// lsfit.java  tailorable code, add more functions as needed 
//             this version up to 7 independent variables, 7D

import java.io.*;
import java.text.*;
// needs simeq.java

public class lsfit
{
  int Apwr[]; // powers of each variable in a term
  int Bpwr[];
  int Cpwr[];
  int Dpwr[];
  int Epwr[];
  int Fpwr[];
  int Gpwr[];
  boolean debug = true; // user can turn off
  double A[][];
  double C[];
  double Y[];
  double Av[]; // powers of variables
  double Bv[];
  double Cv[];
  double Dv[];
  double Ev[];
  double Fv[];
  double Gv[];
  int mm;     // dimension, number of variables
  int n;      // highest polygon power
  int nnn;    // number of terms in polygon
  int ndata;  // number of data points to fit
  DecimalFormat f4 = new DecimalFormat("0.000");

  public lsfit(int mm, int n, int ndata)
  {
    this.n = n;
    this.mm = mm;
    this.ndata = ndata;
    if(mm==2) gen_2d_powers(); // n, mm sets nnn, Apwr, Bpwr ...
    if(mm==3) gen_3d_powers();
    if(mm==4) gen_4d_powers();
    if(mm==5) gen_5d_powers();
    if(mm==6) gen_6d_powers();
    if(mm==7) gen_7d_powers();
    A = new double[nnn][nnn];
    C = new double[nnn]; // computed polynomial coefficients
    Y = new double[nnn];
    Av = new double[n+1]; // powers of variables
    Bv = new double[n+1];
    Cv = new double[n+1];
    Dv = new double[n+1];
    Ev = new double[n+1];
    Fv = new double[n+1];
    Gv = new double[n+1];
    for(int i=0; i<nnn; i++)
    {
      for(int j=0; j<nnn; j++)
      {
        A[i][j] = 0.0;
      }
      Y[i] = 0.0;
    }
  }  

  // 2D
  public void fit2_data(double x, double y,
			double U, boolean last)
  {
    double term_i, term_j;

    Av[0] = 1.0;
    Bv[0] = 1.0;
    for(int k=1; k<=n; k++)
    {
      Av[k] = Av[k-1]*x;
      Bv[k] = Bv[k-1]*y;
    }
    for(int ia=0; ia<nnn; ia++)
    {
      term_i = Av[Apwr[ia]] * Bv[Bpwr[ia]];
      for(int ja=0; ja<nnn; ja++)
      {
	term_j = Av[Apwr[ja]] * Bv[Bpwr[ja]];
	A[ia][ja] = A[ia][ja] + term_i * term_j;
      } // ja
      Y[ia] = Y[ia] + U * term_i;
    } // ia
    if(last)
    {
      new simeq(A, Y, C);
      if(debug)
        for(int i=0; i<nnn; i++)
        {
          System.out.println("C["+i+"]="+C[i]+" x^"+Apwr[i]+" y^"+Bpwr[i]);
        }
    }
  } // end fit2_data 

  public void fit2_bpoly(int nx, int ny,
                         double xg[], double yg[],
                         double ug[][])
  {
    double x, y, U;
    double term_i, term_j;

    for(int i=0; i<nx; i++)
    {
      x = xg[i];
      for(int ii=0; ii<ny; ii++)
      {
        y = yg[ii];
        U = ug[i][ii];
        if(i==0 || i==nx-1 || ii==0 || ii==ny-1 )
	{
	  if(debug) System.out.println("x="+f4.format(x)+", y="+f4.format(y)+
                                       ", u="+f4.format(U));
          Av[0] = 1.0;
          Bv[0] = 1.0;
          for(int iv=1; iv<=n; iv++)
          {
	    Av[iv] = Av[iv-1]*x;
            Bv[iv] = Bv[iv-1]*y;
          }
          for(int ia=0; ia<nnn; ia++)
          {
	    term_i = Av[Apwr[ia]] * Bv[Bpwr[ia]];
	    for(int ja=0; ja<nnn; ja++)
	    {
	      term_j = Av[Apwr[ja]] * Bv[Bpwr[ja]];
	      A[ia][ja] = A[ia][ja] + term_i * term_j;
	    } // ja
	    Y[ia] = Y[ia] + U * term_i;
	  } // ia
	} // end if
      } // ii
    } // i
    new simeq(A, Y, C);
    if(debug)
      for(int i=0; i<nnn; i++)
      {
        System.out.println("C["+i+"]="+C[i]+" x^"+Apwr[i]+" y^"+Bpwr[i]);
      }
  } // end fit2_bpoly 

  // 3D
  public void fit3_data(double x, double y, double z,
			double U, boolean last)
  {
    double term_i, term_j;

    Av[0] = 1.0;
    Bv[0] = 1.0;
    Cv[0] = 1.0;
    for(int iv=1; iv<=n; iv++)
    {
      Av[iv] = Av[iv-1]*x;
      Bv[iv] = Bv[iv-1]*y;
      Cv[iv] = Cv[iv-1]*z;
    }
    for(int ia=0; ia<nnn; ia++)
    {
      term_i = Av[Apwr[ia]] * Bv[Bpwr[ia]] * Cv[Cpwr[ia]];
      for(int ja=0; ja<nnn; ja++)
      {
	term_j = Av[Apwr[ja]] * Bv[Bpwr[ja]] * Cv[Cpwr[ja]];
	A[ia][ja] = A[ia][ja] + term_i * term_j;
      } // ja
      Y[ia] = Y[ia] + U * term_i;
    } // ia
    if(last)
    {
      new simeq(A, Y, C);
      if(debug)
        for(int i=0; i<nnn; i++)
        {
          System.out.println("C["+i+"]="+C[i]+" x^"+Apwr[i]+" y^"+Bpwr[i]+
                             " z^"+Cpwr[i]);
        }
    }
  } // end fit3_data 

  public void fit3_bpoly(int nx, int ny, int nz,
                         double xg[], double yg[], double zg[],
                         double ug[][][])
  {
    double x, y, z;
    double term_i, term_j;

    for(int i=0; i<nx; i++)
    {
      x = xg[i];
      for(int ii=0; ii<ny; ii++)
      {
        y = yg[ii];
        for(int iii=0; iii<nz; iii++)
        {
          z = zg[iii];
          if(i==0 || i==nx-1 || ii==0 || ii==ny-1 || iii==0 || iii==nz-1)
	  {
          System.out.println("x="+f4.format(x)+", y="+f4.format(y)+
                             ", z="+f4.format(z)+", u="+f4.format(ug[i][ii][iii]));
          Av[0] = 1.0;
          Bv[0] = 1.0;
          Cv[0] = 1.0;
          for(int iv=1; iv<=n; iv++)
          {
	    Av[iv] = Av[iv-1]*x;
            Bv[iv] = Bv[iv-1]*y;
	    Cv[iv] = Cv[iv-1]*z;
          }
          for(int ia=0; ia<nnn; ia++)
          {
	    term_i = Av[Apwr[ia]] * Bv[Bpwr[ia]] * Cv[Cpwr[ia]];
	    for(int ja=0; ja<nnn; ja++)
	    {
	      term_j = Av[Apwr[ja]] * Bv[Bpwr[ja]] * Cv[Cpwr[ja]];
	      A[ia][ja] = A[ia][ja] + term_i * term_j;
	    } // ja
	    Y[ia] = Y[ia] + ug[i][ii][iii] * term_i;
	  } // ia
	  } // end if
	} // iii
      } // ii
    } // i
    new simeq(A, Y, C);
    if(debug)
      for(int i=0; i<nnn; i++)
      {
        System.out.println("C["+i+"]="+C[i]+" x^"+Apwr[i]+" y^"+Bpwr[i]+
                           " z^"+Cpwr[i]);
      }
  } // end fit3_bpoly 

  // 4D
  public void fit4_data(double x, double y, double z, double t,
			double U, boolean last)
  {
    double term_i, term_j;

    Av[0] = 1.0;
    Bv[0] = 1.0;
    Cv[0] = 1.0;
    Dv[0] = 1.0;
    for(int iv=1; iv<=n; iv++)
    {
      Av[iv] = Av[iv-1]*x;
      Bv[iv] = Bv[iv-1]*y;
      Cv[iv] = Cv[iv-1]*z;
      Dv[iv] = Dv[iv-1]*t;
    }
    for(int ia=0; ia<nnn; ia++)
    {
      term_i = Av[Apwr[ia]] * Bv[Bpwr[ia]] * Cv[Cpwr[ia]] * Dv[Dpwr[ia]];
      for(int ja=0; ja<nnn; ja++)
      {
	term_j = Av[Apwr[ja]] * Bv[Bpwr[ja]] * Cv[Cpwr[ja]] * Dv[Dpwr[ja]];
	A[ia][ja] = A[ia][ja] + term_i * term_j;
      } // ja
      Y[ia] = Y[ia] + U * term_i;
    } // ia
    if(last)
    {
      new simeq(A, Y, C);
      if(debug)
        for(int i=0; i<nnn; i++)
        {
          System.out.println("C["+i+"]="+C[i]+" x^"+Apwr[i]+" y^"+Bpwr[i]+
                             " z^"+Cpwr[i]+" t^"+Dpwr[i]);
        }
    }
  } // end fit4_data 

  public void fit4_bpoly(int nx, int ny, int nz, int nt,
                         double xg[], double yg[], double zg[],
                         double tg[],
                         double ug[][][][])
  {
    double x, y, z, t;
    double term_i, term_j;

    for(int i=0; i<nx; i++)
    {
      x = xg[i];
      for(int ii=0; ii<ny; ii++)
      {
        y = yg[ii];
        for(int iii=0; iii<nz; iii++)
        {
          z = zg[iii];
          for(int iiii=0; iiii<nt; iiii++)
          {
            t = tg[iiii];
            if(i==0 || i==nx-1 || ii==0 || ii==ny-1 || 
               iii==0 || iii==nz-1 || iiii==0 || iiii==nt-1)
	    {
              Av[0] = 1.0;
              Bv[0] = 1.0;
              Cv[0] = 1.0;
              Dv[0] = 1.0;
              for(int iv=1; iv<=n; iv++)
              {
	        Av[iv] = Av[iv-1]*x;
                Bv[iv] = Bv[iv-1]*y;
	        Cv[iv] = Cv[iv-1]*z;
	        Dv[iv] = Dv[iv-1]*t;
              }
              for(int ia=0; ia<nnn; ia++)
              {
	        term_i = Av[Apwr[ia]] * Bv[Bpwr[ia]] * Cv[Cpwr[ia]] *
                         Dv[Dpwr[ia]];
	        for(int ja=0; ja<nnn; ja++)
	        {
	          term_j = Av[Apwr[ja]] * Bv[Bpwr[ja]] * Cv[Cpwr[ja]] *
                           Dv[Dpwr[ja]];
	          A[ia][ja] = A[ia][ja] + term_i * term_j;
	        } // ja
	        Y[ia] = Y[ia] + ug[i][ii][iii][iiii] * term_i;
	      } // ia
	    } // end if
	  } // iii
	} // iii
      } // ii
    } // i
    new simeq(A, Y, C);
    if(debug)
      for(int i=0; i<nnn; i++)
      {
        System.out.println("C["+i+"]="+C[i]+" x^"+Apwr[i]+" y^"+Bpwr[i]+
                           " z^"+Cpwr[i]+" t^"+Dpwr[i]);
      }
  } // end fit4_bpoly 

  // 5D
  public void fit5_data(double x, double y, double z, double t, double u,
			double U, boolean last)
  {
    double term_i, term_j;

