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Functions and commands 409
polynomial_
regression
Returns the coefficients (an,...a1,a0) of
y=an*x^n+..a1x+a0), where y is the nth order polynomial
which best approximates the points whose coordinates are the
elements in two lists or the rows of a matrix.
polynomial_regression(Lst||Mtrx(A),[Lst],Intg
(n))
Example:
polynomial_regression([[1.0,1.0],[2.0,4.0],[3
.0,9.0],[4.0,16.0]],3)
gives [-0.0,1.0,-
0.0,0.0]
POLYROOT Returns the zeros of the polynomial given as argument (either
as symbolic expression or as a vector of coefficients).
POLYROOT(P(x) or Vect)
Example:
POLYROOT([1,0,-1]} returns [-1, 1]
potential Returns a function whose gradient is the vector field defined
by Vect(V) and VectVar.
potential(Vect(V),VectVar)
Example:
potential([2*x*y+3,x^2-4*z,-4*y],[x,y,z])
gives 2*x^2*y/2+3*x-4*y*z
power_regression Returns the coefficients (m,b) of y=b*x^m, where y is the
monomial which best approximates the points whose
coordinates are the elements in two lists or the rows of a
matrix.
power_regression(Lst|Mtrx(A),[Lst])
Example:
power_regression([[1.0,1.0],[2.0,4.0],[3.0,9.
0],[4.0,16.0]])
gives 2.0,1.0
powerpc Returns the real number d^2–R^2, where d is the distance
between the point and the center of the circle, and R is the
radius of the circle.
powerpc(Crcle,Pnt or Cplx)
Example:
powerpc(circle(0,1+i),3+i) gives 8