9
0.4274196690810000*e0
+ 0.3211106932700000*e1
+ 0.3436330736970000*e2
+ 0.4742561435630000*e3
+ 0.5584587189760000
+(-9.07765503189022E-01 + 4.19477998493344E-01*i)*zz1;
0.4754797951714257*e0^2
+ 1.6317349621954614*e0*e3
+ 0.9465211050062624*e1^2
- 0.9376441343330845*e2^2
- 0.4666028244982478*e3^2
+ 2.5500000000000000*g0*e1
+ 0.2598076211353316*g0*e2
- 2.5500000000000000*g1*e0
- 1.4722431864335457*g1*e3
- 0.2598076211353316*g2*e0
+ 0.4500000000000000*g2*e3
+ 1.4722431864335457*g3*e1
- 0.4500000000000000*g3*e2
+(-4.58665457498096E-01 + 8.88609024317254E-01*i)*zz1;
- 0.2385669606907614*e0^2
+ 3.2634699243909228*e0*e3
+ 1.6455982786485855*e1^2
- 3.2634699243909228*e1*e2
- 0.2385669606907614*e2^2
+ 1.6455982786485855*e3^2
+ 3.0000000000000000*g0*e1
+ 0.5196152422706632*g0*e2
- 3.0000000000000000*g1*e0
- 2.9444863728670914*g1*e3
- 0.5196152422706632*g2*e0
+ 3.0000000000000000*g2*e3
+ 2.9444863728670914*g3*e1
- 3.0000000000000000*g3*e2
+( 9.19151620979603E-01 + 3.93903919313540E-01*i)*zz1;
- 0.3961611384685069*e0^2
+ 4.8952048865863842*e0*e3
- 0.3961611384685069*e1^2
- 4.8952048865863842*e1*e2
+ 2.4300867205405135*e2^2
+ 2.4300867205405135*e3^2
+ 1.9500000000000000*g0*e1
- 1.8186533479473212*g0*e2
- 1.9500000000000000*g1*e0
- 1.8186533479473212*g1*e3
+ 1.8186533479473212*g2*e0
+ 4.0500000000000000*g2*e3
+ 1.8186533479473212*g3*e1
- 4.0500000000000000*g3*e2
+(-8.46695050565337E-01 - 5.32078463525973E-01*i)*zz1;
1.2028336489822089*e0^2
+ 3.2634699243909228*e0*e3
+ 0.2607510293125354*e1^2
+ 4.0290815079912293*e2^2
+ 3.0869988883215558*e3^2
+ 1.9500000000000000*g0*e1
- 2.3382685902179843*g0*e2
- 1.9500000000000000*g1*e0
+ 1.1258330249197702*g1*e3
+ 2.3382685902179843*g2*e0
+ 4.0500000000000000*g2*e3
- 1.1258330249197702*g3*e1
- 4.0500000000000000*g3*e2
+( 8.30728002839399E-01 - 7.52927973598419E-01*i)*zz1;
0.8849480315885287*e0^2
+ 1.3559893414233654*e1^2
+ 1.6317349621954614*e1*e2
+ 2.2980719610930389*e2^2
+ 2.7691132709278756*e3^2
+ 0.4500000000000000*g0*e1
- 0.2598076211353316*g0*e2
- 0.4500000000000000*g1*e0
+ 1.4722431864335457*g1*e3
+ 0.2598076211353316*g2*e0
+ 2.5500000000000000*g2*e3
- 1.4722431864335457*g3*e1
- 2.5500000000000000*g3*e2
+(-1.91939167491528E+00 - 5.38504598419998E-01*i)*zz1;
g0*e0+g1*e1+g2*e2+g3*e3
+( 2.19392546995034E-03 - 1.27130277819968E+00*i)*zz1;
g0^2+g1^2+g2^2+g3^2-e0^2-e1^2-e2^2-e3^2
+( 7.81621842777430E-02 + 1.23746326085593E-01*i)*zz1;
+( 8.51257324218750E-01 - 4.81109619140625E-01*i)*e0
+(-4.38354492187500E-01 + 8.01055908203125E-01*i)*e1
+(-1.33239746093750E-01 + 9.67010498046875E-01*i)*e2
+(-1.24023437500000E-01 + 5.01129150390625E-01*i)*e3
+(-5.13305664062500E-02 + 1.37786865234375E-01*i)*g0
+( 6.94213867187500E-01 + 8.61358642578125E-01*i)*g1
+( 9.71984863281250E-01 - 9.37805175781250E-02*i)*g3
+(-1.08642578125000E-01 + 7.56744384765625E-01*i)*g2
+(-8.14331054687500E-01 - 1.13983154296875E-01*i)*zz1
+(-1.23779296875000E-01 + 8.86138916015625E-01*i);
TITLE : moving Stewart-Gough platform with curve of degree 28, 16 digits
ROOT COUNTS :
total degree : 128
1-homogeneous Bezout number : 128
with partition : {e0 e1 e2 e3 zz1 g0 g1 g2 g3 }
general linear-product Bezout number : 114
based on the set structure :
{e0 e1 e2 e3 zz1 }
{e0 e1 e2 e3 zz1 }{e0 e1 e2 e3 g0 g1 g2 g3 }
{e0 e1 e2 e3 zz1 }{e0 e1 e2 e3 g0 g1 g2 g3 }
{e0 e1 e2 e3 zz1 }{e0 e1 e2 e3 g0 g1 g2 g3 }
{e0 e1 e2 e3 zz1 }{e0 e1 e2 e3 g0 g1 g2 g3 }
{e0 e1 e2 e3 zz1 }{e0 e1 e2 e3 g0 g1 g2 g3 }
{e0 e1 e2 e3 zz1 }{g0 g1 g2 g3 }
{e0 e1 e2 e3 zz1 g0 g1 g2 g3 }{e0 e1 e2 e3 g0 g1 g2 g3 }
{e0 e1 e2 e3 zz1 g0 g1 g2 g3 }
mixed volume : 104
REFERENCES :
M.L. Husty and A. Karger
"Self-motions of Griffis-Duffy type parallel manipulators,"
Proc. 2000 IEEE Int. Conf. Robotics and Automation,
CDROM, San Francisco, CA, April 24--28, 2000.