    Av[0] = 1.0;
    Bv[0] = 1.0;
    Cv[0] = 1.0;
    Dv[0] = 1.0;
    Ev[0] = 1.0;
    for(int iv=1; iv<=n; iv++)
    {
      Av[iv] = Av[iv-1]*x;
      Bv[iv] = Bv[iv-1]*y;
      Cv[iv] = Cv[iv-1]*z;
      Dv[iv] = Dv[iv-1]*t;
      Ev[iv] = Ev[iv-1]*u;
    }
    for(int ia=0; ia<nnn; ia++)
    {
      term_i = Av[Apwr[ia]] * Bv[Bpwr[ia]] * Cv[Cpwr[ia]] * 
               Dv[Dpwr[ia]] * Ev[Epwr[ia]];
      for(int ja=0; ja<nnn; ja++)
      {
	term_j = Av[Apwr[ja]] * Bv[Bpwr[ja]] * Cv[Cpwr[ja]] * 
                 Dv[Dpwr[ja]] * Ev[Epwr[ja]];
	A[ia][ja] = A[ia][ja] + term_i * term_j;
      } // ja
      Y[ia] = Y[ia] + U * term_i;
    } // ia
    if(last)
    {
      new simeq(A, Y, C);
      if(debug)
        for(int i=0; i<nnn; i++)
        {
          System.out.println("C["+i+"]="+C[i]+" x^"+Apwr[i]+" y^"+Bpwr[i]+
                             " z^"+Cpwr[i]+" t^"+Dpwr[i]+
                             " u^"+Epwr[i]);
        }
    }
  } // end fit5_data 

  public void fit5_bpoly(int nx, int ny, int nz, int nt, int nu,
                         double xg[], double yg[], double zg[],
                         double tg[], double ug[],
                         double Ug[][][][][])
  {
    double x, y, z, t, u;
    double term_i, term_j;

    for(int i=0; i<nx; i++)
    {
      x = xg[i];
      for(int ii=0; ii<ny; ii++)
      {
        y = yg[ii];
        for(int iii=0; iii<nz; iii++)
        {
          z = zg[iii];
          for(int iiii=0; iiii<nt; iiii++)
          {
            t = tg[iiii];
            for(int iiiii=0; iiiii<nu; iiiii++)
            {
              u = ug[iiiii];
              if(i==0 || i==nx-1 || ii==0 || ii==ny-1 || 
                 iii==0 || iii==nz-1 || iiii==0 || iiii==nt-1 ||
                 iiiii==0 || iiiii==nu-1)
	      {
                Av[0] = 1.0;
                Bv[0] = 1.0;
                Cv[0] = 1.0;
                Dv[0] = 1.0;
                Ev[0] = 1.0;
                for(int iv=1; iv<=n; iv++)
                {
	          Av[iv] = Av[iv-1]*x;
                  Bv[iv] = Bv[iv-1]*y;
	          Cv[iv] = Cv[iv-1]*z;
	          Dv[iv] = Dv[iv-1]*t;
	          Ev[iv] = Ev[iv-1]*u;
                }
                for(int ia=0; ia<nnn; ia++)
                {
	          term_i = Av[Apwr[ia]] * Bv[Bpwr[ia]] * Cv[Cpwr[ia]] *
                           Dv[Dpwr[ia]] * Ev[Epwr[ia]];
	          for(int ja=0; ja<nnn; ja++)
	          {
	            term_j = Av[Apwr[ja]] * Bv[Bpwr[ja]] * Cv[Cpwr[ja]] *
                             Dv[Dpwr[ja]] * Ev[Epwr[ja]];
	            A[ia][ja] = A[ia][ja] + term_i * term_j;
	          } // ja
	          Y[ia] = Y[ia] + Ug[i][ii][iii][iiii][iiiii] * term_i;
	        } // ia
	      } // end if
	    } // iiiii
	  } // iiii
	} // iii
      } // ii
    } // i
    new simeq(A, Y, C);
    if(debug)
      for(int i=0; i<nnn; i++)
      {
        System.out.println("C["+i+"]="+C[i]+" x^"+Apwr[i]+" y^"+Bpwr[i]+
                           " z^"+Cpwr[i]+" t^"+Dpwr[i]+" u^"+Epwr[i]);
      }
  } // end fit5_bpoly 

  // 6D
  public void fit6_data(double x, double y, double z, double t, double u,
			double v, double U, boolean last)
  {
    double term_i, term_j;

    Av[0] = 1.0;
    Bv[0] = 1.0;
    Cv[0] = 1.0;
    Dv[0] = 1.0;
    Ev[0] = 1.0;
    Fv[0] = 1.0;
    for(int iv=1; iv<=n; iv++)
    {
      Av[iv] = Av[iv-1]*x;
      Bv[iv] = Bv[iv-1]*y;
      Cv[iv] = Cv[iv-1]*z;
      Dv[iv] = Dv[iv-1]*t;
      Ev[iv] = Ev[iv-1]*u;
      Fv[iv] = Fv[iv-1]*v;
    }
    for(int ia=0; ia<nnn; ia++)
    {
      term_i = Av[Apwr[ia]] * Bv[Bpwr[ia]] * Cv[Cpwr[ia]] * 
               Dv[Dpwr[ia]] * Ev[Epwr[ia]] * Fv[Fpwr[ia]];
      for(int ja=0; ja<nnn; ja++)
      {
	term_j = Av[Apwr[ja]] * Bv[Bpwr[ja]] * Cv[Cpwr[ja]] * 
                 Dv[Dpwr[ja]] * Ev[Epwr[ja]] * Fv[Fpwr[ja]];
	A[ia][ja] = A[ia][ja] + term_i * term_j;
      } // ja
      Y[ia] = Y[ia] + U * term_i;
    } // ia
    if(last)
    {
      new simeq(A, Y, C);
      if(debug)
        for(int i=0; i<nnn; i++)
        {
          System.out.println("C["+i+"]="+C[i]+" x^"+Apwr[i]+" y^"+Bpwr[i]+
                             " z^"+Cpwr[i]+" t^"+Dpwr[i]+
                             " u^"+Epwr[i]+" v^"+Fpwr[i]);
        }
    }
  } // end fit6_data 

  public void fit6_bpoly(int nx, int ny, int nz, int nt, int nu, int nv,
                         double xg[], double yg[], double zg[],
                         double tg[], double ug[], double vg[],
                         double Ug[][][][][][])
  {
      double x, y, z, t, u, v;
    double term_i, term_j;

    for(int i=0; i<nx; i++)
    {
      x = xg[i];
      for(int ii=0; ii<ny; ii++)
      {
        y = yg[ii];
        for(int iii=0; iii<nz; iii++)
        {
          z = zg[iii];
          for(int iiii=0; iiii<nt; iiii++)
          {
            t = tg[iiii];
            for(int iiiii=0; iiiii<nu; iiiii++)
            {
              u = ug[iiiii];
              for(int iiiiii=0; iiiiii<nv; iiiiii++)
              {
                v = vg[iiiiii];
                if(i==0 || i==nx-1 || ii==0 || ii==ny-1 || 
                   iii==0 || iii==nz-1 || iiii==0 || iiii==nt-1 ||
                   iiiii==0 || iiiii==nu-1 || iiiiii==0 || iiiiii==nv-1)
	        {
                  Av[0] = 1.0;
                  Bv[0] = 1.0;
                  Cv[0] = 1.0;
                  Dv[0] = 1.0;
                  Ev[0] = 1.0;
                  Fv[0] = 1.0;
                  for(int iv=1; iv<=n; iv++)
                  {
	            Av[iv] = Av[iv-1]*x;
                    Bv[iv] = Bv[iv-1]*y;
	            Cv[iv] = Cv[iv-1]*z;
	            Dv[iv] = Dv[iv-1]*t;
	            Ev[iv] = Ev[iv-1]*u;
	            Fv[iv] = Fv[iv-1]*v;
                  }
                  for(int ia=0; ia<nnn; ia++)
                  {
	            term_i = Av[Apwr[ia]] * Bv[Bpwr[ia]] * Cv[Cpwr[ia]] *
                             Dv[Dpwr[ia]] * Ev[Epwr[ia]] * Fv[Fpwr[ia]];
	            for(int ja=0; ja<nnn; ja++)
	            {
	              term_j = Av[Apwr[ja]] * Bv[Bpwr[ja]] * Cv[Cpwr[ja]] *
                               Dv[Dpwr[ja]] * Ev[Epwr[ja]] * Fv[Fpwr[ja]];
	              A[ia][ja] = A[ia][ja] + term_i * term_j;
	            } // ja
	            Y[ia] = Y[ia] + Ug[i][ii][iii][iiii][iiiii][iiiiii] *
                                    term_i;
	          } // ia
	        } // end if
	      } // iiiiii
	    } // iiiii
	  } // iiii
	} // iii
      } // ii
    } // i
    new simeq(A, Y, C);
    if(debug)
      for(int i=0; i<nnn; i++)
      {
        System.out.println("C["+i+"]="+C[i]+" x^"+Apwr[i]+" y^"+Bpwr[i]+
                           " z^"+Cpwr[i]+" t^"+Dpwr[i]+" u^"+Epwr[i] +
                           " v^"+Fpwr[i]);
      }
  } // end fit6_bpoly 

  // 7D
  public void fit7_data(double x, double y, double z, double t, double u,
			double v, double w, double U, boolean last)
  {
    double term_i, term_j;

    Av[0] = 1.0;
    Bv[0] = 1.0;
    Cv[0] = 1.0;
    Dv[0] = 1.0;
    Ev[0] = 1.0;
    Fv[0] = 1.0;
    Gv[0] = 1.0;
    for(int iv=1; iv<=n; iv++)
    {
      Av[iv] = Av[iv-1]*x;
      Bv[iv] = Bv[iv-1]*y;
      Cv[iv] = Cv[iv-1]*z;
      Dv[iv] = Dv[iv-1]*t;
      Ev[iv] = Ev[iv-1]*u;
      Fv[iv] = Fv[iv-1]*v;
      Gv[iv] = Gv[iv-1]*w;
    }
    for(int ia=0; ia<nnn; ia++)
    {
      term_i = Av[Apwr[ia]] * Bv[Bpwr[ia]] * Cv[Cpwr[ia]] * 
               Dv[Dpwr[ia]] * Ev[Epwr[ia]] * Fv[Fpwr[ia]] *
	       Gv[Gpwr[ia]];
      for(int ja=0; ja<nnn; ja++)
      {
	term_j = Av[Apwr[ja]] * Bv[Bpwr[ja]] * Cv[Cpwr[ja]] * 
                 Dv[Dpwr[ja]] * Ev[Epwr[ja]] * Fv[Fpwr[ja]] *
                 Gv[Gpwr[ja]];
	A[ia][ja] = A[ia][ja] + term_i * term_j;
      } // ja
      Y[ia] = Y[ia] + U * term_i;
    } // ia
    if(last)
    {
      new simeq(A, Y, C);
      if(debug)
        for(int i=0; i<nnn; i++)
        {
          System.out.println("C["+i+"]="+C[i]+" x^"+Apwr[i]+" y^"+Bpwr[i]+
                                " z^"+Cpwr[i]+" t^"+Dpwr[i]+" u^"+Epwr[i]+
                                " v^"+Fpwr[i]+" w^"+Gpwr[i]);
        }
    }
  } // end fit7_data 

  public void fit7_bpoly(int nx, int ny, int nz, int nt, int nu,
                         int nv, int nw,
                         double xg[], double yg[], double zg[],
                         double tg[], double ug[], double vg[],
                         double wg[],  double Ug[][][][][][][])
  {
    double x, y, z, t, u, v, w;
    double term_i, term_j;

    for(int i=0; i<nx; i++)
    {
      x = xg[i];
      for(int ii=0; ii<ny; ii++)
      {
        y = yg[ii];
        for(int iii=0; iii<nz; iii++)
        {
          z = zg[iii];
          for(int iiii=0; iiii<nt; iiii++)
          {
            t = tg[iiii];
            for(int iiiii=0; iiiii<nu; iiiii++)
            {
              u = ug[iiiii];
              for(int iiiiii=0; iiiiii<nv; iiiiii++)
              {
                v = vg[iiiiii];
                for(int iiiiiii=0; iiiiiii<nv; iiiiiii++)
                {
                  w = vg[iiiiiii];
                  if(i==0 || i==nx-1 || ii==0 || ii==ny-1 || 
                     iii==0 || iii==nz-1 || iiii==0 || iiii==nt-1 ||
                     iiiii==0 || iiiii==nu-1 || iiiiii==0 || iiiiii==nv-1 ||
                     iiiiiii==0 || iiiiiii==nw-1)
	          {
                    Av[0] = 1.0;
                    Bv[0] = 1.0;
                    Cv[0] = 1.0;
                    Dv[0] = 1.0;
                    Ev[0] = 1.0;
                    Fv[0] = 1.0;
                    Gv[0] = 1.0;
                    for(int iv=1; iv<=n; iv++)
                    {
	              Av[iv] = Av[iv-1]*x;
                      Bv[iv] = Bv[iv-1]*y;
	              Cv[iv] = Cv[iv-1]*z;
	              Dv[iv] = Dv[iv-1]*t;
	              Ev[iv] = Ev[iv-1]*u;
	              Fv[iv] = Fv[iv-1]*v;
	              Gv[iv] = Gv[iv-1]*w;
                    }
                    for(int ia=0; ia<nnn; ia++)
                    {
	              term_i = Av[Apwr[ia]] * Bv[Bpwr[ia]] * Cv[Cpwr[ia]] *
                               Dv[Dpwr[ia]] * Ev[Epwr[ia]] * Fv[Fpwr[ia]] *
                               Gv[Gpwr[ia]];
	              for(int ja=0; ja<nnn; ja++)
	              {
	                term_j = Av[Apwr[ja]] * Bv[Bpwr[ja]] * Cv[Cpwr[ja]] *
                                 Dv[Dpwr[ja]] * Ev[Epwr[ja]] * Fv[Fpwr[ja]] *
                                 Gv[Gpwr[ja]];
	                A[ia][ja] = A[ia][ja] + term_i * term_j;
	              } // ja
	              Y[ia] = Y[ia] + Ug[i][ii][iii][iiii][iiiii][iiiiii]
                                        [iiiiiii] * term_i;
	            } // ia
	          } // end if
		} // iiiiiii
	      } // iiiiii
	    } // iiiii
	  } // iiii
	} // iii
      } // ii
    } // i
    new simeq(A, Y, C);
    if(debug)
      for(int i=0; i<nnn; i++)
      {
        System.out.println("C["+i+"]="+C[i]+" x^"+Apwr[i]+" y^"+Bpwr[i]+
                              " z^"+Cpwr[i]+" t^"+Dpwr[i]+" u^"+Epwr[i]+
			      " v^"+Fpwr[i]+" w^"+Gpwr[i]);
      }
  } // end fit7_bpoly 

