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

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. **Saddle Node Map**- 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. **Saddle Node ODE**- Find level sets of the system
*f1(x) = F(x)*,*f2(x) = det(DF(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*. 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. **Planar_Singularity**- This derivation only makes sense if
*F*is a scalar-valued function of two variables. Then the derivation is*f1(x)=F(x)*,*f2(x)=grad(F)*. The solutions to this system are singular points on the level sets 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.

Comments to: pisces@geom.umn.edu

Last modified: Tue Nov 28 09:28:10 1995

Copyright © 1995 by The Geometry Center, all rights reserved.