Input/Output:

Level 1/Argument 1

Level 1/Item 1

“global”→

See also:

PROMPT,

STO

 

 

 

PROOT

Type: Command

Description: Polynomial Roots Command: Returns all roots of an n-degree polynomial having real or complex coefficients.

For an nth-order polynomial, the argument must be a real or complex array of length n+1 containing the coefficients listed from highest order to lowest. The result is a real or complex vector of length n containing the computed roots.

PROOT interprets leading coefficients of zero in a limiting sense. As a leading coefficient approaches zero, a root of the polynomial approaches infinity: therefore, if flag –22 is clear (the default), PROOT reports an Infinite Result error if a leading coefficient is zero. If flag –22 is set, PROOT returns a root of (MAXREAL,0) for each leading zero in an array containing real coefficients, and a root of (MAXREAL,MAXREAL) for each leading zero in an array containing complex coefficients.

Access:

 

!ÞPOLYNOMIAL LLPROOT

(Þis the left-shift of the 1key).

Flags:

 

Infinite Result Exception (–22)

 

 

Input/Output:

 

 

 

 

 

 

 

 

 

 

 

 

 

Level 1/Argument 1

 

Level 1/Item 1

 

 

 

 

 

 

 

 

 

[ array ]coefficients

→

[ array ]roots

 

 

 

 

 

Example:

 

Find the roots of the polynomial x4 + 2x3 - 25x2 - 26x + 120:

 

Command:

[ 1 2 –25 –26 120 ] PROOT

 

 

Result:

 

[ 2 –3 4 –5 ]

 

 

See also:

PCOEF, PEVAL

 

 

 

 

 

 

 

PROPFRAC

 

 

 

 

Type:

 

Command

 

 

Description:

 

Toggles between an improper fraction and its corresponding integer and fractional part.

Access:

 

PARITH or Arithmetic, !ÞL

 

 

Input:

 

An improper fraction, or an object that evaluates to an improper fraction. It must not contain real

 

 

numbers. Alternately, the input may be an integer part plus a proper fraction.

Output:

 

An integer part plus a proper fraction; or alternately, if the input was an integer part plus a proper

 

 

fraction, an improper fraction.

 

 

Flags:

 

Exact mode must be set (flag –105 clear).

 

 

 

 

Numeric mode must not be set (flag –3 clear).

 

 

 

 

Radians mode must be set (flag –17 set).

 

 

Example:

 

Express the following as a proper fraction:

 

 

 

 

x3 + 4

 

 

 

 

--------------

 

 

 

 

 

x2

 

 

Command:

PROPFRAC((X^3+4)/X^2))

 

 

Result:

 

X+(4/X^2)

 

 

Full Command and Function Reference 3-179