  public double eval2_poly(double x, double y)
  {
    double ua = 0.0;
    Av[0] = 1.0;
    Bv[0] = 1.0;
    for(int i=1; i<=n; i++)
    {
      Av[i] = Av[i-1]*x;
      Bv[i] = Bv[i-1]*y;
    }
    for(int i=0; i<nnn; i++)
    {
      ua = ua + C[i] * Av[Apwr[i]] * Bv[Bpwr[i]];
    }
    return ua;
  } // end eval2_poly 

  public double eval3_poly(double x, double y, double z)
  {
    double ua = 0.0;
    Av[0] = 1.0;
    Bv[0] = 1.0;
    Cv[0] = 1.0;
    for(int i=1; i<=n; i++)
    {
      Av[i] = Av[i-1]*x;
      Bv[i] = Bv[i-1]*y;
      Cv[i] = Cv[i-1]*z;
    }
    for(int i=0; i<nnn; i++)
    {
      ua = ua + C[i] * Av[Apwr[i]] * Bv[Bpwr[i]] * Cv[Cpwr[i]];
    }
    return ua;
  } // end eval3_poly 

  public double eval4_poly(double x, double y, double z, double t)
  {
    double ua = 0.0;
    Av[0] = 1.0;
    Bv[0] = 1.0;
    Cv[0] = 1.0;
    Dv[0] = 1.0;
    for(int i=1; i<=n; i++)
    {
      Av[i] = Av[i-1]*x;
      Bv[i] = Bv[i-1]*y;
      Cv[i] = Cv[i-1]*z;
      Dv[i] = Dv[i-1]*t;
    }
    for(int i=0; i<nnn; i++)
    {
      ua = ua + C[i] * Av[Apwr[i]] * Bv[Bpwr[i]] * Cv[Cpwr[i]] *
	               Dv[Dpwr[i]];
    }
    return ua;
  } // end eval4_poly 

  public double eval5_poly(double x, double y, double z, double t, double u)
  {
    double ua = 0.0;
    Av[0] = 1.0;
    Bv[0] = 1.0;
    Cv[0] = 1.0;
    Dv[0] = 1.0;
    Ev[0] = 1.0;
    for(int i=1; i<=n; i++)
    {
      Av[i] = Av[i-1]*x;
      Bv[i] = Bv[i-1]*y;
      Cv[i] = Cv[i-1]*z;
      Dv[i] = Dv[i-1]*t;
      Ev[i] = Ev[i-1]*u;
    }
    for(int i=0; i<nnn; i++)
    {
      ua = ua + C[i] * Av[Apwr[i]] * Bv[Bpwr[i]] * Cv[Cpwr[i]] *
	               Dv[Dpwr[i]] * Ev[Epwr[i]];
    }
    return ua;
  } // end eval5_poly 

  public double eval6_poly(double x, double y, double z, double t, double u,
                           double v)
  {
    double ua = 0.0;
    Av[0] = 1.0;
    Bv[0] = 1.0;
    Cv[0] = 1.0;
    Dv[0] = 1.0;
    Ev[0] = 1.0;
    Fv[0] = 1.0;
    for(int i=1; i<=n; i++)
    {
      Av[i] = Av[i-1]*x;
      Bv[i] = Bv[i-1]*y;
      Cv[i] = Cv[i-1]*z;
      Dv[i] = Dv[i-1]*t;
      Ev[i] = Ev[i-1]*u;
      Fv[i] = Fv[i-1]*v;
    }
    for(int i=0; i<nnn; i++)
    {
      ua = ua + C[i] * Av[Apwr[i]] * Bv[Bpwr[i]] * Cv[Cpwr[i]] *
	               Dv[Dpwr[i]] * Ev[Epwr[i]] * Fv[Fpwr[i]];
    }
    return ua;
  } // end eval6_poly 

  public double eval7_poly(double x, double y, double z, double t, double u,
                           double v, double w)
  {
    double ua = 0.0;
    Av[0] = 1.0;
    Bv[0] = 1.0;
    Cv[0] = 1.0;
    Dv[0] = 1.0;
    Ev[0] = 1.0;
    Fv[0] = 1.0;
    Gv[0] = 1.0;
    for(int i=1; i<=n; i++)
    {
      Av[i] = Av[i-1]*x;
      Bv[i] = Bv[i-1]*y;
      Cv[i] = Cv[i-1]*z;
      Dv[i] = Dv[i-1]*t;
      Ev[i] = Ev[i-1]*u;
      Fv[i] = Fv[i-1]*v;
      Gv[i] = Gv[i-1]*w;
    }
    for(int i=0; i<nnn; i++)
    {
      ua = ua + C[i] * Av[Apwr[i]] * Bv[Bpwr[i]] * Cv[Cpwr[i]] *
	               Dv[Dpwr[i]] * Ev[Epwr[i]] * Fv[Fpwr[i]] *
                       Gv[Gpwr[i]];
    }
    return ua;
  } // end eval7_poly 

  void gen_2d_powers()
  {
    int pwrsix[]={0,1,3,6,10,15,21,28}; // start of each order
    int pwrs[][]={{0,0},
                  {1,0},{0,1},
		  {2,0},{1,1},{0,2},
		  {3,0},{2,1},{1,2},{0,3},
                  {4,0},{3,1},{2,2},{1,3},{0,4},
                  {5,0},{4,1},{3,2},{2,3},{1,4},{0,5},
                  {6,0},{5,1},{4,2},{3,3},{2,4},{1,5},{0,6}};
    nnn = pwrsix[n+1];
    Apwr = new int[nnn]; // powers of each variable in a term
    Bpwr = new int[nnn];

    if(debug) System.out.println("terms used to find fit ");
    for(int i=0; i<=n; i++) // power requested 
    {
      for(int ii=pwrsix[i]; ii<pwrsix[i+1]; ii++)
      {
	Apwr[ii]=pwrs[ii][0];
	Bpwr[ii]=pwrs[ii][1];
	if(debug)System.out.println(ii+"   a^"+Apwr[ii]+" * b^"+
                                    Bpwr[ii]);
      }
      if(debug) System.out.println(" ");
    }
  } /* end gen_2d_powers */

  void gen_3d_powers()
  {
    int pwrsix[]={0,1,4,10,20,35,56,84}; // start of each order
    int pwrs[][]={{0,0,0},{1,0,0},{0,1,0},{0,0,1},
		  {2,0,0},{1,1,0},{1,0,1},{0,2,0},
		  {0,1,1},{0,0,2},{3,0,0},{2,1,0},
                  {2,0,1},{1,2,0},{1,1,1},{1,0,2},
		  {0,3,0},{0,2,1},{0,1,2},{0,0,3},
                  {4,0,0},{3,1,0},{3,0,1},{2,2,0},
                  {2,1,1},{2,0,2},{1,3,0},{1,2,1},
                  {1,1,2},{1,0,3},{0,4,0},{0,3,1},
                  {0,2,2},{0,1,3},{0,0,4},{5,0,0},
                  {4,1,0},{3,2,0},{2,3,0},{1,4,0},
                  {0,5,0},{4,0,1},{3,1,1},{2,2,1},
                  {1,3,1},{0,4,1},{3,0,2},{2,1,2},
                  {1,2,2},{0,3,2},{2,0,3},{1,1,3},
                  {0,2,3},{1,0,4},{0,1,4},{0,0,5},
                  {6,0,0},{5,1,0},{4,2,0},{3,3,0},
                  {2,4,0},{1,5,0},{0,6,0},{5,0,1},
                  {4,1,1},{3,2,1},{2,3,1},{1,4,1},
                  {0,5,1},{4,0,2},{3,1,2},{2,2,2},
                  {1,3,2},{0,4,2},{3,0,3},{2,1,3},
                  {1,2,3},{0,3,3},{2,0,4},{1,1,4},
                  {0,2,4},{1,0,5},{0,1,5},{0,0,6} };
    nnn = pwrsix[n+1];
    Apwr = new int[nnn]; // powers of each variable in a term
    Bpwr = new int[nnn];
    Cpwr = new int[nnn];

    if(debug) System.out.println("terms used to find fit ");
    for(int i=0; i<=n; i++) // power requested 
    {
      for(int ii=pwrsix[i]; ii<pwrsix[i+1]; ii++)
      {
	Apwr[ii]=pwrs[ii][0];
	Bpwr[ii]=pwrs[ii][1];
	Cpwr[ii]=pwrs[ii][2];
	if(debug)System.out.println(ii+"   a^"+Apwr[ii]+" * b^"+
                                    Bpwr[ii]+" * c^"+Cpwr[ii]);
      }
      if(debug) System.out.println(" ");
    }
  } /* end gen_3d_powers */

  void gen_4d_powers()
  {
    int pwrsix[]={0,1,5,15,35,70,126,210}; // start of each order
    int pwrs[][]={{0,0,0,0},
      {1,0,0,0},{0,1,0,0},{0,0,1,0},{0,0,0,1},
      {2,0,0,0},{1,1,0,0},{0,2,0,0},{1,0,1,0},{0,1,1,0},
      {0,0,2,0},{1,0,0,1},{0,1,0,1},{0,0,1,1},{0,0,0,2},
      {3,0,0,0},{2,1,0,0},{1,2,0,0},{0,3,0,0},{2,0,1,0},
      {1,1,1,0},{0,2,1,0},{1,0,2,0},{0,1,2,0},{0,0,3,0},
      {2,0,0,1},{1,1,0,1},{0,2,0,1},{1,0,1,1},{0,1,1,1},
      {0,0,2,1},{1,0,0,2},{0,1,0,2},{0,0,1,2},{0,0,0,3},
      {4,0,0,0},{3,1,0,0},{2,2,0,0},{1,3,0,0},{0,4,0,0},
      {3,0,1,0},{2,1,1,0},{1,2,1,0},{0,3,1,0},{2,0,2,0},
      {1,1,2,0},{0,2,2,0},{1,0,3,0},{0,1,3,0},{0,0,4,0},
      {3,0,0,1},{2,1,0,1},{1,2,0,1},{0,3,0,1},{2,0,1,1},
      {1,1,1,1},{0,2,1,1},{1,0,2,1},{0,1,2,1},{0,0,3,1},
      {2,0,0,2},{1,1,0,2},{0,2,0,2},{1,0,1,2},{0,1,1,2},
      {0,0,2,2},{1,0,0,3},{0,1,0,3},{0,0,1,3},{0,0,0,4},
      {5,0,0,0},{4,1,0,0},{3,2,0,0},{2,3,0,0},{1,4,0,0},
      {0,5,0,0},{4,0,1,0},{3,1,1,0},{2,2,1,0},{1,3,1,0},
      {0,4,1,0},{3,0,2,0},{2,1,2,0},{1,2,2,0},{0,3,2,0},
      {2,0,3,0},{1,1,3,0},{0,2,3,0},{1,0,4,0},{0,1,4,0},
      {0,0,5,0},{4,0,0,1},{3,1,0,1},{2,2,0,1},{1,3,0,1},
      {0,4,0,1},{3,0,1,1},{2,1,1,1},{1,2,1,1},{0,3,1,1},
      {2,0,2,1},{1,1,2,1},{0,2,2,1},{1,0,3,1},{0,1,3,1},
      {0,0,4,1},{3,0,0,2},{2,1,0,2},{1,2,0,2},{0,3,0,2},
      {2,0,1,2},{1,1,1,2},{0,2,1,2},{1,0,2,2},{0,1,2,2},
      {0,0,3,2},{2,0,0,3},{1,1,0,3},{0,2,0,3},{1,0,1,3},
      {0,1,1,3},{0,0,2,3},{1,0,0,4},{0,1,0,4},{0,0,1,4},
      {0,0,0,5},
      {6,0,0,0},{5,1,0,0},{4,2,0,0},{3,3,0,0},{2,4,0,0},
      {1,5,0,0},{0,6,0,0},{5,0,1,0},{4,1,1,0},{3,2,1,0},
      {2,3,1,0},{1,4,1,0},{0,5,1,0},{4,0,2,0},{3,1,2,0},
      {2,2,2,0},{1,3,2,0},{0,4,2,0},{3,0,3,0},{2,1,3,0},
      {1,2,3,0},{0,3,3,0},{2,0,4,0},{1,1,4,0},{0,2,4,0},
      {1,0,5,0},{0,1,5,0},{0,0,6,0},{5,0,0,1},{4,1,0,1},
      {3,2,0,1},{2,3,0,1},{1,4,0,1},{0,5,0,1},{4,0,1,1},
      {3,1,1,1},{2,2,1,1},{1,3,1,1},{0,4,1,1},{3,0,2,1},
      {2,1,2,1},{1,2,2,1},{0,3,2,1},{2,0,3,1},{1,1,3,1},
      {0,2,3,1},{1,0,4,1},{0,1,4,1},{0,0,5,1},{4,0,0,2},
      {3,1,0,2},{2,2,0,2},{1,3,0,2},{0,4,0,2},{3,0,1,2},
      {2,1,1,2},{1,2,1,2},{0,3,1,2},{2,0,2,2},{1,1,2,2},
      {0,2,2,2},{1,0,3,2},{0,1,3,2},{0,0,4,2},{3,0,0,3},
      {2,1,0,3},{1,2,0,3},{0,3,0,3},{2,0,1,3},{1,1,1,3},
      {0,2,1,3},{1,0,2,3},{0,1,2,3},{0,0,3,3},{2,0,0,4},
      {1,1,0,4},{0,2,0,4},{1,0,1,4},{0,1,1,4},{0,0,2,4},
      {1,0,0,5},{0,1,0,5},{0,0,1,5},{0,0,0,6}};