C.W. Wampler.
"Forward displacement analysis of general six-in-parallel
SPS (Stewart) platform manipulators using soma coordinates,"
Mech. Mach. Theory} 31(3): 331--337, 1996.
A.J. Sommese, J. Verschelde, and C.W. Wampler:
"Using Monodromy to Decompose Solution Sets of Polynomial Systems
into Irreducible Components". Submitted for publication.
DESCRIPTION :
The Maple code below generates a polynomial system whose coefficients
are computed with 64 decimal places. The above system has those
coefficients rounded to standard machine floating-point numbers.
Also, the system has been sliced with a random hyperplane and
embedded with an extra slack variable (zz1) in order to find forty
generic points (listed below under "THE SOLUTIONS" banner).
With monodromy, the forty generic points are grouped into a partition
of 13 sets as follows:
{ { 1 3 4 5 6 7 8 10 11 13 14 15 16 18 19 20 21 23 24 25 26 27
28 30 33 35 37 39 },
{ 2 }, { 9 }, { 12 }, { 17 }, { 22 }, { 29 }, { 31 }, { 32 }, { 34 },
{ 36 }, { 38 }, { 40 } }
Only the first set of 28 generic points corresponds to a physically
meaningful solution. The other 12 lines lead to degenerate assemblies.
MAPLE OUTPUT :
|\^/| Maple V Release 5 (WMI Campus Wide License)
._|\| |/|_. Copyright (c) 1981-1997 by Waterloo Maple Inc. All rights
\ MAPLE / reserved. Maple and Maple V are registered trademarks of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
>
# Generating the equations for Stewart platform with Soma coordinates.
> Digits := 64:
> with(linalg):
> steweqs := proc(a1,a2,a3,a4,a5,b1,b2,b3,b4,b5,
> L0,L1,L2,L3,L4,L5::numeric)
> local g, e, p0,p1,p2,p3,p4,p5,p6,p7,i,i3,i4,lam,
> cp,r3,r4,amb,bma:
> g := vector([g0,g1,g2,g3]):
> e := vector([e0,e1,e2,e3]):
> p6 := innerprod(g,e):
> p7 := innerprod(g,g) - innerprod(e,e):
> i3 := matrix(3,3,[1,0,0,0,1,0,0,0,1]):
> i4 := matrix(4,4,[1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1]):
> for i from 1 to 5 do
> cp := crossprod(b.i,a.i):
> r3 := evalm(evalm(b.i &* transpose(a.i))
> +evalm(a.i &* transpose(b.i))
> -scalarmul(i3,innerprod(a.i,b.i))):
> r4 := matrix(4,4,
> [ innerprod(a.i,b.i), cp[1], cp[2], cp[3],
> cp[1], r3[1,1], r3[1,2], r3[1,3],
> cp[2], r3[2,1], r3[2,2], r3[2,3],
> cp[3], r3[3,1], r3[3,2], r3[3,3] ]):
> A.i := scalarmul(evalm(scalarmul(i4,innerprod(b.i,b.i)
> + innerprod(a.i,a.i) - (L.i)^2 + (L0)^2)
> - scalarmul(r4,2)),(1/L0)):
> lam := matrix(3,3,[0,-a.i[3]-b.i[3],a.i[2]+b.i[2],
> a.i[3]+b.i[3],0,-a.i[1]-b.i[1],
> -a.i[2]-b.i[2],a.i[1]+b.i[1],0]):
> amb := evalm(a.i - b.i): bma := evalm(b.i - a.i):
> B.i := matrix(4,4,[0,amb[1],amb[2],amb[3],
> bma[1],-lam[1,1],-lam[1,2],-lam[1,3],
> bma[2],-lam[2,1],-lam[2,2],-lam[2,3],
> bma[3],-lam[3,1],-lam[3,2],-lam[3,3]]):
> p.i := innerprod(e,evalm(A.i &* e))
> + 2*innerprod(g,evalm(B.i &* e)):
> od:
> p0 := sum('rand()/1.0e+12*e.i','i'=0..3) + rand()/1.0e+12:
> lprint(p0);for i from 1 to 5 do
> lprint(p.i);
> od;
> lprint(p6); lprint(p7);
> end:
> s:= 0.7: t := evalf(Pi/3):
> a0 := [0,0,0]:
> a2 := [1-cos(2*t),sin(2*t),0]:
> a4 := [1-cos(4*t),sin(4*t),0]:
> a6 := a0:
> a1 := 0.5*(a0+a2):
> a3 := 0.5*(a2+a4):
> a5 := 0.5*(a4+a6):
> b1 := s*(a0-a5): b2 := s*(a1-a5): b3 := s*(a2-a5):
> b4 := s*(a3-a5): b5 := s*(a4-a5):
> b0 := [0,0,0]:
# quaternion elementary matrices
> Q0 := matrix(4,4,[ 1,0,0,0, 0, 1,0,0, 0,0, 1,0, 0,0,0, 1]):
> Qi := matrix(4,4,[0,0,0, 1, 0,0,-1,0, 0,1, 0,0, -1,0,0,0]):
> Qj := matrix(4,4,[0,0, 1,0, 0,0,0, 1, -1,0,0,0, 0,-1,0,0]):
> Qk := matrix(4,4,[0,-1,0,0, 1,0,0,0, 0,0,0, 1, 0,0,-1,0]):
# make a unit-length 4-vector (manually randomized)
> ee := [.456,-.337,.628,.193]:
> ee := ee/sqrt(innerprod(ee,ee)):
# form the quaternion for rotation
> E := evalm(scalarmul(Q0,ee[1]) + scalarmul(Qi,ee[2])
> + scalarmul(Qj,ee[3]) + scalarmul(Qk,ee[4])):
# choose a position vector (manually randomized)
> posn := [.476,-.381,.933]:
# compute compatible leg lengths
> for i from 0 to 5 do
> # b.i as quaternion in end-effector coordinates
> bquat1 := evalm(scalarmul(Qi,b.i[1]) + scalarmul(Qj,b.i[2])
> + scalarmul(Qk,b.i[3])):
> # transform to base coordinates
> bquat0 := evalm( E &* evalm( bquat1 &* transpose(E) ) ):
> # extract vector
> bvec := [bquat0[1,4],bquat0[2,4],bquat0[3,4]]:
> lvec := -a.i + posn + bvec:
> L.i := sqrt( innerprod( lvec,lvec ) ):
> od:
>
> steweqs(a1,a2,a3,a4,a5,b1,b2,b3,b4,b5,L0,L1,L2,L3,L4,L5);
bytes used=3002260, alloc=1179432, time=0.28
bytes used=4002488, alloc=1310480, time=0.36
.4274196690810000000000000000000000000000000000000000000000000000*e0+.321110693\
