fit_sin.adb  demonstrate that a lsfit to a specified power,
does not give the same coefficients as a truncated approximation
and is a more accurate fit.
approximation 2D power 3, sin(X+Y) =
 X + Y - (X^3 + 3X^2*Y + 3X*Y^2 + Y^3)/6
  1.000 X
  1.000 Y
 -0.166 X^3
 -0.500 X^2*Y
 -0.500 X*Y^2
 -0.166 Y^3

lsfit terms
a^ 0 b^ 0

a^ 1 b^ 0
a^ 0 b^ 1

a^ 2 b^ 0
a^ 1 b^ 1
a^ 0 b^ 2

a^ 3 b^ 0
a^ 2 b^ 1
a^ 1 b^ 2
a^ 0 b^ 3

X= 7.00000000000000E-01, Y= 1.00000000000000E+00
      Err3= 1.10498143785802E-01
X= 8.00000000000000E-01, Y= 9.00000000000000E-01
      Err3= 1.10498143785802E-01
X= 8.00000000000000E-01, Y= 1.00000000000000E+00
      Err3= 1.45847630878195E-01
X= 9.00000000000000E-01, Y= 8.00000000000000E-01
      Err3= 1.10498143785802E-01
X= 9.00000000000000E-01, Y= 9.00000000000000E-01
      Err3= 1.45847630878195E-01
X= 9.00000000000000E-01, Y= 1.00000000000000E+00
      Err3= 1.89466754354081E-01
X= 1.00000000000000E+00, Y= 7.00000000000000E-01
      Err3= 1.10498143785802E-01
X= 1.00000000000000E+00, Y= 8.00000000000000E-01
      Err3= 1.45847630878195E-01
X= 1.00000000000000E+00, Y= 9.00000000000000E-01
      Err3= 1.89466754354081E-01
X= 1.00000000000000E+00, Y= 1.00000000000000E+00
      Err3= 2.42630760159015E-01
lsfit coefficients
C(  1)= -9.1315E-03 x^0 y^0
C(  2)=  1.0716E+00 x^1 y^0
C(  3)=  1.0716E+00 x^0 y^1
C(  4)= -1.3694E-01 x^2 y^0
C(  5)= -2.7919E-01 x^1 y^1
C(  6)= -1.3694E-01 x^0 y^2
C(  7)= -8.4267E-02 x^3 y^0
C(  8)= -2.5680E-01 x^2 y^1
C(  9)= -2.5680E-01 x^1 y^2
C( 10)= -8.4267E-02 x^0 y^3
approximation 2D power 3 maxerr= 2.42630760159015E-01

lsfit 3,2 maxerr= 1.03944238908847E-02

approximation 2D power 5, sin(X+Y) =
 X + Y - (X^3 + 3X^2*Y + 3X*Y^2 + Y^3)/6 +
 (X^5 + 5X^4*Y + 10X^3*Y^2 + 10X^2*Y^2 + 5X*Y^4 + Y^5)/120