    nnn = pwrsix[n+1];
    Apwr = new int[nnn]; // powers of each variable in a term
    Bpwr = new int[nnn];
    Cpwr = new int[nnn];
    Dpwr = new int[nnn];

    if(debug) System.out.println("terms used to find fit ");
    for(int i=0; i<=n; i++) // power requested 
    {
      for(int ii=pwrsix[i]; ii<pwrsix[i+1]; ii++)
      {
	Apwr[ii]=pwrs[ii][0];
	Bpwr[ii]=pwrs[ii][1];
	Cpwr[ii]=pwrs[ii][2];
	Dpwr[ii]=pwrs[ii][3];
	if(debug)System.out.println(ii+"   a^"+Apwr[ii]+
                                       " * b^"+Bpwr[ii]+
                                       " * c^"+Cpwr[ii]+
                                       " * d^"+Dpwr[ii]);
      }
      if(debug) System.out.println(" ");
    }
  } /* end gen_4d_powers */

  void gen_5d_powers()
  {
    int pwrsix[]={0,1,6,21,56,126,252,463}; // start of each order
    int pwrs[][]={{0,0,0,0,0},
      {1,0,0,0,0},{0,1,0,0,0},{0,0,1,0,0},{0,0,0,1,0},{0,0,0,0,1},
      {2,0,0,0,0},{1,1,0,0,0},{0,2,0,0,0},{1,0,1,0,0},{0,1,1,0,0},
      {0,0,2,0,0},{1,0,0,1,0},{0,1,0,1,0},{0,0,1,1,0},{0,0,0,2,0},
      {1,0,0,0,1},{0,1,0,0,1},{0,0,1,0,1},{0,0,0,1,1},{0,0,0,0,2},
      {3,0,0,0,0},{2,1,0,0,0},{1,2,0,0,0},{0,3,0,0,0},{2,0,1,0,0},
      {1,1,1,0,0},{0,2,1,0,0},{1,0,2,0,0},{0,1,2,0,0},{0,0,3,0,0},
      {2,0,0,1,0},{1,1,0,1,0},{0,2,0,1,0},{1,0,1,1,0},{0,1,1,1,0},
      {0,0,2,1,0},{1,0,0,2,0},{0,1,0,2,0},{0,0,1,2,0},{0,0,0,3,0},
      {2,0,0,0,1},{1,1,0,0,1},{0,2,0,0,1},{1,0,1,0,1},{0,1,1,0,1},
      {0,0,2,0,1},{1,0,0,1,1},{0,1,0,1,1},{0,0,1,1,1},{0,0,0,2,1},
      {1,0,0,0,2},{0,1,0,0,2},{0,0,1,0,2},{0,0,0,1,2},{0,0,0,0,3},
      {4,0,0,0,0},{3,1,0,0,0},{2,2,0,0,0},{1,3,0,0,0},{0,4,0,0,0},
      {3,0,1,0,0},{2,1,1,0,0},{1,2,1,0,0},{0,3,1,0,0},{2,0,2,0,0},
      {1,1,2,0,0},{0,2,2,0,0},{1,0,3,0,0},{0,1,3,0,0},{0,0,4,0,0},
      {3,0,0,1,0},{2,1,0,1,0},{1,2,0,1,0},{0,3,0,1,0},{2,0,1,1,0},
      {1,1,1,1,0},{0,2,1,1,0},{1,0,2,1,0},{0,1,2,1,0},{0,0,3,1,0},
      {2,0,0,2,0},{1,1,0,2,0},{0,2,0,2,0},{1,0,1,2,0},{0,1,1,2,0},
      {0,0,2,2,0},{1,0,0,3,0},{0,1,0,3,0},{0,0,1,3,0},{0,0,0,4,0},
      {3,0,0,0,1},{2,1,0,0,1},{1,2,0,0,1},{0,3,0,0,1},{2,0,1,0,1},
      {1,1,1,0,1},{0,2,1,0,1},{1,0,2,0,1},{0,1,2,0,1},{0,0,3,0,1},
      {2,0,0,1,1},{1,1,0,1,1},{0,2,0,1,1},{1,0,1,1,1},{0,1,1,1,1},
      {0,0,2,1,1},{1,0,0,2,1},{0,1,0,2,1},{0,0,1,2,1},{0,0,0,3,1},
      {2,0,0,0,2},{1,1,0,0,2},{0,2,0,0,2},{1,0,1,0,2},{0,1,1,0,2},
      {0,0,2,0,2},{1,0,0,1,2},{0,1,0,1,2},{0,0,1,1,2},{0,0,0,2,2},
      {1,0,0,0,3},{0,1,0,0,3},{0,0,1,0,3},{0,0,0,1,3},{0,0,0,0,4},
      {5,0,0,0,0},{4,1,0,0,0},{3,2,0,0,0},{2,3,0,0,0},{1,4,0,0,0},
      {0,5,0,0,0},{4,0,1,0,0},{3,1,1,0,0},{2,2,1,0,0},{1,3,1,0,0},
      {0,4,1,0,0},{3,0,2,0,0},{2,1,2,0,0},{1,2,2,0,0},{0,3,2,0,0},
      {2,0,3,0,0},{1,1,3,0,0},{0,2,3,0,0},{1,0,4,0,0},{0,1,4,0,0},
      {0,0,5,0,0},{4,0,0,1,0},{3,1,0,1,0},{2,2,0,1,0},{1,3,0,1,0},
      {0,4,0,1,0},{3,0,1,1,0},{2,1,1,1,0},{1,2,1,1,0},{0,3,1,1,0},
      {2,0,2,1,0},{1,1,2,1,0},{0,2,2,1,0},{1,0,3,1,0},{0,1,3,1,0},
      {0,0,4,1,0},{3,0,0,2,0},{2,1,0,2,0},{1,2,0,2,0},{0,3,0,2,0},
      {2,0,1,2,0},{1,1,1,2,0},{0,2,1,2,0},{1,0,2,2,0},{0,1,2,2,0},
      {0,0,3,2,0},{2,0,0,3,0},{1,1,0,3,0},{0,2,0,3,0},{1,0,1,3,0},
      {0,1,1,3,0},{0,0,2,3,0},{1,0,0,4,0},{0,1,0,4,0},{0,0,1,4,0},
      {0,0,0,5,0},{4,0,0,0,1},{3,1,0,0,1},{2,2,0,0,1},{1,3,0,0,1},
      {0,4,0,0,1},{3,0,1,0,1},{2,1,1,0,1},{1,2,1,0,1},{0,3,1,0,1},
      {2,0,2,0,1},{1,1,2,0,1},{0,2,2,0,1},{1,0,3,0,1},{0,1,3,0,1},
      {0,0,4,0,1},{3,0,0,1,1},{2,1,0,1,1},{1,2,0,1,1},{0,3,0,1,1},
      {2,0,1,1,1},{1,1,1,1,1},{0,2,1,1,1},{1,0,2,1,1},{0,1,2,1,1},
      {0,0,3,1,1},{2,0,0,2,1},{1,1,0,2,1},{0,2,0,2,1},{1,0,1,2,1},
      {0,1,1,2,1},{0,0,2,2,1},{1,0,0,3,1},{0,1,0,3,1},{0,0,1,3,1},
      {0,0,0,4,1},{3,0,0,0,2},{2,1,0,0,2},{1,2,0,0,2},{0,3,0,0,2},
      {2,0,1,0,2},{1,1,1,0,2},{0,2,1,0,2},{1,0,2,0,2},{0,1,2,0,2},
      {0,0,3,0,2},{2,0,0,1,2},{1,1,0,1,2},{0,2,0,1,2},{1,0,1,1,2},
      {0,1,1,1,2},{0,0,2,1,2},{1,0,0,2,2},{0,1,0,2,2},{0,0,1,2,2},
      {0,0,0,3,2},{2,0,0,0,3},{1,1,0,0,3},{0,2,0,0,3},{1,0,1,0,3},
      {0,1,1,0,3},{0,0,2,0,3},{1,0,0,1,3},{0,1,0,1,3},{0,0,1,1,3},
      {0,0,0,2,3},{1,0,0,0,4},{0,1,0,0,4},{0,0,1,0,4},{0,0,0,1,4},
      {0,0,0,0,5},
      {6,0,0,0,0},{5,1,0,0,0},{4,2,0,0,0},{3,3,0,0,0},{2,4,0,0,0},
      {1,5,0,0,0},{0,6,0,0,0},{5,0,1,0,0},{4,1,1,0,0},{3,2,1,0,0},
      {2,3,1,0,0},{1,4,1,0,0},{0,5,1,0,0},{4,0,2,0,0},{3,1,2,0,0},
      {2,2,2,0,0},{1,3,2,0,0},{0,4,2,0,0},{3,0,3,0,0},{2,1,3,0,0},
      {1,2,3,0,0},{0,3,3,0,0},{2,0,4,0,0},{1,1,4,0,0},{0,2,4,0,0},
      {1,0,5,0,0},{0,1,5,0,0},{0,0,6,0,0},{5,0,0,1,0},{4,1,0,1,0},
      {3,2,0,1,0},{2,3,0,1,0},{1,4,0,1,0},{0,5,0,1,0},{4,0,1,1,0},
      {3,1,1,1,0},{2,2,1,1,0},{1,3,1,1,0},{0,4,1,1,0},{3,0,2,1,0},
      {2,1,2,1,0},{1,2,2,1,0},{0,3,2,1,0},{2,0,3,1,0},{1,1,3,1,0},
      {0,2,3,1,0},{1,0,4,1,0},{0,1,4,1,0},{0,0,5,1,0},{4,0,0,2,0},
      {3,1,0,2,0},{2,2,0,2,0},{1,3,0,2,0},{0,4,0,2,0},{3,0,1,2,0},
      {2,1,1,2,0},{1,2,1,2,0},{0,3,1,2,0},{2,0,2,2,0},{1,1,2,2,0},
      {0,2,2,2,0},{1,0,3,2,0},{0,1,3,2,0},{0,0,4,2,0},{3,0,0,3,0},
      {2,1,0,3,0},{1,2,0,3,0},{0,3,0,3,0},{2,0,1,3,0},{1,1,1,3,0},
      {0,2,1,3,0},{1,0,2,3,0},{0,1,2,3,0},{0,0,3,3,0},{2,0,0,4,0},
      {1,1,0,4,0},{0,2,0,4,0},{1,0,1,4,0},{0,1,1,4,0},{0,0,2,4,0},
      {1,0,0,5,0},{0,1,0,5,0},{0,0,1,5,0},{0,0,0,6,0},{5,0,0,0,1},
      {4,1,0,0,1},{3,2,0,0,1},{2,3,0,0,1},{1,4,0,0,1},{0,5,0,0,1},
      {4,0,1,0,1},{3,1,1,0,1},{2,2,1,0,1},{1,3,1,0,1},{0,4,1,0,1},
      {3,0,2,0,1},{2,1,2,0,1},{1,2,2,0,1},{0,3,2,0,1},{2,0,3,0,1},
      {1,1,3,0,1},{0,2,3,0,1},{1,0,4,0,1},{0,1,4,0,1},{0,0,5,0,1},
      {4,0,0,1,1},{3,1,0,1,1},{2,2,0,1,1},{1,3,0,1,1},{0,4,0,1,1},
      {3,0,1,1,1},{2,1,1,1,1},{1,2,1,1,1},{0,3,1,1,1},{2,0,2,1,1},
      {1,1,2,1,1},{0,2,2,1,1},{1,0,3,1,1},{0,1,3,1,1},{0,0,4,1,1},
      {3,0,0,2,1},{2,1,0,2,1},{1,2,0,2,1},{0,3,0,2,1},{2,0,1,2,1},
      {1,1,1,2,1},{0,2,1,2,1},{1,0,2,2,1},{0,1,2,2,1},{0,0,3,2,1},
      {2,0,0,3,1},{1,1,0,3,1},{0,2,0,3,1},{1,0,1,3,1},{0,1,1,3,1},
      {0,0,2,3,1},{1,0,0,4,1},{0,1,0,4,1},{0,0,1,4,1},{0,0,0,5,1},
      {4,0,0,0,2},{3,1,0,0,2},{2,2,0,0,2},{1,3,0,0,2},{0,4,0,0,2},
      {3,0,1,0,2},{2,1,1,0,2},{1,2,1,0,2},{0,3,1,0,2},{2,0,2,0,2},
      {1,1,2,0,2},{0,2,2,0,2},{1,0,3,0,2},{0,1,3,0,2},{0,0,4,0,2},
      {3,0,0,1,2},{2,1,0,1,2},{1,2,0,1,2},{0,3,0,1,2},{2,0,1,1,2},
      {1,1,1,1,2},{0,2,1,1,2},{1,0,2,1,2},{0,1,2,1,2},{0,0,3,1,2},
      {2,0,0,2,2},{1,1,0,2,2},{0,2,0,2,2},{1,0,1,2,2},{0,1,1,2,2},
      {0,0,2,2,2},{1,0,0,3,2},{0,1,0,3,2},{0,0,1,3,2},{0,0,0,4,2},
      {3,0,0,0,3},{2,1,0,0,3},{1,2,0,0,3},{0,3,0,0,3},{2,0,1,0,3},
      {1,1,1,0,3},{0,2,1,0,3},{1,0,2,0,3},{0,1,2,0,3},{0,0,3,0,3},
      {2,0,0,1,3},{1,1,0,1,3},{0,2,0,1,3},{1,0,1,1,3},{0,1,1,1,3},
      {0,0,2,1,3},{1,0,0,2,3},{0,1,0,2,3},{0,0,1,2,3},{0,0,0,3,3},
      {2,0,0,0,4},{1,1,0,0,4},{0,2,0,0,4},{1,0,1,0,4},{0,1,1,0,4},
      {0,0,2,0,4},{1,0,0,1,4},{0,1,0,1,4},{0,0,1,1,4},{0,0,0,2,4},
      {1,0,0,0,5},{0,1,0,0,5},{0,0,1,0,5},{0,0,0,1,5},{0,0,0,0,6}};

