The ComprehensiveMinimalPolynomial function will compute a complete case discussion of the minimal polynomial of a matrix of multivariate polynomials.
ComprehensiveMinimalPolynomial(A, v, R, options)
ComprehensiveMinimalPolynomial(A, v, rs, R, options)
ComprehensiveMinimalPolynomial(A, v, cs, R, options)
ComprehensiveMinimalPolynomial(A, v, F, R, options)
ComprehensiveMinimalPolynomial(A, v, F, H, R, options)
| Variable | Description |
|---|---|
A |
Square matrix of multivariate polynomials over R |
v |
Variable to use for the computed minimal polynmoials |
rs |
Regular system |
cs |
Constructible set |
F |
List of polynomials over R representing equality constraints on the parameters |
H |
List of polynomials over R representing inequation constraints on the parameters |
R |
Polynomial ring |
| Option name | Default value | Description |
|---|---|---|
'outputType' |
'CS' |
When set to 'CS' or 'ConstructibleSet' the output will contain constructible sets, when set to 'RS' or 'RegularSystem', the output will contain regular systems. |
| Output structure | Options |
|---|---|
[p, rs] |
'outputType' is 'RegularSystem' or 'RS' |
[p, cs] |
'outputType' is 'ConstructibleSet' or 'CS' |
Where p is the minimal polynomial of the input matrix for all parameter values in the zero set of cs or rs. Together, all the constructible sets or regular systems form a partition of the input constructible set, regular system or set of equations and inequations.