# The Derived Model Panel

### The Pisces Derived Model Panel.

Perhaps one of the most powerful features of Pisces is its ability to create new models from pre-existing models. This process of "deriving" a new model is carried out via the derived model panel. We call the process of converting from one model to another model a derivation.

Let F denote the current model. The domain of the model is determined by the current state of the model panel and may be changed using the permutation panel.

The currently-implemented derived models are:

None
Find level sets of the current model. The range of the current model is the same as the coded range.
Fixed Points Map
Find level sets of the model f(x) = F(x)-x. In order for this derivation to make sense, the dimension of the coded domain of F must equal the dimension of the coded range of F. Naturally, in order to compute a level set of f in Pisces, the user must inflate the domain by at least one variable using the permutation panel.
Find level sets of the system f1(x) = F(x)-x, f2(x) = det(DF(x)-I) where I is the identity matrix. In order for this derivation to make sense, the dimension of the coded domain of F must equal the dimension of the coded range of F. In order to compute a level set of f in Pisces, the user must inflate the domain by at least two variables using the permutation panel.
Fixed Points ODE
Find level sets of the model f(x) = F(x). (If we think of F as being a vector field, then we are finding equilibria.) In order for this derivation to make sense, the dimension of the coded domain of F must equal the dimension of the coded range of F. Naturally, in order to compute a level set of f in Pisces, the user must inflate the domain by at least one variable using the permutation panel.