2700000000000000000000000000000000000000000000000000000*e1+.3436330736970000000\
000000000000000000000000000000000000000000000*e2+.47425614356300000000000000000\
00000000000000000000000000000000000*e3+.558458718976000000000000000000000000000\
0000000000000000000000000
.4754797951714256907610170495728580301292529883658249929120204446*e0^2+1.631734\
962195461413336000176199220026560082780927329892680053109*e0*e3+.94652110500626\
24243866576710994843961755191456049013316039333344*e1^2-.9376441343330845101159\
048150070210680095454833514040231637182248*e2^2-.466602824498247776490264193480\
3947019632793261123276844718053350*e3^2+2.5500000000000000000000000000000000000\
00000000000000000000000000*g0*e1+.259807621135331594029116951225880855041420788\
0715570942083710470*g0*e2-2.550000000000000000000000000000000000000000000000000\
000000000000*g1*e0-1.4722431864335456994983293902799915119013844657388235338474\
35933*g1*e3-.2598076211353315940291169512258808550414207880715570942083710470*
g2*e0+.4500000000000000000000000000000000000000000000000000000000000000*g2*e3+1\
.472243186433545699498329390279991511901384465738823533847435933*g3*e1-.4500000\
000000000000000000000000000000000000000000000000000000000*g3*e2
-.2385669606907613864423982989129933443173584503277106800778524719*e0^2+3.26346\
9924390922826672000352398440053120165561854659785360106216*e0*e3+1.645598278648\
585548060164187193512119867706178628594674689799087*e1^2-3.26346992439092282667\
2000352398440053120165561854659785360106216*e1*e2-.2385669606907613864423982989\
129933443173584503277106800778524719*e2^2+1.64559827864858554806016418719351211\
9867706178628594674689799087*e3^2+3.0000000000000000000000000000000000000000000\
00000000000000000000*g0*e1+.519615242270663188058233902451761710082841576143114\
1884167420940*g0*e2-3.000000000000000000000000000000000000000000000000000000000\
000000*g1*e0-2.944486372867091398996658780559983023802768931477647067694871866*
g1*e3-.5196152422706631880582339024517617100828415761431141884167420940*g2*e0+3\
.000000000000000000000000000000000000000000000000000000000000000*g2*e3+2.944486\
372867091398996658780559983023802768931477647067694871866*g3*e1-3.0000000000000\
00000000000000000000000000000000000000000000000000*g3*e2
-.3961611384685068585545268002101502041695838795441600969753183077*e0^2+4.89520\
4886586384240008000528597660079680248342781989678040159328*e0*e3-.3961611384685\
068585545268002101502041695838795441600969753183077*e1^2-4.89520488658638424000\
8000528597660079680248342781989678040159328*e1*e2+2.430086720540513543199316928\
949607992108013063890297935176159031*e2^2+2.43008672054051354319931692894960799\
2108013063890297935176159031*e3^2+1.9500000000000000000000000000000000000000000\
00000000000000000000*g0*e1-1.81865334794732115820381865858116598528994551650089\
9659458597329*g0*e2-1.950000000000000000000000000000000000000000000000000000000\
000000*g1*e0-1.818653347947321158203818658581165985289945516500899659458597329*
g1*e3+1.818653347947321158203818658581165985289945516500899659458597329*g2*e0+4\
.050000000000000000000000000000000000000000000000000000000000000*g2*e3+1.818653\
347947321158203818658581165985289945516500899659458597329*g3*e1-4.0500000000000\
00000000000000000000000000000000000000000000000000*g3*e2
1.202833648982208877931323178365830527915910018086814743222320274*e0^2+3.263469\
924390922826672000352398440053120165561854659785360106216*e0*e3+.26075102931253\
54106800419353125777958233777036086620658384944944*e1^2-.\
3588886170170184637147738068774296122257265959916772104319336304e-63*e1*e2+4.02\
9081507991229279685166907525588724193506961521272775373797613*e2^2+3.0869988883\
21555812433885664472335992100974647043120097989971833*e3^2+1.950000000000000000\
000000000000000000000000000000000000000000000*g0*e1-2.3382685902179843462620525\
61032927695372787092644013847875339422*g0*e2-1.95000000000000000000000000000000\
0000000000000000000000000000000*g1*e0+1.125833024919770240792840121978817038512\
823414976747408236274536*g1*e3+2.3382685902179843462620525610329276953727870926\
44013847875339422*g2*e0+4.05000000000000000000000000000000000000000000000000000\
0000000000*g2*e3-1.125833024919770240792840121978817038512823414976747408236274\
536*g3*e1-4.050000000000000000000000000000000000000000000000000000000000000*g3*
e2
.8849480315885286592824346300901293576388824589374391672077656634*e0^2+1.355989\
341423365392908075251616755723685148616176515505899678553*e1^2+1.63173496219546\
1413336000176199220026560082780927329892680053108*e1*e2+2.298071961093038860159\
