.9335334029124727D-01 abs= 1.000D+00 -7.9335334029135041D-01 6.0876142900823615D-01 abs= 1.000D+00 -3.8268343236514379D-01 -9.2387953251118782D-01 abs= 1.000D+00 CHECK -1.2939952928614495D-16 2.2326433236907750D-16 err= 2.581D-16 -1.2939952928614495D-16 -2.2326433236907750D-16 err= 2.581D-16 -2.2328601641252721D-15 -1.3765572882962207D-15 err= 2.623D-15 -2.8040991837535723D-15 -5.1679309703150933D-15 err= 5.880D-15 -5.7980573467397711D-13 5.4460659614820328D-13 err= 7.955D-13 9.0427420868129105D-12 -8.5099416933815536D-12 err= 1.242D-11 6.9214021992079766D-13 -6.4614760482244182D-13 err= 9.469D-13 -2.4143982169447242D-12 5.6376550563314032D-13 err= 2.479D-12 1.3129748107631469D-11 -4.4734143960726419D-12 err= 1.387D-11 -1.8962442293463111D-12 5.6127416625008364D-12 err= 5.924D-12 1.0956885931597080D-12 -1.3164091398985139D-13 err= 1.104D-12 -4.8878680508450401D-12 -1.4698998176401398D-12 err= 5.104D-12 1.3898539733857361D-11 4.0081352408079252D-12 err= 1.446D-11 2.1927674519889306D-12 -7.3972845535640042D-13 err= 2.314D-12 8.4018844670203513D-13 2.9369277734607457D-13 err= 8.900D-13 -5.5093377234437246D-12 -6.3599938033079284D-12 err= 8.414D-12 5.8107749704603903D-12 1.0093957977406684D-11 err= 1.165D-11 1.2619110942822809D-12 1.7366542774156779D-12 err= 2.147D-12 2.6104137840037012D-13 3.0857759923674788D-13 err= 4.042D-13 -1.2408948651607132D-12 -1.1115477895756731D-11 err= 1.118D-11 -9.8787807361472302D-13 5.2666017705781110D-13 err= 1.119D-12 1.3608000360224026D-13 6.5408938573589814D-13 err= 6.681D-13 4.8839810505314080D-12 -1.0908540753638493D-11 err= 1.195D-11 1.6977001401907721D-12 2.1066119768736735D-12 err= 2.706D-12 EXAMPLE 7c. 36 ZEROS EVENLY DISTRIBUTE ON A CIRCLE OF' RADIUS 1. CENTERED AT 0,0 COEFFICIENTS degree=36 1.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 0.0000000000000000D+00 1.0000000000000000D+00 0.0000000000000000D+00 ZEROS 7.0710678118654757D-01 7.0710678118654757D-01 abs= 1.000D+00 -8.1915204428899180D-01 5.7357643635104605D-01 abs= 1.000D+00 -5.7357643635104605D-01 -8.1915204428899180D-01 abs= 1.000D+00 8.1915204428899180D-01 -5.7357643635104605D-01 abs= 1.000D+00 4.2261826174069939D-01 9.0630778703664994D-01 abs= 1.000D+00 -9.0630778703664994D-01 4.2261826174069939D-01 abs= 1.000D+00 -4.2261826174069939D-01 -9.0630778703664994D-01 abs= 1.000D+00 7.0710678118654924D-01 -7.0710678118654791D-01 abs= 1.000D+00 2.5881904510252141D-01 9.6592582628906809D-01 abs= 1.000D+00 -7.0710678118654757D-01 7.0710678118654713D-01 abs= 1.000D+00 -2.5881904510252057D-01 -9.6592582628906776D-01 abs= 1.000D+00 9.9619469809174932D-01 -8.7155742747659304D-02 abs= 1.000D+00 8.7155742747647938D-02 9.9619469809175909D-01 abs= 1.000D+00 -9.6592582628908885D-01 2.5881904510253201D-01 abs= 1.000D+00 -8.7155742747646828D-02 -9.9619469809175765D-01 abs= 1.000D+00 9.9619469809173566D-01 8.7155742747691514D-02 abs= 1.000D+00 -2.5881904510252007D-01 9.6592582628901713D-01 abs= 1.000D+00 -9.6592582628889467D-01 -2.5881904510254267D-01 abs= 1.000D+00 2.5881904510251968D-01 -9.6592582628899204D-01 abs= 1.000D+00 8.1915204428901267D-01 5.7357643635103328D-01 abs= 1.000D+00 -4.2261826174066275D-01 9.0630778703663706D-01 abs= 1.000D+00 -7.0710678118657189D-01 -7.0710678118657500D-01 abs= 1.000D+00 5.7357643635103583D-01 -8.1915204428902844D-01 abs= 1.000D+00 9.0630778703663506D-01 4.2261826174065031D-01 abs= 1.000D+00 -5.7357643635103628D-01 8.1915204428900379D-01 abs= 1.000D+00 -9.0630778703657000D-01 -4.2261826174053801D-01 abs= 1.000D+00 4.2261826174062433D-01 -9.0630778703663339D-01 abs= 1.000D+00 5.7357643635104716D-01 8.1915204428898447D-01 abs= 1.000D+00 -9.9619469809181049D-01 8.7155742747607665D-02 abs= 1.000D+00 -8.1915204428908761D-01 -5.7357643635097322D-01 abs= 1.000D+00 9.6592582628904855D-01 -2.5881904510250658D-01 abs= 1.000D+00 -8.7155742747695969D-02 9.9619469809173067D-01 abs= 1.000D+00 -9.9619469809169459D-01 -8.7155742747791726D-02 abs= 1.000D+00 8.7155742747705434D-02 -9.9619469809172045D-01 abs= 1.000D+00 9.0630778703664938D-01 -4.2261826174069778D-01 abs= 1.000D+00 9.6592582628901491D-01 2.5881904510251480D-01 abs= 1.000D+00 CHECK -2.9371036852632315D-16 0.0000000000000000D+00 err= 2.937D-16 5.8565890852235736D-16 -1.7372984561364602D-15 err= 1.833D-15 5.8563180346804522D-16 -1.7372984561364602D-15 err= 1.833D-15 5.8565890852235736D-16 -1.7372984561364602D-15 err= 1.833D-15 1.7611780089854534D-15 -1.1464082721318603D-15 err= 2.101D-15 1.7611780089854534D-15 -1.1464082721318603D-15 err= 2.101D-15 1.7611780089854534D-15 -1.1464082721318603D-15 err= 2.101D-15 -5.3990882944998653D-14 -3.3913952375563827D-14 err= 6.376D-14 8.0534537372223269D-16 2.4278715431320930D-14 err= 2.429D-14 8.4987897795707479D-15 -1.1304677896908921D-14 err= 1.414D-14 2.0092326240284120D-14 -1.6926022215757452D-15 err= 2.016D-14 -1.3944216239647933D-13 2.8378402329876790D-14 err= 1.423D-13 -4.5426444723883908D-13 -4.0980996943379769D-13 err= 6.118D-13 -8.1966912098864475D-13 1.9943660438392907D-13 err= 8.436D-13 -3.9864162318381524D-13 -4.4476303472399878D-13 err= 5.973D-13 2.4908416622617074D-13 -1.2263793496350428D-12 err= 1.251D-12 1.7854513982736020D-12 -4.5256101654806563D-13 err= 1.842D-12 5.8327993924058887D-12 -2.3792697819531236D-12 err= 6.299D-12 2.6612899167374748D-12 -6.7286225148479456D-13 err= 2.745D-12 -3.5109030483218562D-13 8.0898997353515134D-13 err= 8.819D-13 9.7906313048165550D-13 1.0005545383103692D-12 err= 1.400D-12 -1.3190143964038337D-12 -7.9132663963199512D-14 err= 1.321D-12 -8.6876415349851355D-13 1.0593337188349872D-12 err= 1.370D-12 1.2334909298399727D-12 1.3757964223166247D-12 err= 1.848D-12 -1.5121259279438082D-13 5.3727595289432273D-13 err= 5.581D-13 5.0647190841203102D-12 4.0501157386619441D-12 err= 6.485D-12 1.6831629406216519D-12 2.1983375948601835D-12 err= 2.769D-12 1.9423069923252267D-13 1.8245349892379026D-13 err= 2.665D-13 -2.1712245864851547D-12 -2.0150725570577607D-12 err= 2.962D-12 -1.3208040347198469D-12 4.1278561786154550D-12 err= 4.334D-12 8.1856192695383898D-13 -3.0921571997789138D-13 err= 8.750D-13 4.1438304610591503D-13 -1.4019982549039189D-12 err= 1.462D-12 1.4077100517536224D-12 -4.9493275553228952D-12 err= 5.146D-12 7.5098521151728548D-13 -1.7733307159403626D-12 err= 1.926D-12 4.4098635875768066D-14 -4.5203668282492449D-14 err= 6.315D-14 1.9117575429075835D-12 -2.8991286910202974D-13 err= 1.934D-12 end 419.for test driver for cpoly