HP HP-28S - Page 38

HP-28S
• Zero: A root has been found.
• Sign reversal: Two adjacent points have been found where the
function changes it sign. Possibly, the function has a discontinuity at
this point.
• Extremum: The solver found an extremum (local maximum or
minimum) or hit ±MAXR.
• Bad Guess(es): When evaluating the function at the initial guess
points it causes an error.
• Constant?: The function always returns the same value.
continued
SOLVR:
Verification
Also, there are the following buttons present in the solver menu. They
can be used to verify a solution:
• EXPR= Only present if the function is an expression or program.
When pressed the expression/program is evaluated using the current
values of the variables. The result should be 0.
• LEFT= Only present if the function is an equation. When pressed it
evaluates the left side of the equation.
• RT= Only present if the function is an equation. When pressed it
evaluates the right side of the equation. Left and right side should be
equal.
The quit the interactive menu press any other menu key are activate the
CURSOR menu.
ISOL Isolate a unique variable in a formula. See ALGEBRA Menu.
QUAD Symbolically solves a quadratic equation. Example (flag 34 clear):
'X^2-5*X+6' 'X' QUAD returns '(5+s1)/2'.
s1 indicates an arbitrary sign so the two solutions are (5+1)/2=3 and
(5-1)/2=2.
This result is only returned when the "principal value" flag 34 has been
turned off. If it is set the solution for s1=1 is returned which is 3.
It is possible to use formal names:
'X^2-3*X-A*X+3*A' 'X' QUAD returns
'(-(-3-A)+s1*√((-3-A)^2-4*(3*A)))/2'. COLCT converts this to:
'.5*(3+√((-3-A)^2-12*A)*s1+A)'. It is easy to prove that this is
equivalent to the correct solution '.5*(3+A+s1*(A-3))' but the
calculator cannot perform this simplification.
• If A has an associated value then the result is evaluated using this
value.
• Variable s1 can be set to +1 and –1 to get the two results.
• If the input expression is not a polynomial of degree 2 then a Taylor
series expansion of the expression is performed up to degree 2 and
then the roots of this expansion are calculated.
SHOW Show implicit references to a variable. See ALGEBRA Menu.
ROOT Root is a version of the solver that can be used in a progam.
Example: <<X DUP * 7 - >> 'X' 0 ROOT returns 2.645…
• Stack level 3 contains the function which can be an expression, an
equation or a program, see STEQ above.
• Level 2 contains the name of the variable that the solver solves for.
• Level 1 contains an initial guess or multiple initial guesses in a list as
described in SOLVR above.
• The return value is a single value for X.
38