🚀 go-pugleaf

a correction is applied below:

Jon wrote:
> If T*N+a[0] is the nth degree polynomial where T=(t,t^2,t^3,...,t^n), 
> N=(a[1],a[2],a[3],...,a[n]), if T is described from two orthogonal 
> systems, its linear requirement precipitates.  T remains invariant
> despite the coordinate system used to describe it. Consequently, my 
> revised web site showing the details,
> 
> APPLICATION OF
> http://mypeoplepc.com/members/jon8338/polynomial/id7.html
> 
> EXAMPLE
> 
> (t-2)(t-3)(t-4)=0
> (t^2-5t+6)(t-4)=0
>       t-4
> -------------
> t^3-5t^2+ 6t
>    -4t^2+20t-24
> ----------------
> t^3-9t^2+26t-24
> 
> N=+/-(26,-9,1)
> N*U[2]=0 at U[2]=(4,13,13)
>               i    j  k
> U[3]=NxU[2]= 26   -9  1 =(-130,-334,374)
>               4   13 13
> 
> N/|N|=
> u[1]=( .944,-.327,.036)=(u[11],u[12],u[13])
> u[2]=( .212, .691,.691)=(u[21],u[22],u[23])
> u[3]=(-.249,-.640,.717)=(u[31],u[32],u[33])
> 
> (-a[0]/|N|)u[1]=(.8717)u[1]
> Q = +/-(-.823,.285,-.0314)
> 
>     .212  -.249       1 0 0
> A = .691  -.640    I= 0 1 0
>     .691   .717       0 0 1
> 
> T = (AA^T -I)^-1 Q   =(1.085,6.552,6.607)=(t,t^2,t^3)
> 
> t = 1.085  throw out
> t = 2.560~3
> t = 1.876~2
> 
> 
> EXAMPLE
> 
> n=8
> 
> T=[((AA^T-I)^-1)^T((AA^T-I)^-1)]^-1((AA^T-I)^-1)^T Q
correct above to,
T=[(AA^T-I)^T(AA^T-I)]^-1(AA^T-I)^T Q

> 
> (Least Squares)
> 
>           LEAST SQUARES SOLUTION TO MATRIX               
> k   a[k]                   SUMMARY           
> 0  -30     t^k         |t^k|         t        ERROR   
> 1    9   2.384E-01   2.384E-01   2.384E-01  -2.731E+01   
> 2    9   2.031E+01   2.031E+01   4.507E+00   1.590E+06   
> 3    1  -1.902E+01   1.902E+01   2.669E+00   2.557E+04   
> 4    3  -4.038E+00   4.038E+00   1.418E+00   2.165E+02   
> 5    6   4.742E+00   4.742E+00   9.485E-01   1.830E+00   
> 6    1  -3.753E+01   3.753E+01   1.830E+00   1.416E+03   
> 7    1   3.320E+01   3.320E+01   1.649E+00   6.553E+02   
> 8    9   3.010E+01   3.010E+01   1.530E+00   3.787E+02   
> 
> 
> Jon Giffen
> jon8338@peoplepc.com
>