lsfit terms
a^ 0 b^ 0

a^ 1 b^ 0
a^ 0 b^ 1

a^ 2 b^ 0
a^ 1 b^ 1
a^ 0 b^ 2

a^ 3 b^ 0
a^ 2 b^ 1
a^ 1 b^ 2
a^ 0 b^ 3

a^ 4 b^ 0
a^ 3 b^ 1
a^ 2 b^ 2
a^ 1 b^ 3
a^ 0 b^ 4

a^ 5 b^ 0
a^ 4 b^ 1
a^ 3 b^ 2
a^ 2 b^ 3
a^ 1 b^ 4
a^ 0 b^ 5

X= 8.00000000000000E-01, Y= 1.00000000000000E+00
      Err5= 1.16163691218049E-02
X= 9.00000000000000E-01, Y= 9.00000000000000E-01
      Err5= 1.16163691218047E-02
X= 9.00000000000000E-01, Y= 1.00000000000000E+00
      Err5= 1.68748289792521E-02
X= 1.00000000000000E+00, Y= 8.00000000000000E-01
      Err5= 1.16163691218049E-02
X= 1.00000000000000E+00, Y= 9.00000000000000E-01
      Err5= 1.68748289792519E-02
X= 1.00000000000000E+00, Y= 1.00000000000000E+00
      Err5= 2.40359065076516E-02
lsfit coefficients
C(  1)=  8.6762E-05 x^0 y^0
C(  2)=  9.9803E-01 x^1 y^0
C(  3)=  9.9803E-01 x^0 y^1
C(  4)=  1.0595E-02 x^2 y^0
C(  5)=  1.5672E-02 x^1 y^1
C(  6)=  1.0595E-02 x^0 y^2
C(  7)= -1.8973E-01 x^3 y^0
C(  8)= -5.4328E-01 x^2 y^1
C(  9)= -5.4328E-01 x^1 y^2
C( 10)= -1.8973E-01 x^0 y^3
C( 11)=  2.2487E-02 x^4 y^0
C( 12)=  4.8456E-02 x^3 y^1
C( 13)=  7.1559E-02 x^2 y^2
C( 14)=  4.8456E-02 x^1 y^3
C( 15)=  2.2487E-02 x^0 y^4
C( 16)=  0.0000E+00 x^5 y^0
C( 17)=  2.1065E-02 x^4 y^1
C( 18)=  4.3401E-02 x^3 y^2
C( 19)=  4.3401E-02 x^2 y^3
C( 20)=  2.1065E-02 x^1 y^4
C( 21)=  0.0000E+00 x^0 y^5
approximation 2D power 5 maxerr= 2.40359065076516E-02

lsfit 5,2 maxerr= 8.67617575744907E-05

approximation 3D power 3, sin(X+Y+Z) =
 X + Y + Z -
 (X^3 + Y^3 + Z^3 + 6X*Y*Z +
  3X^2*Y + 3X^2*Z + 3X*Y^2 + 3X*Z^2 + 3*Y^2Z + 3*Y*Z^2)/6

lsfit terms
a^ 0 b^ 0 c^ 0

a^ 1 b^ 0 c^ 0
a^ 0 b^ 1 c^ 0
a^ 0 b^ 0 c^ 1

a^ 2 b^ 0 c^ 0
a^ 1 b^ 1 c^ 0
a^ 1 b^ 0 c^ 1
a^ 0 b^ 2 c^ 0
a^ 0 b^ 1 c^ 1
a^ 0 b^ 0 c^ 2

a^ 3 b^ 0 c^ 0
a^ 2 b^ 1 c^ 0
a^ 2 b^ 0 c^ 1
a^ 1 b^ 2 c^ 0
a^ 1 b^ 1 c^ 1
a^ 1 b^ 0 c^ 2
a^ 0 b^ 3 c^ 0
a^ 0 b^ 2 c^ 1
a^ 0 b^ 1 c^ 2
a^ 0 b^ 0 c^ 3

X= 6.00000000000000E-01, Y= 7.00000000000000E-01, Z= 7.00000000000000E-01
                      Err3= 2.42630760159015E-01
X= 7.00000000000000E-01, Y= 6.00000000000000E-01, Z= 7.00000000000000E-01
                      Err3= 2.42630760159015E-01
X= 7.00000000000000E-01, Y= 7.00000000000000E-01, Z= 6.00000000000000E-01
                      Err3= 2.42630760159016E-01
X= 7.00000000000000E-01, Y= 7.00000000000000E-01, Z= 7.00000000000000E-01
                      Err3= 3.06709366648874E-01
lsfit coefficients
C(  1)= -1.5578E-02 x^0 y^0 z^0
C(  2)=  1.0947E+00 x^1 y^0 z^0
C(  3)=  1.0947E+00 x^0 y^1 z^0
C(  4)=  1.0947E+00 x^0 y^0 z^1
C(  5)= -1.5986E-01 x^2 y^0 z^0
C(  6)= -3.2238E-01 x^1 y^1 z^0
C(  7)= -3.2238E-01 x^1 y^0 z^1
C(  8)= -1.5986E-01 x^0 y^2 z^0
C(  9)= -3.2238E-01 x^0 y^1 z^1
C( 10)= -1.5986E-01 x^0 y^0 z^2
C( 11)= -7.8044E-02 x^3 y^0 z^0
C( 12)= -2.3606E-01 x^2 y^1 z^0
C( 13)= -2.3606E-01 x^2 y^0 z^1
C( 14)= -2.3606E-01 x^1 y^2 z^0
C( 15)= -4.7503E-01 x^1 y^1 z^1
C( 16)= -2.3606E-01 x^1 y^0 z^2
C( 17)= -7.8044E-02 x^0 y^3 z^0
C( 18)= -2.3606E-01 x^0 y^2 z^1
C( 19)= -2.3606E-01 x^0 y^1 z^2
C( 20)= -7.8044E-02 x^0 y^0 z^3
approximation 3D power 3 maxerr= 3.06709366648874E-01

lsfit 3,3 maxerr= 1.78649639819268E-02

fit_sin.adb ending