    nnn = pwrsix[n+1];
    Apwr = new int[nnn]; // powers of each variable in a term
    Bpwr = new int[nnn];
    Cpwr = new int[nnn];
    Dpwr = new int[nnn];
    Epwr = new int[nnn];

    if(debug) System.out.println("terms used to find fit ");
    for(int i=0; i<=n; i++) // power requested 
    {
      for(int ii=pwrsix[i]; ii<pwrsix[i+1]; ii++)
      {
	Apwr[ii]=pwrs[ii][0];
	Bpwr[ii]=pwrs[ii][1];
	Cpwr[ii]=pwrs[ii][2];
	Dpwr[ii]=pwrs[ii][3];
	Epwr[ii]=pwrs[ii][4];
	if(debug)System.out.println(ii+"   a^"+Apwr[ii]+
                                       " * b^"+Bpwr[ii]+
                                       " * c^"+Cpwr[ii]+
                                       " * d^"+Dpwr[ii]+
                                       " * e^"+Epwr[ii]);
      }
      if(debug) System.out.println(" ");
    }
  } /* end gen_5d_powers */

  void gen_6d_powers()
  {
    int pwrsix[]={0,1,7,28,84,210,462,924}; // start of each order
    int pwrs[][]={{0,0,0,0,0,0},
                  {1,0,0,0,0,0},{0,1,0,0,0,0},{0,0,1,0,0,0},{0,0,0,1,0,0},
                  {0,0,0,0,1,0},{0,0,0,0,0,1},
		  {2,0,0,0,0,0},{1,1,0,0,0,0},{0,2,0,0,0,0},{1,0,1,0,0,0},
		  {0,1,1,0,0,0},{0,0,2,0,0,0},{1,0,0,1,0,0},{0,1,0,1,0,0},
		  {0,0,1,1,0,0},{0,0,0,2,0,0},{1,0,0,0,1,0},{0,1,0,0,1,0},
		  {0,0,1,0,1,0},{0,0,0,1,1,0},{0,0,0,0,2,0},{1,0,0,0,0,1},
		  {0,1,0,0,0,1},{0,0,1,0,0,1},{0,0,0,1,0,1},{0,0,0,0,1,1},
		  {0,0,0,0,0,2},
		  {3,0,0,0,0,0},{2,1,0,0,0,0},{1,2,0,0,0,0},{0,3,0,0,0,0},
		  {2,0,1,0,0,0},{1,1,1,0,0,0},{0,2,1,0,0,0},{1,0,2,0,0,0},
		  {0,1,2,0,0,0},{0,0,3,0,0,0},{2,0,0,1,0,0},{1,1,0,1,0,0},
		  {0,2,0,1,0,0},{1,0,1,1,0,0},{0,1,1,1,0,0},{0,0,2,1,0,0},
		  {1,0,0,2,0,0},{0,1,0,2,0,0},{0,0,1,2,0,0},{0,0,0,3,0,0},
		  {2,0,0,0,1,0},{1,1,0,0,1,0},{0,2,0,0,1,0},{1,0,1,0,1,0},
		  {0,1,1,0,1,0},{0,0,2,0,1,0},{1,0,0,1,1,0},{0,1,0,1,1,0},
		  {0,0,1,1,1,0},{0,0,0,2,1,0},{1,0,0,0,2,0},{0,1,0,0,2,0},
		  {0,0,1,0,2,0},{0,0,0,1,2,0},{0,0,0,0,3,0},{2,0,0,0,0,1},
		  {1,1,0,0,0,1},{0,2,0,0,0,1},{1,0,1,0,0,1},{0,1,1,0,0,1},
		  {0,0,2,0,0,1},{1,0,0,1,0,1},{0,1,0,1,0,1},{0,0,1,1,0,1},
		  {0,0,0,2,0,1},{1,0,0,0,1,1},{0,1,0,0,1,1},{0,0,1,0,1,1},
		  {0,0,0,1,1,1},{0,0,0,0,2,1},{1,0,0,0,0,2},{0,1,0,0,0,2},
		  {0,0,1,0,0,2},{0,0,0,1,0,2},{0,0,0,0,1,2},{0,0,0,0,0,3},
		  {4,0,0,0,0,0},{3,1,0,0,0,0},{2,2,0,0,0,0},{1,3,0,0,0,0},
		  {0,4,0,0,0,0},{3,0,1,0,0,0},{2,1,1,0,0,0},{1,2,1,0,0,0},
		  {0,3,1,0,0,0},{2,0,2,0,0,0},{1,1,2,0,0,0},{0,2,2,0,0,0},
		  {1,0,3,0,0,0},{0,1,3,0,0,0},{0,0,4,0,0,0},{3,0,0,1,0,0},
		  {2,1,0,1,0,0},{1,2,0,1,0,0},{0,3,0,1,0,0},{2,0,1,1,0,0},
		  {1,1,1,1,0,0},{0,2,1,1,0,0},{1,0,2,1,0,0},{0,1,2,1,0,0},
		  {0,0,3,1,0,0},{2,0,0,2,0,0},{1,1,0,2,0,0},{0,2,0,2,0,0},
		  {1,0,1,2,0,0},{0,1,1,2,0,0},{0,0,2,2,0,0},{1,0,0,3,0,0},
		  {0,1,0,3,0,0},{0,0,1,3,0,0},{0,0,0,4,0,0},{3,0,0,0,1,0},
		  {2,1,0,0,1,0},{1,2,0,0,1,0},{0,3,0,0,1,0},{2,0,1,0,1,0},
		  {1,1,1,0,1,0},{0,2,1,0,1,0},{1,0,2,0,1,0},{0,1,2,0,1,0},
		  {0,0,3,0,1,0},{2,0,0,1,1,0},{1,1,0,1,1,0},{0,2,0,1,1,0},
		  {1,0,1,1,1,0},{0,1,1,1,1,0},{0,0,2,1,1,0},{1,0,0,2,1,0},
		  {0,1,0,2,1,0},{0,0,1,2,1,0},{0,0,0,3,1,0},{2,0,0,0,2,0},
		  {1,1,0,0,2,0},{0,2,0,0,2,0},{1,0,1,0,2,0},{0,1,1,0,2,0},
		  {0,0,2,0,2,0},{1,0,0,1,2,0},{0,1,0,1,2,0},{0,0,1,1,2,0},
		  {0,0,0,2,2,0},{1,0,0,0,3,0},{0,1,0,0,3,0},{0,0,1,0,3,0},
		  {0,0,0,1,3,0},{0,0,0,0,4,0},{3,0,0,0,0,1},{2,1,0,0,0,1},
		  {1,2,0,0,0,1},{0,3,0,0,0,1},{2,0,1,0,0,1},{1,1,1,0,0,1},
		  {0,2,1,0,0,1},{1,0,2,0,0,1},{0,1,2,0,0,1},{0,0,3,0,0,1},
		  {2,0,0,1,0,1},{1,1,0,1,0,1},{0,2,0,1,0,1},{1,0,1,1,0,1},
		  {0,1,1,1,0,1},{0,0,2,1,0,1},{1,0,0,2,0,1},{0,1,0,2,0,1},
		  {0,0,1,2,0,1},{0,0,0,3,0,1},{2,0,0,0,1,1},{1,1,0,0,1,1},
		  {0,2,0,0,1,1},{1,0,1,0,1,1},{0,1,1,0,1,1},{0,0,2,0,1,1},
		  {1,0,0,1,1,1},{0,1,0,1,1,1},{0,0,1,1,1,1},{0,0,0,2,1,1},
		  {1,0,0,0,2,1},{0,1,0,0,2,1},{0,0,1,0,2,1},{0,0,0,1,2,1},
		  {0,0,0,0,3,1},{2,0,0,0,0,2},{1,1,0,0,0,2},{0,2,0,0,0,2},
		  {1,0,1,0,0,2},{0,1,1,0,0,2},{0,0,2,0,0,2},{1,0,0,1,0,2},
		  {0,1,0,1,0,2},{0,0,1,1,0,2},{0,0,0,2,0,2},{1,0,0,0,1,2},
		  {0,1,0,0,1,2},{0,0,1,0,1,2},{0,0,0,1,1,2},{0,0,0,0,2,2},
		  {1,0,0,0,0,3},{0,1,0,0,0,3},{0,0,1,0,0,3},{0,0,0,1,0,3},
		  {0,0,0,0,1,3},{0,0,0,0,0,4},
		  {5,0,0,0,0,0},{4,1,0,0,0,0},{3,2,0,0,0,0},{2,3,0,0,0,0},
		  {1,4,0,0,0,0},{0,5,0,0,0,0},{4,0,1,0,0,0},{3,1,1,0,0,0},
		  {2,2,1,0,0,0},{1,3,1,0,0,0},{0,4,1,0,0,0},{3,0,2,0,0,0},
		  {2,1,2,0,0,0},{1,2,2,0,0,0},{0,3,2,0,0,0},{2,0,3,0,0,0},
		  {1,1,3,0,0,0},{0,2,3,0,0,0},{1,0,4,0,0,0},{0,1,4,0,0,0},
		  {0,0,5,0,0,0},{4,0,0,1,0,0},{3,1,0,1,0,0},{2,2,0,1,0,0},
		  {1,3,0,1,0,0},{0,4,0,1,0,0},{3,0,1,1,0,0},{2,1,1,1,0,0},
		  {1,2,1,1,0,0},{0,3,1,1,0,0},{2,0,2,1,0,0},{1,1,2,1,0,0},
		  {0,2,2,1,0,0},{1,0,3,1,0,0},{0,1,3,1,0,0},{0,0,4,1,0,0},
		  {3,0,0,2,0,0},{2,1,0,2,0,0},{1,2,0,2,0,0},{0,3,0,2,0,0},
		  {2,0,1,2,0,0},{1,1,1,2,0,0},{0,2,1,2,0,0},{1,0,2,2,0,0},
		  {0,1,2,2,0,0},{0,0,3,2,0,0},{2,0,0,3,0,0},{1,1,0,3,0,0},
		  {0,2,0,3,0,0},{1,0,1,3,0,0},{0,1,1,3,0,0},{0,0,2,3,0,0},
		  {1,0,0,4,0,0},{0,1,0,4,0,0},{0,0,1,4,0,0},{0,0,0,5,0,0},
		  {4,0,0,0,1,0},{3,1,0,0,1,0},{2,2,0,0,1,0},{1,3,0,0,1,0},
		  {0,4,0,0,1,0},{3,0,1,0,1,0},{2,1,1,0,1,0},{1,2,1,0,1,0},
		  {0,3,1,0,1,0},{2,0,2,0,1,0},{1,1,2,0,1,0},{0,2,2,0,1,0},
		  {1,0,3,0,1,0},{0,1,3,0,1,0},{0,0,4,0,1,0},{3,0,0,1,1,0},
		  {2,1,0,1,1,0},{1,2,0,1,1,0},{0,3,0,1,1,0},{2,0,1,1,1,0},
		  {1,1,1,1,1,0},{0,2,1,1,1,0},{1,0,2,1,1,0},{0,1,2,1,1,0},
		  {0,0,3,1,1,0},{2,0,0,2,1,0},{1,1,0,2,1,0},{0,2,0,2,1,0},
		  {1,0,1,2,1,0},{0,1,1,2,1,0},{0,0,2,2,1,0},{1,0,0,3,1,0},
		  {0,1,0,3,1,0},{0,0,1,3,1,0},{0,0,0,4,1,0},{3,0,0,0,2,0},
		  {2,1,0,0,2,0},{1,2,0,0,2,0},{0,3,0,0,2,0},{2,0,1,0,2,0},
		  {1,1,1,0,2,0},{0,2,1,0,2,0},{1,0,2,0,2,0},{0,1,2,0,2,0},
		  {0,0,3,0,2,0},{2,0,0,1,2,0},{1,1,0,1,2,0},{0,2,0,1,2,0},
		  {1,0,1,1,2,0},{0,1,1,1,2,0},{0,0,2,1,2,0},{1,0,0,2,2,0},
		  {0,1,0,2,2,0},{0,0,1,2,2,0},{0,0,0,3,2,0},{2,0,0,0,3,0},
		  {1,1,0,0,3,0},{0,2,0,0,3,0},{1,0,1,0,3,0},{0,1,1,0,3,0},
		  {0,0,2,0,3,0},{1,0,0,1,3,0},{0,1,0,1,3,0},{0,0,1,1,3,0},
		  {0,0,0,2,3,0},{1,0,0,0,4,0},{0,1,0,0,4,0},{0,0,1,0,4,0},
		  {0,0,0,1,4,0},{0,0,0,0,5,0},{4,0,0,0,0,1},{3,1,0,0,0,1},
		  {2,2,0,0,0,1},{1,3,0,0,0,1},{0,4,0,0,0,1},{3,0,1,0,0,1},
		  {2,1,1,0,0,1},{1,2,1,0,0,1},{0,3,1,0,0,1},{2,0,2,0,0,1},
		  {1,1,2,0,0,1},{0,2,2,0,0,1},{1,0,3,0,0,1},{0,1,3,0,0,1},
		  {0,0,4,0,0,1},{3,0,0,1,0,1},{2,1,0,1,0,1},{1,2,0,1,0,1},
		  {0,3,0,1,0,1},{2,0,1,1,0,1},{1,1,1,1,0,1},{0,2,1,1,0,1},
		  {1,0,2,1,0,1},{0,1,2,1,0,1},{0,0,3,1,0,1},{2,0,0,2,0,1},
		  {1,1,0,2,0,1},{0,2,0,2,0,1},{1,0,1,2,0,1},{0,1,1,2,0,1},
		  {0,0,2,2,0,1},{1,0,0,3,0,1},{0,1,0,3,0,1},{0,0,1,3,0,1},
		  {0,0,0,4,0,1},{3,0,0,0,1,1},{2,1,0,0,1,1},{1,2,0,0,1,1},
		  {0,3,0,0,1,1},{2,0,1,0,1,1},{1,1,1,0,1,1},{0,2,1,0,1,1},
		  {1,0,2,0,1,1},{0,1,2,0,1,1},{0,0,3,0,1,1},{2,0,0,1,1,1},
		  {1,1,0,1,1,1},{0,2,0,1,1,1},{1,0,1,1,1,1},{0,1,1,1,1,1},
		  {0,0,2,1,1,1},{1,0,0,2,1,1},{0,1,0,2,1,1},{0,0,1,2,1,1},
		  {0,0,0,3,1,1},{2,0,0,0,2,1},{1,1,0,0,2,1},{0,2,0,0,2,1},
		  {1,0,1,0,2,1},{0,1,1,0,2,1},{0,0,2,0,2,1},{1,0,0,1,2,1},
		  {0,1,0,1,2,1},{0,0,1,1,2,1},{0,0,0,2,2,1},{1,0,0,0,3,1},
		  {0,1,0,0,3,1},{0,0,1,0,3,1},{0,0,0,1,3,1},{0,0,0,0,4,1},
		  {3,0,0,0,0,2},{2,1,0,0,0,2},{1,2,0,0,0,2},{0,3,0,0,0,2},
		  {2,0,1,0,0,2},{1,1,1,0,0,2},{0,2,1,0,0,2},{1,0,2,0,0,2},
		  {0,1,2,0,0,2},{0,0,3,0,0,2},{2,0,0,1,0,2},{1,1,0,1,0,2},
		  {0,2,0,1,0,2},{1,0,1,1,0,2},{0,1,1,1,0,2},{0,0,2,1,0,2},
		  {1,0,0,2,0,2},{0,1,0,2,0,2},{0,0,1,2,0,2},{0,0,0,3,0,2},
		  {2,0,0,0,1,2},{1,1,0,0,1,2},{0,2,0,0,1,2},{1,0,1,0,1,2},
		  {0,1,1,0,1,2},{0,0,2,0,1,2},{1,0,0,1,1,2},{0,1,0,1,1,2},
		  {0,0,1,1,1,2},{0,0,0,2,1,2},{1,0,0,0,2,2},{0,1,0,0,2,2},
