# Help System (web edition)

```Operations on polynomials with real or complex coefficients.

The following POL operations are working on polynomials saved in
MAT files (by MAT SAVE, for example). The resulting polynomials will
be found in corresponding MAT files (by MAT LOAD, for example).

POL P=P1+P2
POL P=P1-P2
POL P=P1*P2
POL Q=P1/P2       (residual not saved)
POL Q(R)=P1/P2    (R will be the residual)
POL D=DER(P)      Q(x)=P'(x) (derivative of P(x))
POL R=ROOTS(P)    Roots of algebraic equation P(x)=0
POL P=PRODUCT(R)  P(x)=(x-r1)(x-r2)... (inverse operation for ROOTS)
POL V=P(X)        V=values of polynomial P on components of vector X
POL L=LAG(P,k)    L is P(n-k) expanded to a polynomial of n.

Representation of polynomials in MAT files is described on next page.

A polynomial of degree n with complex coefficients
P(z)=A0+iB0 + (A1+iB1)z + (A2+iB2)z^2 +...+ (An+iBn)z^n
can be written as a matrix

MATRIX P ///
A0 B0
A1 B1
A2 B2
.. ..
An Bn

which must be saved in a MAT file P.MAT by MAT SAVE P.
If the coefficients are real, the second column may be omitted.
Any matrix saved as a MAT file can be used as a polynomial in the
POL operations. Eventual excessive columns 3,4,... are not used.