rf23d.m

·         Maple procedure rf23d.m: Computation of the reduced form for 2D and 3D BPWLS (A1,A2,B1). See Josep Ferrer, M. Dolors Magret, and Marta Peña, Int. J. Bifurcation Chaos 20, 2795 (2010).

Usage: from MAPLE commad line (for example, in a MAPLE worksheet) load the file with the command:

> read `cf23d.m`;

Then, a typical call to the procedure is:

> A1R,A2R,B1R,S,r:=cf23d(A1,A2,B1);

Description of the parameters:

Input parameters:

A1,A2: NxN matrices (type Matrix), with s.t.: A1 e(i) = A2 e(i), i=2,N

B1: N-dimensional vector (type Vector)

with N=2 or 3.

Output parameters:

A1R,A2R,B1R: are the corresponding reduced forms

S: is the basis change matrix, i.e.: A1C = S^-1 A1S, A2C = S^-1 A2S, B1C = S^-1 B1

r: is the rank of the observability matrix

cf23d.m

·         Maple procedure cf23d.m: Computation of the canonical form for 2D and 3D BPWLS (A1,A2,B1). See J. Ferrer, M. D. Magret, J. R. Pacha, and M. Peña. Planar bimodal piecewise systems. Bifurcation diagrams. Bol. Soc. Esp. Mat. Appl., 51, 55—62 (2010).

 Usage: form MAPLE command line (for example, in a MAPLE worksheet) load the file with the command:

> read `cf23d.m`;

Then, a typical call to the procedure is:

> A1C,A2C,B1C,S,r:=cf23d(A1,A2,B1);

Description of the parameters:

Input parameters:

A1,A2: NxN matrices (type Matrix), with s.t.: A1 e(i) = A2 e(i), i=2,N

B1: N-dimensional vector (type Vector)

with N=2 or 3.

Output parameters:

A1C,A2C,B1C: are the corresponding canonical forms

S: is the basis change matrix, i.e.: A1C = S^-1 A1S, A2C = S^-1 A2S, B1C = S^-1 B1

r: is the rank of the observability matrix

The Maple worksheet cf-examples.mw gives some examples of the use of this proceure.