		  {0,0,1,0,2,2},{0,0,0,1,2,2},{0,0,0,0,3,2},{2,0,0,0,0,3},
		  {1,1,0,0,0,3},{0,2,0,0,0,3},{1,0,1,0,0,3},{0,1,1,0,0,3},
		  {0,0,2,0,0,3},{1,0,0,1,0,3},{0,1,0,1,0,3},{0,0,1,1,0,3},
		  {0,0,0,2,0,3},{1,0,0,0,1,3},{0,1,0,0,1,3},{0,0,1,0,1,3},
		  {0,0,0,1,1,3},{0,0,0,0,2,3},{1,0,0,0,0,4},{0,1,0,0,0,4},
		  {0,0,1,0,0,4},{0,0,0,1,0,4},{0,0,0,0,1,4},{0,0,0,0,0,5},
		  {6,0,0,0,0,0},{5,1,0,0,0,0},{4,2,0,0,0,0},{3,3,0,0,0,0},
		  {2,4,0,0,0,0},{1,5,0,0,0,0},{0,6,0,0,0,0},{5,0,1,0,0,0},
		  {4,1,1,0,0,0},{3,2,1,0,0,0},{2,3,1,0,0,0},{1,4,1,0,0,0},
		  {0,5,1,0,0,0},{4,0,2,0,0,0},{3,1,2,0,0,0},{2,2,2,0,0,0},
		  {1,3,2,0,0,0},{0,4,2,0,0,0},{3,0,3,0,0,0},{2,1,3,0,0,0},
		  {1,2,3,0,0,0},{0,3,3,0,0,0},{2,0,4,0,0,0},{1,1,4,0,0,0},
		  {0,2,4,0,0,0},{1,0,5,0,0,0},{0,1,5,0,0,0},{0,0,6,0,0,0},
		  {5,0,0,1,0,0},{4,1,0,1,0,0},{3,2,0,1,0,0},{2,3,0,1,0,0},
		  {1,4,0,1,0,0},{0,5,0,1,0,0},{4,0,1,1,0,0},{3,1,1,1,0,0},
		  {2,2,1,1,0,0},{1,3,1,1,0,0},{0,4,1,1,0,0},{3,0,2,1,0,0},
		  {2,1,2,1,0,0},{1,2,2,1,0,0},{0,3,2,1,0,0},{2,0,3,1,0,0},
		  {1,1,3,1,0,0},{0,2,3,1,0,0},{1,0,4,1,0,0},{0,1,4,1,0,0},
		  {0,0,5,1,0,0},{4,0,0,2,0,0},{3,1,0,2,0,0},{2,2,0,2,0,0},
		  {1,3,0,2,0,0},{0,4,0,2,0,0},{3,0,1,2,0,0},{2,1,1,2,0,0},
		  {1,2,1,2,0,0},{0,3,1,2,0,0},{2,0,2,2,0,0},{1,1,2,2,0,0},
		  {0,2,2,2,0,0},{1,0,3,2,0,0},{0,1,3,2,0,0},{0,0,4,2,0,0},
		  {3,0,0,3,0,0},{2,1,0,3,0,0},{1,2,0,3,0,0},{0,3,0,3,0,0},
		  {2,0,1,3,0,0},{1,1,1,3,0,0},{0,2,1,3,0,0},{1,0,2,3,0,0},
		  {0,1,2,3,0,0},{0,0,3,3,0,0},{2,0,0,4,0,0},{1,1,0,4,0,0},
		  {0,2,0,4,0,0},{1,0,1,4,0,0},{0,1,1,4,0,0},{0,0,2,4,0,0},
		  {1,0,0,5,0,0},{0,1,0,5,0,0},{0,0,1,5,0,0},{0,0,0,6,0,0},
		  {5,0,0,0,1,0},{4,1,0,0,1,0},{3,2,0,0,1,0},{2,3,0,0,1,0},
		  {1,4,0,0,1,0},{0,5,0,0,1,0},{4,0,1,0,1,0},{3,1,1,0,1,0},
		  {2,2,1,0,1,0},{1,3,1,0,1,0},{0,4,1,0,1,0},{3,0,2,0,1,0},
		  {2,1,2,0,1,0},{1,2,2,0,1,0},{0,3,2,0,1,0},{2,0,3,0,1,0},
		  {1,1,3,0,1,0},{0,2,3,0,1,0},{1,0,4,0,1,0},{0,1,4,0,1,0},
		  {0,0,5,0,1,0},{4,0,0,1,1,0},{3,1,0,1,1,0},{2,2,0,1,1,0},
		  {1,3,0,1,1,0},{0,4,0,1,1,0},{3,0,1,1,1,0},{2,1,1,1,1,0},
		  {1,2,1,1,1,0},{0,3,1,1,1,0},{2,0,2,1,1,0},{1,1,2,1,1,0},
		  {0,2,2,1,1,0},{1,0,3,1,1,0},{0,1,3,1,1,0},{0,0,4,1,1,0},
		  {3,0,0,2,1,0},{2,1,0,2,1,0},{1,2,0,2,1,0},{0,3,0,2,1,0},
		  {2,0,1,2,1,0},{1,1,1,2,1,0},{0,2,1,2,1,0},{1,0,2,2,1,0},
		  {0,1,2,2,1,0},{0,0,3,2,1,0},{2,0,0,3,1,0},{1,1,0,3,1,0},
		  {0,2,0,3,1,0},{1,0,1,3,1,0},{0,1,1,3,1,0},{0,0,2,3,1,0},
		  {1,0,0,4,1,0},{0,1,0,4,1,0},{0,0,1,4,1,0},{0,0,0,5,1,0},
		  {4,0,0,0,2,0},{3,1,0,0,2,0},{2,2,0,0,2,0},{1,3,0,0,2,0},
		  {0,4,0,0,2,0},{3,0,1,0,2,0},{2,1,1,0,2,0},{1,2,1,0,2,0},
		  {0,3,1,0,2,0},{2,0,2,0,2,0},{1,1,2,0,2,0},{0,2,2,0,2,0},
		  {1,0,3,0,2,0},{0,1,3,0,2,0},{0,0,4,0,2,0},{3,0,0,1,2,0},
		  {2,1,0,1,2,0},{1,2,0,1,2,0},{0,3,0,1,2,0},{2,0,1,1,2,0},
		  {1,1,1,1,2,0},{0,2,1,1,2,0},{1,0,2,1,2,0},{0,1,2,1,2,0},
		  {0,0,3,1,2,0},{2,0,0,2,2,0},{1,1,0,2,2,0},{0,2,0,2,2,0},
		  {1,0,1,2,2,0},{0,1,1,2,2,0},{0,0,2,2,2,0},{1,0,0,3,2,0},
		  {0,1,0,3,2,0},{0,0,1,3,2,0},{0,0,0,4,2,0},{3,0,0,0,3,0},
		  {2,1,0,0,3,0},{1,2,0,0,3,0},{0,3,0,0,3,0},{2,0,1,0,3,0},
		  {1,1,1,0,3,0},{0,2,1,0,3,0},{1,0,2,0,3,0},{0,1,2,0,3,0},
		  {0,0,3,0,3,0},{2,0,0,1,3,0},{1,1,0,1,3,0},{0,2,0,1,3,0},
		  {1,0,1,1,3,0},{0,1,1,1,3,0},{0,0,2,1,3,0},{1,0,0,2,3,0},
		  {0,1,0,2,3,0},{0,0,1,2,3,0},{0,0,0,3,3,0},{2,0,0,0,4,0},
		  {1,1,0,0,4,0},{0,2,0,0,4,0},{1,0,1,0,4,0},{0,1,1,0,4,0},
		  {0,0,2,0,4,0},{1,0,0,1,4,0},{0,1,0,1,4,0},{0,0,1,1,4,0},
		  {0,0,0,2,4,0},{1,0,0,0,5,0},{0,1,0,0,5,0},{0,0,1,0,5,0},
		  {0,0,0,1,5,0},{0,0,0,0,6,0},{5,0,0,0,0,1},{4,1,0,0,0,1},
		  {3,2,0,0,0,1},{2,3,0,0,0,1},{1,4,0,0,0,1},{0,5,0,0,0,1},
		  {4,0,1,0,0,1},{3,1,1,0,0,1},{2,2,1,0,0,1},{1,3,1,0,0,1},
		  {0,4,1,0,0,1},{3,0,2,0,0,1},{2,1,2,0,0,1},{1,2,2,0,0,1},
		  {0,3,2,0,0,1},{2,0,3,0,0,1},{1,1,3,0,0,1},{0,2,3,0,0,1},
		  {1,0,4,0,0,1},{0,1,4,0,0,1},{0,0,5,0,0,1},{4,0,0,1,0,1},
		  {3,1,0,1,0,1},{2,2,0,1,0,1},{1,3,0,1,0,1},{0,4,0,1,0,1},
		  {3,0,1,1,0,1},{2,1,1,1,0,1},{1,2,1,1,0,1},{0,3,1,1,0,1},
		  {2,0,2,1,0,1},{1,1,2,1,0,1},{0,2,2,1,0,1},{1,0,3,1,0,1},
		  {0,1,3,1,0,1},{0,0,4,1,0,1},{3,0,0,2,0,1},{2,1,0,2,0,1},
		  {1,2,0,2,0,1},{0,3,0,2,0,1},{2,0,1,2,0,1},{1,1,1,2,0,1},
		  {0,2,1,2,0,1},{1,0,2,2,0,1},{0,1,2,2,0,1},{0,0,3,2,0,1},
		  {2,0,0,3,0,1},{1,1,0,3,0,1},{0,2,0,3,0,1},{1,0,1,3,0,1},
		  {0,1,1,3,0,1},{0,0,2,3,0,1},{1,0,0,4,0,1},{0,1,0,4,0,1},
		  {0,0,1,4,0,1},{0,0,0,5,0,1},{4,0,0,0,1,1},{3,1,0,0,1,1},
		  {2,2,0,0,1,1},{1,3,0,0,1,1},{0,4,0,0,1,1},{3,0,1,0,1,1},
		  {2,1,1,0,1,1},{1,2,1,0,1,1},{0,3,1,0,1,1},{2,0,2,0,1,1},
		  {1,1,2,0,1,1},{0,2,2,0,1,1},{1,0,3,0,1,1},{0,1,3,0,1,1},
		  {0,0,4,0,1,1},{3,0,0,1,1,1},{2,1,0,1,1,1},{1,2,0,1,1,1},
		  {0,3,0,1,1,1},{2,0,1,1,1,1},{1,1,1,1,1,1},{0,2,1,1,1,1},
		  {1,0,2,1,1,1},{0,1,2,1,1,1},{0,0,3,1,1,1},{2,0,0,2,1,1},
		  {1,1,0,2,1,1},{0,2,0,2,1,1},{1,0,1,2,1,1},{0,1,1,2,1,1},
		  {0,0,2,2,1,1},{1,0,0,3,1,1},{0,1,0,3,1,1},{0,0,1,3,1,1},
		  {0,0,0,4,1,1},{3,0,0,0,2,1},{2,1,0,0,2,1},{1,2,0,0,2,1},
		  {0,3,0,0,2,1},{2,0,1,0,2,1},{1,1,1,0,2,1},{0,2,1,0,2,1},
		  {1,0,2,0,2,1},{0,1,2,0,2,1},{0,0,3,0,2,1},{2,0,0,1,2,1},
		  {1,1,0,1,2,1},{0,2,0,1,2,1},{1,0,1,1,2,1},{0,1,1,1,2,1},
		  {0,0,2,1,2,1},{1,0,0,2,2,1},{0,1,0,2,2,1},{0,0,1,2,2,1},
		  {0,0,0,3,2,1},{2,0,0,0,3,1},{1,1,0,0,3,1},{0,2,0,0,3,1},
		  {1,0,1,0,3,1},{0,1,1,0,3,1},{0,0,2,0,3,1},{1,0,0,1,3,1},
		  {0,1,0,1,3,1},{0,0,1,1,3,1},{0,0,0,2,3,1},{1,0,0,0,4,1},
		  {0,1,0,0,4,1},{0,0,1,0,4,1},{0,0,0,1,4,1},{0,0,0,0,5,1},
		  {4,0,0,0,0,2},{3,1,0,0,0,2},{2,2,0,0,0,2},{1,3,0,0,0,2},
		  {0,4,0,0,0,2},{3,0,1,0,0,2},{2,1,1,0,0,2},{1,2,1,0,0,2},
		  {0,3,1,0,0,2},{2,0,2,0,0,2},{1,1,2,0,0,2},{0,2,2,0,0,2},
		  {1,0,3,0,0,2},{0,1,3,0,0,2},{0,0,4,0,0,2},{3,0,0,1,0,2},
		  {2,1,0,1,0,2},{1,2,0,1,0,2},{0,3,0,1,0,2},{2,0,1,1,0,2},
		  {1,1,1,1,0,2},{0,2,1,1,0,2},{1,0,2,1,0,2},{0,1,2,1,0,2},
		  {0,0,3,1,0,2},{2,0,0,2,0,2},{1,1,0,2,0,2},{0,2,0,2,0,2},
		  {1,0,1,2,0,2},{0,1,1,2,0,2},{0,0,2,2,0,2},{1,0,0,3,0,2},
		  {0,1,0,3,0,2},{0,0,1,3,0,2},{0,0,0,4,0,2},{3,0,0,0,1,2},
		  {2,1,0,0,1,2},{1,2,0,0,1,2},{0,3,0,0,1,2},{2,0,1,0,1,2},
		  {1,1,1,0,1,2},{0,2,1,0,1,2},{1,0,2,0,1,2},{0,1,2,0,1,2},
		  {0,0,3,0,1,2},{2,0,0,1,1,2},{1,1,0,1,1,2},{0,2,0,1,1,2},
		  {1,0,1,1,1,2},{0,1,1,1,1,2},{0,0,2,1,1,2},{1,0,0,2,1,2},
		  {0,1,0,2,1,2},{0,0,1,2,1,2},{0,0,0,3,1,2},{2,0,0,0,2,2},
		  {1,1,0,0,2,2},{0,2,0,0,2,2},{1,0,1,0,2,2},{0,1,1,0,2,2},
		  {0,0,2,0,2,2},{1,0,0,1,2,2},{0,1,0,1,2,2},{0,0,1,1,2,2},
		  {0,0,0,2,2,2},{1,0,0,0,3,2},{0,1,0,0,3,2},{0,0,1,0,3,2},
		  {0,0,0,1,3,2},{0,0,0,0,4,2},{3,0,0,0,0,3},{2,1,0,0,0,3},
		  {1,2,0,0,0,3},{0,3,0,0,0,3},{2,0,1,0,0,3},{1,1,1,0,0,3},
		  {0,2,1,0,0,3},{1,0,2,0,0,3},{0,1,2,0,0,3},{0,0,3,0,0,3},
		  {2,0,0,1,0,3},{1,1,0,1,0,3},{0,2,0,1,0,3},{1,0,1,1,0,3},
		  {0,1,1,1,0,3},{0,0,2,1,0,3},{1,0,0,2,0,3},{0,1,0,2,0,3},
		  {0,0,1,2,0,3},{0,0,0,3,0,3},{2,0,0,0,1,3},{1,1,0,0,1,3},
		  {0,2,0,0,1,3},{1,0,1,0,1,3},{0,1,1,0,1,3},{0,0,2,0,1,3},
		  {1,0,0,1,1,3},{0,1,0,1,1,3},{0,0,1,1,1,3},{0,0,0,2,1,3},
		  {1,0,0,0,2,3},{0,1,0,0,2,3},{0,0,1,0,2,3},{0,0,0,1,2,3},
		  {0,0,0,0,3,3},{2,0,0,0,0,4},{1,1,0,0,0,4},{0,2,0,0,0,4},
		  {1,0,1,0,0,4},{0,1,1,0,0,4},{0,0,2,0,0,4},{1,0,0,1,0,4},
		  {0,1,0,1,0,4},{0,0,1,1,0,4},{0,0,0,2,0,4},{1,0,0,0,1,4},
		  {0,1,0,0,1,4},{0,0,1,0,1,4},{0,0,0,1,1,4},{0,0,0,0,2,4},
		  {1,0,0,0,0,5},{0,1,0,0,0,5},{0,0,1,0,0,5},{0,0,0,1,0,5},
		  {0,0,0,0,1,5},{0,0,0,0,0,6}};
    nnn = pwrsix[n+1];
    Apwr = new int[nnn]; // powers of each variable in a term
    Bpwr = new int[nnn];
    Cpwr = new int[nnn];
    Dpwr = new int[nnn];
    Epwr = new int[nnn];
    Fpwr = new int[nnn];