356494670008455777680930654668183283504333*e2^2+2.76911327092787559378499711619\
6634821823947087893744521975417223*e3^2+.45000000000000000000000000000000000000\
00000000000000000000000000*g0*e1-.259807621135331594029116951225880855041420788\
0715570942083710470*g0*e2-.4500000000000000000000000000000000000000000000000000\
000000000000*g1*e0+1.4722431864335456994983293902799915119013844657388235338474\
35932*g1*e3+.2598076211353315940291169512258808550414207880715570942083710470*
g2*e0+2.550000000000000000000000000000000000000000000000000000000000000*g2*e3-1\
.472243186433545699498329390279991511901384465738823533847435932*g3*e1-2.550000\
000000000000000000000000000000000000000000000000000000000*g3*e2
g0*e0+g1*e1+g2*e2+g3*e3
g0^2+g1^2+g2^2+g3^2-e0^2-e1^2-e2^2-e3^2
> quit
bytes used=4797652, alloc=1310480, time=0.43
THE SOLUTIONS :
40 9
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -1.48438074474057E-01 -1.55391255435241E-01
e1 : -5.55606051914426E-01 -3.59565497022757E-01
e2 : -4.87178488350974E-01 -2.03492035324726E-01
e3 : -3.14580385354791E-01 5.30945570216332E-01
zz1 : -2.15492820903153E-16 -7.79430823861707E-17
g0 : 8.59290307310757E-01 3.61080655741729E-01
g1 : -4.58593367816421E-02 -1.51532578926567E-01
g2 : 6.13747047862749E-01 -1.37622606496260E+00
g3 : -1.20130310603567E+00 -5.68039002779291E-01
== err : 1.212E-14 = rco : 8.930E-03 = res : 4.005E-15 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -5.32558953461333E-01 -1.28551953197101E+00
e1 : -1.48439009566397E+00 6.14946110280492E-01
e2 : 1.24690730885340E-17 -4.63197753844789E-16
e3 : 3.07473055140246E-01 7.42195047831986E-01
zz1 : 6.49300129298972E-16 5.68851642606902E-16
g0 : -2.94720908232990E-01 2.62273478469422E+00
g1 : 3.19571144591420E+00 7.44002927513516E-01
g2 : 2.89665021264361E-01 6.99209054967416E-01
g3 : 9.77534267914650E-01 -1.84871298995980E+00
== err : 2.589E-14 = rco : 1.170E-03 = res : 1.507E-14 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -9.56158492856731E-02 -5.06649048429525E-01
e1 : -5.47958198674134E-01 -5.22348116244995E-01
e2 : 2.55012294081442E-01 2.36668196985043E-01
e3 : -9.05135445324796E-01 6.38803141490814E-01
zz1 : 1.99660537692452E-16 3.77919961822788E-17
g0 : 7.25282392165719E-01 -1.86763952036966E-01
g1 : 1.90517009487388E-02 -1.20154407615399E+00
g2 : 8.16554295016211E-01 1.66120888174140E-02
g3 : -6.99144307744753E-01 5.49215117873058E-02
== err : 1.087E-14 = rco : 7.258E-03 = res : 7.515E-15 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -9.88056803424891E-01 1.21260292620834E+00
e1 : 1.01579066522318E-01 -1.92362762837322E-01
e2 : 7.59406406295330E-01 1.43284056144257E-01
e3 : -9.06090716817414E-01 -1.06642317406276E+00
zz1 : -8.16014929947172E-16 3.28577145599533E-16
g0 : -3.12754981677889E+00 -2.05627616994110E+00
g1 : -6.15047833850333E-01 7.40214465057389E-01
g2 : 1.06739727097601E+00 3.08625918312184E+00
g3 : 3.29712486284252E+00 -2.85481366614200E+00
== err : 1.188E-13 = rco : 5.772E-04 = res : 1.921E-14 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -5.89881342193301E-01 1.48233935218654E-01
e1 : -1.89320499730005E-01 -7.56456383469425E-01
e2 : -1.92287258434538E-01 -5.66526918055693E-01
e3 : -3.78408872014304E-01 7.89078909044235E-01
zz1 : 1.75972308301129E-16 -3.51186768169656E-16
g0 : 8.85035608644098E-02 1.11937657294991E+00
g1 : -8.56343020765430E-01 -1.88045252010160E-01
g2 : 7.52437647036130E-01 -5.64444295297181E-01
g3 : -3.73785077433241E-02 -8.21937615158540E-01
== err : 9.356E-15 = rco : 9.707E-03 = res : 5.093E-15 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -1.22227903006918E-01 1.46793591359832E-03
e1 : -7.61594924009143E-03 5.84332312384611E-03
e2 : -6.64863444624758E-01 -7.06543802843383E-01
e3 : -5.80491114456532E-01 5.06662999968071E-01
zz1 : 1.38855046002653E-16 -1.98139064262702E-17
g0 : -5.12120995768957E-01 -4.96608501130273E-01
g1 : -2.81335343967133E-01 2.63324584131741E-01
g2 : 1.12465274659447E-01 -6.00531001873690E-02
g3 : -6.63991642348220E-02 -2.90758569797230E-02
== err : 2.526E-15 = rco : 1.183E-02 = res : 2.707E-15 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : 5.50491259332876E-02 -3.22335289952687E-01
e1 : -1.86866504749989E-02 2.39497782160239E-01
e2 : -8.47637421091282E-01 -6.60774748946337E-02
e3 : -6.00331838292078E-01 1.76220278921239E-01
zz1 : 1.87662143745166E-16 -2.66148654098913E-17
g0 : -5.54283027792299E-01 -4.88908158629909E-01
g1 : 7.66342069828655E-01 -4.46552091218090E-01
g2 : 3.14861404327333E-01 1.85255017235696E-01
g3 : -6.11589518242162E-01 9.66532038582146E-02
