Type GMAP is a collection of at most NV polynomials. It foes not require the INIT for DAMAPs since it is not connected to phase space at all.

GMAP main function is to solve systems of equations defined by Taylor Series.

For example:

EQ%V(1)= 2.D0*X(1)+1.D-2*X(2)**2 + 1.D-1*X(1)*X(2) -10.D0 + 0.1d0 *(1.d0.mono.'001')
EQ%V(2)= 5.D0*X(2)+1.D-2*X(2)**2 +0.1D0*SIN(X(1)*X(2)**2)-10.D0
 

Here we have two equations and two unknowns. In addition we have a parameter in the third variable.

• 2x₁+ 10^-2 x₂² + 10^-1 x₁x₂ -10 + 10^-1 x₃ = 0

• 5x₂+ 10^-2 x₂² + 10^-1 sin(x₁x₂ ) -10  = 0

Since there are two equations to invert, the command to allocate EQ is ALLOC(EQ,2).

By default, the NV Taylor Series are allocated.

Solving these two equations is equivalent to the following inversion and evaluation:

 Solution = EQ^-1(0,0,x₃)

A TPSA inversion is given by the operator .oo.

Click here for a program solving the above equation. It is first solved with a parameter and then without.