    if(debug) System.out.println("terms used to find fit ");
    for(int i=0; i<=n; i++) // power requested 
    {
      for(int ii=pwrsix[i]; ii<pwrsix[i+1]; ii++)
      {
	Apwr[ii]=pwrs[ii][0];
	Bpwr[ii]=pwrs[ii][1];
	Cpwr[ii]=pwrs[ii][2];
	Dpwr[ii]=pwrs[ii][3];
	Epwr[ii]=pwrs[ii][4];
	Fpwr[ii]=pwrs[ii][5];
	if(debug)System.out.println(ii+"   a^"+Apwr[ii]+
                                       " * b^"+Bpwr[ii]+
                                       " * c^"+Cpwr[ii]+
                                       " * d^"+Dpwr[ii]+
                                       " * e^"+Epwr[ii]+
                                       " * f^"+Fpwr[ii]);
      }
      if(debug) System.out.println(" ");
    }
  } /* end gen_6d_powers */

  void gen_7d_powers()
  {
    int pwrsix[]={0,1,8,36,120,330}; // start of each order
    int pwrs[][]={
{0,0,0,0,0,0,0},

{1,0,0,0,0,0,0},
{0,1,0,0,0,0,0},
{0,0,1,0,0,0,0},
{0,0,0,1,0,0,0},
{0,0,0,0,1,0,0},
{0,0,0,0,0,1,0},
{0,0,0,0,0,0,1},

{2,0,0,0,0,0,0},
{1,1,0,0,0,0,0},
{0,2,0,0,0,0,0},
{1,0,1,0,0,0,0},
{0,1,1,0,0,0,0},
{0,0,2,0,0,0,0},
{1,0,0,1,0,0,0},
{0,1,0,1,0,0,0},
{0,0,1,1,0,0,0},
{0,0,0,2,0,0,0},
{1,0,0,0,1,0,0},
{0,1,0,0,1,0,0},
{0,0,1,0,1,0,0},
{0,0,0,1,1,0,0},
{0,0,0,0,2,0,0},
{1,0,0,0,0,1,0},
{0,1,0,0,0,1,0},
{0,0,1,0,0,1,0},
{0,0,0,1,0,1,0},
{0,0,0,0,1,1,0},
{0,0,0,0,0,2,0},
{1,0,0,0,0,0,1},
{0,1,0,0,0,0,1},
{0,0,1,0,0,0,1},
{0,0,0,1,0,0,1},
{0,0,0,0,1,0,1},
{0,0,0,0,0,1,1},
{0,0,0,0,0,0,2},