== err : 3.235E-15 = rco : 1.440E-02 = res : 2.869E-15 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -8.87083226499744E-01 -7.44321271984439E-01
e1 : 4.32145463604572E-01 -3.79349733701380E-01
e2 : -2.56615540247307E-01 1.84544844174751E-01
e3 : -4.84731395758054E-01 7.93948799217729E-01
zz1 : 6.11608700736067E-17 2.01207469046307E-16
g0 : -2.60050902093344E+00 2.89331992260517E+00
g1 : -1.97894195082578E+00 -1.77792638894292E+00
g2 : 1.34766384583328E+00 1.62632372205135E-01
g3 : 1.83643158592341E+00 2.09681066718061E+00
== err : 5.058E-14 = rco : 1.272E-03 = res : 1.615E-14 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -4.34588248605692E-01 7.39640566148906E-02
e1 : -1.28109503990892E-01 -7.52728926957432E-01
e2 : 7.39640566148909E-02 4.34588248605691E-01
e3 : -7.52728926957432E-01 1.28109503990893E-01
zz1 : -3.12275851532565E-16 -2.71856852440563E-16
g0 : -9.48172107841148E-01 -9.08104695403718E-01
g1 : 1.16346543530699E+00 -1.57260201288339E+00
g2 : -1.98971855994516E-01 8.27482370716825E-01
g3 : -1.50292176066624E+00 -7.54047399582884E-01
== err : 2.353E-14 = rco : 2.881E-03 = res : 7.938E-15 ==
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -1.50673474595669E+00 -1.41526799953415E+00
e1 : 7.33791862561205E-01 8.16415480060614E-01
e2 : 1.33116054716414E-01 -5.81523975540296E-01
e3 : -4.12903760695019E-01 1.14407481638565E+00
zz1 : 1.00058046554760E-15 -3.03000559846567E-17
g0 : -9.76868349988821E-01 1.05099631646724E+00
g1 : -7.64794880423997E-01 -7.93672492934760E-01
g2 : -3.75161260973895E-01 -1.60468330870364E+00
g3 : 1.66098616074575E+00 1.20373242463037E+00
== err : 3.649E-14 = rco : 2.068E-03 = res : 1.560E-14 ==
solution 11 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -3.73607569033981E-01 -1.49405008168632E-01
e1 : -4.03003047770084E-01 8.00378514485192E-01
e2 : 3.30519091862982E-01 -4.76509121481968E-01
e3 : -8.07454376804530E-01 -6.20069278045316E-02
zz1 : 1.11250200801952E-17 -2.75918978673200E-16
g0 : -2.44570986420797E-01 1.80430863930989E-01
g1 : -7.33301921619395E-02 -1.02404850041928E-01
g2 : 6.12188823472420E-01 -2.36271976475263E-01
g3 : 3.53961264725583E-01 -5.44980212633444E-01
== err : 7.660E-15 = rco : 9.886E-03 = res : 3.764E-15 ==
solution 12 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -3.43229780718855E-01 1.88885124747253E-01
e1 : 7.36156067419217E-16 -9.65702599010456E-16
e2 : -3.77770249494511E-01 -6.86459561437708E-01
e3 : -5.94491418875778E-01 3.27158632856233E-01
zz1 : -1.20243552270692E-15 -2.71784664773649E-16
g0 : 1.68715968251837E+00 -1.46965920689405E+00
g1 : -3.23350810968271E-01 1.77945393138532E-01
g2 : 2.37925838052249E+00 3.68252982692548E+00
g3 : 3.27813707688064E+00 -1.89882279421537E+00
== err : 7.000E-13 = rco : 1.252E-04 = res : 2.251E-14 ==
solution 13 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -1.11135574703998E+00 2.85188082649702E-01
e1 : 5.50902155684916E-02 -2.08329064260354E-01
e2 : -2.43287951272557E-01 -8.12882937861965E-01
e3 : -3.69666991291838E-02 4.73025304741268E-01
zz1 : -1.87873448604204E-16 -1.30752383771939E-16
g0 : -3.38939546312493E-01 1.14269581695493E+00
g1 : -6.95218159292834E-01 1.77831293626544E-01
g2 : -1.02027603207058E+00 -4.88324146996282E-01
g3 : 5.38022859064211E-01 -2.51723401025989E-01
== err : 1.580E-14 = rco : 7.227E-03 = res : 4.951E-15 ==
solution 14 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -4.66293035132945E-01 -6.09304036067815E-01
e1 : -1.85477523453763E-01 -6.62478822860001E-02
e2 : 2.66838416753030E-01 2.32034709471756E-01
e3 : -8.25063836710777E-01 4.25859812667563E-01
zz1 : -6.64635954499564E-17 -9.19615512773795E-17
g0 : 6.42388541771035E-01 9.46727201298488E-01
g1 : -1.72457013368882E-01 -2.96092305986949E-01
g2 : 6.82471143778350E-01 -4.18011920806141E-01
g3 : 8.99875196392361E-01 -4.07826400628468E-01
== err : 9.184E-15 = rco : 8.947E-03 = res : 3.497E-15 ==
solution 15 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : 5.74506297155147E-02 -2.70747210452052E-01
e1 : -4.46392549741397E-01 -2.95929835422330E-02
e2 : -4.29713702941772E-01 2.94889062574274E-01
e3 : -6.15719986786183E-01 5.03771472640828E-02
zz1 : -1.24222167392538E-17 4.74869441735522E-19
g0 : 6.96194054761633E-01 3.25176356572310E-01
g1 : 5.71611464780918E-01 -6.64966101793495E-01
g2 : 2.97392838385332E-01 2.14777227437124E-01
g3 : -5.59120591414741E-01 1.25621211104198E-01
== err : 3.860E-15 = rco : 1.248E-02 = res : 1.665E-15 ==
solution 16 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -1.50340991007312E+00 -2.19127062426504E+00
e1 : 3.54009107842206E-01 2.06208473594280E+00
