HP 50g Graphing manual Pmini, Polar, Finds the minimal polynomial of a matrix, An nxn matrix a

Access:	…µPMIN
Input/Output:
		Level 1/Argument 1	Level 1/Item 1
		(x,y)	→
See also:	PDIM, PMAX, XRNG, YRNG
PMINI
Type:	Command
Description:	Finds the minimal polynomial of a matrix.
Access:	Matrices, !Ø LEIGENVECTORS
Input:	An nxn matrix A.
Output:	A matrix whose first zerorow contains the minimal		polynomial of A. In stepbystep mode,
	PMINI shows the rowreduction steps.
Flags:	Exact mode must be set (flag –105 clear).
	Numeric mode must not be set (flag –3 clear).
	Stepbystep mode can be set (flag –100 set).

Example: Find the minimal polynomial of Command: PMINI([[0,1][1,0]])

01

1 0

:

		1 0 0 1	1
		0 1 1 0	X
Result:		0 0 0 0 X2 – 1		So, the minimal polynomial is X21 , as it is in the first row to contain entirely
	zeros, except for the result.
See also:	JORDAN, PCAR
POLAR	Command
Type:
Description:	Polar Plot Type Command: Sets the plot type to POLAR.
	When the plot type is POLAR, the DRAW command plots the current equation in polar
	coordinates, where the independent variable is the polar angle and the dependent variable is the
	radius. The current equation is specified in the reserved variable EQ.
	The plotting parameters are specified in the reserved variable PPAR, which has this form:
				{ (xmin, ymin) (xmax, ymax) indep res axes ptype depend }
	For plot type POLAR, the elements of PPAR are used as follows:
	•	(xmin, ymin) is a complex number specifying the lower left corner of PICT (the lower left corner
		of the display range). The default value is (–6.5,–3.1) for the HP 48gII and (–6.5,–3.9) for the
		HP 50g and 49g+.
	•	(xmax, ymax) is a complex number specifying the upper right corner of PICT (the upper right
		corner of the display range). The default value is (6.5,3.2) for the HP 48gII and (6.5,4.0) for the
		HP 50g and 49g+.
	•	indep is a name specifying the independent variable, or a list containing such a name and two
		numbers specifying the minimum and maximum values for the independent variable (the
		plotting range). The default value of indep is X.

3172 Full Command and Function Reference