{3,0,0,0,0,0,0},
{2,1,0,0,0,0,0},
{1,2,0,0,0,0,0},
{0,3,0,0,0,0,0},
{2,0,1,0,0,0,0},
{1,1,1,0,0,0,0},
{0,2,1,0,0,0,0},
{1,0,2,0,0,0,0},
{0,1,2,0,0,0,0},
{0,0,3,0,0,0,0},
{2,0,0,1,0,0,0},
{1,1,0,1,0,0,0},
{0,2,0,1,0,0,0},
{1,0,1,1,0,0,0},
{0,1,1,1,0,0,0},
{0,0,2,1,0,0,0},
{1,0,0,2,0,0,0},
{0,1,0,2,0,0,0},
{0,0,1,2,0,0,0},
{0,0,0,3,0,0,0},
{2,0,0,0,1,0,0},
{1,1,0,0,1,0,0},
{0,2,0,0,1,0,0},
{1,0,1,0,1,0,0},
{0,1,1,0,1,0,0},
{0,0,2,0,1,0,0},
{1,0,0,1,1,0,0},
{0,1,0,1,1,0,0},
{0,0,1,1,1,0,0},
{0,0,0,2,1,0,0},
{1,0,0,0,2,0,0},
{0,1,0,0,2,0,0},
{0,0,1,0,2,0,0},
{0,0,0,1,2,0,0},
{0,0,0,0,3,0,0},
{2,0,0,0,0,1,0},
{1,1,0,0,0,1,0},
{0,2,0,0,0,1,0},
{1,0,1,0,0,1,0},
{0,1,1,0,0,1,0},
{0,0,2,0,0,1,0},
{1,0,0,1,0,1,0},
{0,1,0,1,0,1,0},
{0,0,1,1,0,1,0},
{0,0,0,2,0,1,0},
{1,0,0,0,1,1,0},
{0,1,0,0,1,1,0},
{0,0,1,0,1,1,0},
{0,0,0,1,1,1,0},
{0,0,0,0,2,1,0},
{1,0,0,0,0,2,0},
{0,1,0,0,0,2,0},
{0,0,1,0,0,2,0},
{0,0,0,1,0,2,0},
{0,0,0,0,1,2,0},
{0,0,0,0,0,3,0},
{2,0,0,0,0,0,1},
{1,1,0,0,0,0,1},
{0,2,0,0,0,0,1},
{1,0,1,0,0,0,1},
{0,1,1,0,0,0,1},
{0,0,2,0,0,0,1},
{1,0,0,1,0,0,1},
{0,1,0,1,0,0,1},
{0,0,1,1,0,0,1},
{0,0,0,2,0,0,1},
{1,0,0,0,1,0,1},
{0,1,0,0,1,0,1},
{0,0,1,0,1,0,1},
{0,0,0,1,1,0,1},
{0,0,0,0,2,0,1},
{1,0,0,0,0,1,1},
{0,1,0,0,0,1,1},
{0,0,1,0,0,1,1},
{0,0,0,1,0,1,1},
{0,0,0,0,1,1,1},
{0,0,0,0,0,2,1},
{1,0,0,0,0,0,2},
{0,1,0,0,0,0,2},
{0,0,1,0,0,0,2},
{0,0,0,1,0,0,2},
{0,0,0,0,1,0,2},
{0,0,0,0,0,1,2},
{0,0,0,0,0,0,3},

{4,0,0,0,0,0,0},
{3,1,0,0,0,0,0},
{2,2,0,0,0,0,0},
{1,3,0,0,0,0,0},
{0,4,0,0,0,0,0},
{3,0,1,0,0,0,0},
{2,1,1,0,0,0,0},
{1,2,1,0,0,0,0},
{0,3,1,0,0,0,0},
{2,0,2,0,0,0,0},
{1,1,2,0,0,0,0},
{0,2,2,0,0,0,0},
{1,0,3,0,0,0,0},
{0,1,3,0,0,0,0},
{0,0,4,0,0,0,0},
{3,0,0,1,0,0,0},
{2,1,0,1,0,0,0},
{1,2,0,1,0,0,0},
{0,3,0,1,0,0,0},
{2,0,1,1,0,0,0},
{1,1,1,1,0,0,0},
{0,2,1,1,0,0,0},
{1,0,2,1,0,0,0},
{0,1,2,1,0,0,0},
{0,0,3,1,0,0,0},
{2,0,0,2,0,0,0},
{1,1,0,2,0,0,0},
{0,2,0,2,0,0,0},
{1,0,1,2,0,0,0},
{0,1,1,2,0,0,0},
{0,0,2,2,0,0,0},
{1,0,0,3,0,0,0},
{0,1,0,3,0,0,0},
{0,0,1,3,0,0,0},
{0,0,0,4,0,0,0},
{3,0,0,0,1,0,0},
{2,1,0,0,1,0,0},
{1,2,0,0,1,0,0},
{0,3,0,0,1,0,0},
{2,0,1,0,1,0,0},
{1,1,1,0,1,0,0},
{0,2,1,0,1,0,0},
{1,0,2,0,1,0,0},
{0,1,2,0,1,0,0},
{0,0,3,0,1,0,0},
{2,0,0,1,1,0,0},
{1,1,0,1,1,0,0},
{0,2,0,1,1,0,0},
{1,0,1,1,1,0,0},
{0,1,1,1,1,0,0},
{0,0,2,1,1,0,0},
{1,0,0,2,1,0,0},
{0,1,0,2,1,0,0},
{0,0,1,2,1,0,0},
{0,0,0,3,1,0,0},
{2,0,0,0,2,0,0},
{1,1,0,0,2,0,0},
{0,2,0,0,2,0,0},
{1,0,1,0,2,0,0},
{0,1,1,0,2,0,0},
{0,0,2,0,2,0,0},
{1,0,0,1,2,0,0},
{0,1,0,1,2,0,0},
{0,0,1,1,2,0,0},
{0,0,0,2,2,0,0},
{1,0,0,0,3,0,0},
{0,1,0,0,3,0,0},
{0,0,1,0,3,0,0},
{0,0,0,1,3,0,0},
{0,0,0,0,4,0,0},
{3,0,0,0,0,1,0},
{2,1,0,0,0,1,0},
{1,2,0,0,0,1,0},
{0,3,0,0,0,1,0},
{2,0,1,0,0,1,0},
{1,1,1,0,0,1,0},
{0,2,1,0,0,1,0},
{1,0,2,0,0,1,0},
{0,1,2,0,0,1,0},
{0,0,3,0,0,1,0},
{2,0,0,1,0,1,0},
{1,1,0,1,0,1,0},
{0,2,0,1,0,1,0},
{1,0,1,1,0,1,0},
{0,1,1,1,0,1,0},
{0,0,2,1,0,1,0},
{1,0,0,2,0,1,0},
{0,1,0,2,0,1,0},
{0,0,1,2,0,1,0},
{0,0,0,3,0,1,0},
{2,0,0,0,1,1,0},
{1,1,0,0,1,1,0},
{0,2,0,0,1,1,0},
{1,0,1,0,1,1,0},
{0,1,1,0,1,1,0},
{0,0,2,0,1,1,0},
{1,0,0,1,1,1,0},
{0,1,0,1,1,1,0},
{0,0,1,1,1,1,0},
{0,0,0,2,1,1,0},
{1,0,0,0,2,1,0},
{0,1,0,0,2,1,0},
{0,0,1,0,2,1,0},
{0,0,0,1,2,1,0},
{0,0,0,0,3,1,0},
{2,0,0,0,0,2,0},
{1,1,0,0,0,2,0},
{0,2,0,0,0,2,0},
{1,0,1,0,0,2,0},
{0,1,1,0,0,2,0},
{0,0,2,0,0,2,0},
{1,0,0,1,0,2,0},
{0,1,0,1,0,2,0},
{0,0,1,1,0,2,0},
{0,0,0,2,0,2,0},
{1,0,0,0,1,2,0},
{0,1,0,0,1,2,0},
{0,0,1,0,1,2,0},
{0,0,0,1,1,2,0},
{0,0,0,0,2,2,0},
{1,0,0,0,0,3,0},
{0,1,0,0,0,3,0},
{0,0,1,0,0,3,0},
{0,0,0,1,0,3,0},
{0,0,0,0,1,3,0},
{0,0,0,0,0,4,0},
{3,0,0,0,0,0,1},
{2,1,0,0,0,0,1},
{1,2,0,0,0,0,1},
{0,3,0,0,0,0,1},
{2,0,1,0,0,0,1},
{1,1,1,0,0,0,1},
{0,2,1,0,0,0,1},
{1,0,2,0,0,0,1},
{0,1,2,0,0,0,1},
{0,0,3,0,0,0,1},
{2,0,0,1,0,0,1},
{1,1,0,1,0,0,1},
{0,2,0,1,0,0,1},
{1,0,1,1,0,0,1},
{0,1,1,1,0,0,1},
{0,0,2,1,0,0,1},
{1,0,0,2,0,0,1},
{0,1,0,2,0,0,1},
{0,0,1,2,0,0,1},
{0,0,0,3,0,0,1},
{2,0,0,0,1,0,1},
{1,1,0,0,1,0,1},
{0,2,0,0,1,0,1},
{1,0,1,0,1,0,1},
{0,1,1,0,1,0,1},
{0,0,2,0,1,0,1},
{1,0,0,1,1,0,1},
{0,1,0,1,1,0,1},
{0,0,1,1,1,0,1},
{0,0,0,2,1,0,1},
{1,0,0,0,2,0,1},
{0,1,0,0,2,0,1},
{0,0,1,0,2,0,1},
{0,0,0,1,2,0,1},
{0,0,0,0,3,0,1},
{2,0,0,0,0,1,1},
{1,1,0,0,0,1,1},
{0,2,0,0,0,1,1},
{1,0,1,0,0,1,1},
{0,1,1,0,0,1,1},
{0,0,2,0,0,1,1},
{1,0,0,1,0,1,1},
{0,1,0,1,0,1,1},
{0,0,1,1,0,1,1},
{0,0,0,2,0,1,1},
{1,0,0,0,1,1,1},
{0,1,0,0,1,1,1},
{0,0,1,0,1,1,1},
{0,0,0,1,1,1,1},
{0,0,0,0,2,1,1},
{1,0,0,0,0,2,1},
{0,1,0,0,0,2,1},
{0,0,1,0,0,2,1},
{0,0,0,1,0,2,1},
{0,0,0,0,1,2,1},
{0,0,0,0,0,3,1},
{2,0,0,0,0,0,2},
{1,1,0,0,0,0,2},
{0,2,0,0,0,0,2},
{1,0,1,0,0,0,2},
{0,1,1,0,0,0,2},
{0,0,2,0,0,0,2},
{1,0,0,1,0,0,2},
{0,1,0,1,0,0,2},
{0,0,1,1,0,0,2},
{0,0,0,2,0,0,2},
{1,0,0,0,1,0,2},
{0,1,0,0,1,0,2},
{0,0,1,0,1,0,2},
{0,0,0,1,1,0,2},
{0,0,0,0,2,0,2},
{1,0,0,0,0,1,2},
{0,1,0,0,0,1,2},
{0,0,1,0,0,1,2},
{0,0,0,1,0,1,2},
{0,0,0,0,1,1,2},
{0,0,0,0,0,2,2},
{1,0,0,0,0,0,3},
{0,1,0,0,0,0,3},
{0,0,1,0,0,0,3},
{0,0,0,1,0,0,3},
{0,0,0,0,1,0,3},
{0,0,0,0,0,1,3},
{0,0,0,0,0,0,4}};

    nnn = pwrsix[n+1];
    Apwr = new int[nnn]; // powers of each variable in a term
    Bpwr = new int[nnn];
    Cpwr = new int[nnn];
    Dpwr = new int[nnn];
    Epwr = new int[nnn];
    Fpwr = new int[nnn];
    Gpwr = new int[nnn];

    if(debug) System.out.println("terms used to find fit ");
    for(int i=0; i<=n; i++) // power requested 
    {
      for(int ii=pwrsix[i]; ii<pwrsix[i+1]; ii++)
      {
	Apwr[ii]=pwrs[ii][0];
	Bpwr[ii]=pwrs[ii][1];
	Cpwr[ii]=pwrs[ii][2];
	Dpwr[ii]=pwrs[ii][3];
	Epwr[ii]=pwrs[ii][4];
	Fpwr[ii]=pwrs[ii][5];
	Gpwr[ii]=pwrs[ii][6];
	if(debug)System.out.println(ii+"   a^"+Apwr[ii]+
                                       " * b^"+Bpwr[ii]+
                                       " * c^"+Cpwr[ii]+
                                       " * d^"+Dpwr[ii]+
                                       " * e^"+Epwr[ii]+
                                       " * f^"+Fpwr[ii]+
                                       " * g^"+Gpwr[ii]);
      }
      if(debug) System.out.println(" ");
    }
  } /* end gen_7d_powers */

} // end class lsfit