e2 : 1.31453566885128E-01 1.95678486293840E-02
e3 : -1.57551266364993E-01 5.64485140811857E-01
zz1 : 8.01266999819058E-16 -4.99687196577450E-16
g0 : -2.62537335161983E-01 -5.87059340915626E-01
g1 : -7.44739853010740E-01 -1.21056650517505E+00
g2 : 4.73562030734455E-01 -2.44786422443185E+00
g3 : 2.01149194542482E+00 2.00922758391591E+00
== err : 3.446E-14 = rco : 1.684E-03 = res : 2.018E-14 ==
solution 17 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -2.82681002699553E-01 9.73555773073272E-01
e1 : -5.62082687654968E-01 -1.63205953003380E-01
e2 : -9.73555773073273E-01 -2.82681002699553E-01
e3 : 1.63205953003380E-01 -5.62082687654968E-01
zz1 : -8.54993190641829E-17 -1.00615918042765E-16
g0 : 2.00330274582214E-01 2.10007727442612E-01
g1 : -3.24783981195451E-02 -1.90062586406928E-01
g2 : -3.63761219193722E-01 7.29858605439177E-01
g3 : -7.27107386684475E-01 -2.98787257673590E-01
== err : 4.207E-15 = rco : 7.260E-03 = res : 3.969E-15 ==
solution 18 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -2.08182921069295E-01 2.00963823335626E-01
e1 : -5.59492236158607E-01 6.61850334390932E-01
e2 : 3.76443795498158E-01 -3.85938122424418E-01
e3 : -8.83861702421334E-01 -3.49604342652111E-01
zz1 : 1.80467945391832E-16 -8.56663713376640E-17
g0 : -1.79022087233375E-01 -8.56626141921062E-02
g1 : -3.54674695435725E-01 2.59075863236097E-02
g2 : 9.83603090697912E-01 6.95241650577972E-02
g3 : 3.78927642136921E-01 -8.52274587396155E-01
== err : 7.088E-15 = rco : 1.029E-02 = res : 4.254E-15 ==
solution 19 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : 2.65200867585171E-01 -5.32550555096368E-01
e1 : -8.46713964474316E-01 -4.52643982901882E-01
e2 : -4.41887517321640E-01 -2.38024432406574E-01
e3 : -5.23081704827689E-01 9.58900540725950E-01
zz1 : -3.71156206581110E-16 -2.65864124647006E-16
g0 : 1.12157779926615E-01 1.06089822174614E-01
g1 : -7.97196258886798E-01 1.48175040858261E+00
g2 : 1.68023190284064E-02 1.02099425795213E-02
g3 : 1.37616431184107E+00 7.37411464505068E-01
== err : 2.079E-14 = rco : 4.228E-03 = res : 1.167E-14 ==
solution 20 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -1.80590497547288E-01 2.52041884640394E-01
e1 : -4.67331917490344E-02 -6.56157822836103E-02
e2 : -7.99237423661833E-01 4.22299942453178E-01
e3 : -4.04042943392827E-01 -4.88710499551954E-01
zz1 : 6.04335119184264E-17 5.81337842658402E-18
g0 : -6.86319093380620E-01 2.78459329787431E-01
g1 : -8.37167368582923E-02 -3.27260969218441E-01
g2 : 1.88497580862119E-01 -6.79239312635420E-02
g3 : -1.69556691759450E-01 3.53250150176907E-02
== err : 3.855E-15 = rco : 1.646E-02 = res : 3.093E-15 ==
solution 21 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -5.56881807090072E-02 -3.48945221160743E-01
e1 : 1.71040189700667E-01 7.11441447802262E-01
e2 : -1.57972976430050E-01 -3.17540818718293E-01
e3 : -1.12870354324596E+00 6.28608029567744E-02
zz1 : -1.50631588071727E-16 -3.72836732859831E-17
g0 : -1.04295181376374E-01 -1.98091364192577E-01
g1 : 1.79786218804542E-01 -5.35554211525086E-01
g2 : 9.64846611017076E-01 2.62162353816063E-01
g3 : 2.59657213062923E-01 -2.19490550934808E-01
== err : 1.128E-14 = rco : 1.424E-02 = res : 3.062E-15 ==
solution 22 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -1.76381861540846E+00 -1.81700575804150E+00
e1 : 1.04904876352436E+00 -1.01834115240775E+00
e2 : -1.81700575804150E+00 1.76381861540846E+00
e3 : 1.01834115240775E+00 1.04904876352436E+00
zz1 : 2.94863101889353E-15 1.98481332963243E-15
g0 : -1.35724671981132E+00 -5.57758657556197E+00
g1 : 1.63768505194711E+00 -2.41386346807848E+00
g2 : -8.31861943435547E+00 -1.46644072962372E+00
g3 : -2.47690665903757E+00 6.38529322859322E+00
== err : 3.728E-13 = rco : 2.031E-04 = res : 1.156E-13 ==
solution 23 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -7.38790117999524E-01 7.26432729390881E-01
e1 : 9.56796923321886E-02 -1.73747960403236E-01
e2 : 7.01886343916924E-02 2.01143524521281E-01
e3 : -6.27357607845239E-01 -6.82793213682442E-01
zz1 : 3.37756704107858E-16 1.66391930111474E-16
g0 : -1.76948843183201E+00 -1.11754638379776E+00
g1 : -3.42247528223629E-01 3.98173351992134E-01
g2 : 4.06335789728096E-01 8.24901321620302E-01
g3 : 1.29580163896184E+00 -1.76510847077742E+00
== err : 1.549E-14 = rco : 2.471E-03 = res : 6.484E-15 ==
solution 24 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -6.95293109726137E-01 -7.61294567442440E-01
e1 : -3.55871152701303E-01 -1.26792760069688E+00
e2 : -8.92260430052972E-02 7.93136623299699E-01
e3 : -2.45314093894621E-01 9.69917656276211E-01
zz1 : 7.30799754462246E-18 2.35753721285871E-17
g0 : 3.36692768294886E-01 -7.33577139910739E-01
g1 : -3.51573889332471E-01 -4.72415799739670E-01
g2 : -5.27772062110089E-01 -1.74278929620091E+00
g3 : -5.45871444601290E-01 3.06034752099006E-01
== err : 1.019E-14 = rco : 3.790E-03 = res : 7.438E-15 ==
solution 25 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -8.03020464744769E-02 -1.24609169964651E+00
e1 : -2.25669695512308E+00 -2.52979035887690E-01
e2 : 8.31432498504307E-01 2.75726667337719E-01
e3 : -1.79637580397054E-01 1.09453420973495E+00
zz1 : -4.72780273882810E-16 -2.51882988961521E-17
g0 : -9.25352323940438E-01 5.21967424690533E-02
g1 : -3.53130436596914E-02 1.75274004640313E+00
g2 : 2.30972892877035E-01 3.25466553785757E-01
g3 : 2.30317769493165E+00 3.20691877702626E-01
== err : 2.266E-14 = rco : 3.216E-03 = res : 2.025E-14 ==
solution 26 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -7.59218249765552E-01 7.77033519633102E-01
e1 : 4.07870375893931E-01 2.03639552457683E-01
e2 : -2.29293318371914E-01 -9.05198969958336E-02
e3 : -6.03329405811296E-01 -7.72588024912358E-01
zz1 : 1.56201210374007E-16 3.61288828112418E-17
g0 : -2.76453982071872E+00 -3.24558010573054E+00
g1 : -1.66312668646062E+00 1.84359662776753E+00
g2 : 1.30425565689974E+00 -2.12649017801221E-01
g3 : 2.57042151639929E+00 -2.19771379086359E+00
== err : 2.797E-14 = rco : 7.170E-04 = res : 2.022E-14 ==
solution 27 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -4.19828391818171E-01 5.51293261056937E-01
e1 : -2.61115509537493E-01 -3.26314271644636E-01
e2 : -1.64581459150254E-01 -1.80387252574579E-01
e3 : -5.03131472181127E-01 -1.45203295924683E-01
zz1 : 2.66641914503708E-17 -7.02970928840738E-18
g0 : -8.78046771651265E-01 6.87798872756982E-01
g1 : -3.91239246848324E-01 -3.94351703184389E-01
g2 : 6.04346009486806E-01 -4.30376053605092E-01
g3 : -7.00255485591096E-01 -9.51412277506198E-01
== err : 6.416E-15 = rco : 5.026E-03 = res : 2.706E-15 ==
solution 28 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -8.08173951124805E-04 -3.95814437557234E-03
e1 : 2.93276014999545E-02 4.68451629126263E-02
e2 : -4.65294604767171E-01 -7.63067759373892E-01
e3 : -8.59535688266572E-01 5.24747288971360E-01
zz1 : -2.14270032292151E-16 3.82301511972056E-16
g0 : -4.96714148831728E-01 -8.23210602496579E-01
g1 : -7.57792297557447E-02 4.31941002410087E-02
g2 : 1.98899481785159E+00 -1.21632735696220E+00
g3 : -1.08472186180968E+00 -1.76914569877016E+00
== err : 1.400E-14 = rco : 3.649E-03 = res : 9.228E-15 ==
solution 29 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -3.43229780718852E-01 -1.88885124747254E-01
e1 : -3.62340547962468E-17 -1.08311411561133E-16
e2 : -3.77770249494509E-01 6.86459561437707E-01
e3 : -5.94491418875779E-01 -3.27158632856231E-01
zz1 : 7.33388137443779E-17 -1.33139053462759E-16
g0 : 1.43385693805924E-01 3.97484658062661E-01
g1 : -3.23350810968265E-01 -1.77945393138526E-01
g2 : 2.34909282859685E-01 -5.94981849500597E-01
g3 : 6.04242093027430E-01 4.17620010571389E-02
== err : 4.535E-15 = rco : 7.023E-03 = res : 2.716E-15 ==
solution 30 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -5.42905751059759E-01 -3.73905394784773E-01
e1 : -1.98663711627306E-01 -2.39661302111630E-01
e2 : -1.04431019201392E-01 -1.43580467527595E-01
e3 : -4.78077366645703E-01 6.03284381742369E-01
zz1 : 1.99517964843375E-16 3.65206604977538E-17
g0 : 1.17815329977881E+00 2.27616409262983E+00
g1 : -3.71710666759458E-01 8.85417517880300E-01
g2 : 7.12695718627795E-01 5.21280815553488E-02
g3 : 2.25226340888292E+00 -1.07115247385213E+00
== err : 5.176E-14 = rco : 1.204E-03 = res : 6.224E-15 ==
solution 31 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -2.94362542845874E-01 -2.12091226705875E-01
e1 : -3.67352780494183E-01 5.09850880054225E-01
e2 : -2.12091226705874E-01 2.94362542845875E-01
e3 : -5.09850880054226E-01 -3.67352780494183E-01
zz1 : 2.36022563559731E-17 1.37400657242640E-16
g0 : 8.44851340533635E-01 -6.66736123884881E-01
g1 : -3.62495597533386E-01 -8.92446993892576E-01
g2 : 7.05611455321899E-01 1.43939144583217E-01
g3 : 3.21568541138220E-01 4.29829646743379E-01
== err : 1.080E-14 = rco : 5.273E-03 = res : 3.398E-15 ==
solution 32 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -2.82681002699553E-01 -9.73555773073272E-01
e1 : -5.62082687654967E-01 1.63205953003380E-01
e2 : -9.73555773073272E-01 2.82681002699553E-01
e3 : 1.63205953003380E-01 5.62082687654968E-01
zz1 : 8.58626971892502E-17 4.14407960190540E-17
g0 : 2.12126683103103E+00 1.63397758868450E+00
g1 : 1.03214702052816E+00 -9.18990651554986E-01
g2 : 1.48022409693339E+00 -2.65079516188799E+00
g3 : -1.83616062464639E+00 -7.65838160974115E-01
== err : 1.332E-14 = rco : 1.088E-03 = res : 1.096E-14 ==
solution 33 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : 1.05726829085217E+00 -2.43168619960850E+00
e1 : 3.29999585200736E+00 -1.39005698453846E+00
e2 : -1.95165148018298E+00 6.34596806920244E-01
e3 : -2.95065854155163E+00 2.67291049071408E+00
zz1 : -2.15719382862322E-15 3.14978351536132E-16
g0 : 1.36824165944754E+00 -2.00078361481804E+00
g1 : 7.85666766105385E-01 -1.39935272513920E+00
g2 : 4.95054820263612E+00 -3.20335264485742E+00
g3 : -1.63936293210348E+00 -2.08120305283003E+00
== err : 1.675E-13 = rco : 3.149E-04 = res : 9.387E-14 ==
solution 34 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -2.94362542845875E-01 2.12091226705874E-01
e1 : -3.67352780494183E-01 -5.09850880054225E-01
e2 : -2.12091226705874E-01 -2.94362542845874E-01
e3 : -5.09850880054225E-01 3.67352780494183E-01
zz1 : -1.87128531594864E-17 -6.12180912422560E-17
g0 : -1.17131687595257E-01 8.82920407842497E-01
g1 : -7.36937761145876E-01 -7.73756486845626E-01
g2 : 4.89427171364282E-01 -1.10592217271211E+00
g3 : -1.34463493959998E+00 -5.53874831308901E-02
== err : 1.224E-14 = rco : 7.848E-03 = res : 3.560E-15 ==
solution 35 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -3.49360620247853E-01 2.30047216901684E-02
e1 : -3.38877555466154E-01 4.56199810585220E-01
e2 : -1.87466418991302E-01 2.66590640776239E-01
e3 : -4.97406840036144E-01 -5.22782198296671E-01
zz1 : 8.96729055449147E-18 4.95653919823374E-17
g0 : 6.44856162707626E-01 -8.99446972026704E-01
g1 : -5.69701061644318E-01 -6.45892841703243E-01
g2 : 5.59784892379968E-01 2.28406197473404E-01
g3 : 5.08065716247885E-01 2.59052265284079E-01
== err : 1.137E-14 = rco : 3.903E-03 = res : 4.214E-15 ==
solution 36 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -5.32558953461330E-01 1.28551953197101E+00
e1 : -1.48439009566397E+00 -6.14946110280489E-01
e2 : 8.44365427750539E-17 -2.67741550322617E-16
e3 : 3.07473055140244E-01 -7.42195047831987E-01
zz1 : -3.16302443723418E-16 7.94177338558722E-16
g0 : 9.35090350871384E-01 1.80490589258713E+00
g1 : -1.91688762789244E+00 6.76060795479168E-01
g2 : 2.89665021264360E-01 -6.99209054967417E-01
g3 : 2.67502406418309E-01 -7.07586546943527E-01
== err : 4.514E-14 = rco : 2.579E-03 = res : 1.384E-14 ==
solution 37 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -9.61645007748109E-01 1.93351509528057E-01
e1 : -2.04054411073748E-01 6.71772307713711E-02
e2 : -1.66127517995746E-01 -1.37165444495566E+00
e3 : -5.23383097690656E-02 7.74122323114933E-01
zz1 : 3.48636113061328E-17 2.11977285578910E-16
g0 : -6.87814327698244E-02 -1.39014187466571E+00
g1 : -1.10067690249910E+00 -3.23577312090887E-01
g2 : 9.09473928260297E-01 -8.62474700559367E-01
g3 : -3.37302920438085E-01 -9.49704794858953E-01
== err : 1.337E-14 = rco : 6.638E-03 = res : 8.563E-15 ==
solution 38 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -4.34588248605691E-01 -7.39640566148914E-02
e1 : -1.28109503990892E-01 7.52728926957432E-01
e2 : 7.39640566148910E-02 -4.34588248605691E-01
e3 : -7.52728926957432E-01 -1.28109503990892E-01
zz1 : -2.10333421005222E-18 -1.75408228107293E-16
g0 : 2.12201484253731E-01 2.54347038936496E-01
g1 : 3.11239584686058E-02 -4.37224004386142E-01
g2 : 4.54785800472704E-01 3.32891221378053E-01
g3 : 5.06904256603294E-01 -3.78294077255499E-01
== err : 3.668E-15 = rco : 1.153E-02 = res : 2.033E-15 ==
solution 39 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -4.01917898426231E-01 -5.48582593715559E-01
e1 : -7.31641679223678E-02 2.29955524527603E-02
e2 : -1.86804655215451E-01 3.60779370352018E-01
e3 : -6.30429470138312E-01 2.17425014558696E-01
zz1 : -1.53942851233933E-16 -2.48716734787179E-17
g0 : 6.72991004814270E-01 1.10126001631239E+00
g1 : -2.45542706197377E-01 -3.65172792529507E-01
g2 : 9.36864726249782E-01 -6.60267485016623E-01
g3 : 7.60983705755866E-01 -2.60039699195899E-01
== err : 8.004E-15 = rco : 6.469E-03 = res : 3.674E-15 ==
solution 40 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
e0 : -1.76381861540848E+00 1.81700575804150E+00
e1 : 1.04904876352436E+00 1.01834115240776E+00
e2 : -1.81700575804150E+00 -1.76381861540848E+00
e3 : 1.01834115240776E+00 -1.04904876352436E+00
zz1 : 8.28625324534201E-16 -2.46710886732799E-15
g0 : -8.53638761082544E+00 1.38985158911337E-01
g1 : -1.50229293997123E+00 6.55874239405574E+00
g2 : -2.88001801770486E+00 -5.71270016139040E+00
g3 : 1.66797226693968E+00 -3.24531523667493E+00
== err : 8.555E-13 = rco : 1.908E-04 = res : 1.291E-13 ==