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+--- Thread: root of a quadratic equation (/thread-4554.html)
root of a quadratic equation - tigger - 08-22-2015 09:41 AM
These two equations help to solve a root of a quadratic equation:
<< 2 ->LIST SWAP / EVAL SWAP -2 / DUP SQ ROT - v/ DUP2 + ROT ROT - >>
<< 3 PICK / SWAP ROT -2 * / DUP SQ ROT - SQRT DUP2 * ROT ROT - >>
[quote='tigger' pid='40913' dateline='1440236517']
<< 2 ->LIST SWAP / EVAL SWAP -2 / DUP SQ ROT - v/ DUP2 + ROT ROT - >>
The calculator put a blank between the - and the 2 automatically. This could have been the mistake in the program.
<< 2 ->LIST SWAP / EVAL SWAP - 2 / DUP SQ ROT - v/ DUP2 + ROT ROT - >>
<< 3 PICK / SWAP ROT -2 * / DUP SQ ROT - SQRT DUP2 * ROT ROT - >>
Is there a sign for SQRT on this page?
When I punched the keys in the calculator itself made a blank between the - and the 2. How could I know that the calculator made this mistake?
Does the HP always makes mistakes like this?
How can I avoid this kind of mistakes?
There might be any hope and help to rectify these short programs?
RE: root of a quadratic equation - Thomas Klemm - 08-22-2015 12:03 PM
Why not using PROOT?
Code:
\<< { 3 } \->ARRY PROOT OBJ\-> DROP \>>Cheers
Thomas
RE: root of a quadratic equation - tigger - 08-22-2015 05:17 PM
When I type the first "\" before << I get "Invalid Syntax".
Without the first "\" I get: Error "Can't find Selection.
Could you write me what I did wrong?
RE: root of a quadratic equation - Hlib - 08-22-2015 06:55 PM
e.g. for -x^2+3x+1=0
input:
-1 3 1
<< 3 →ARRY PROOT OBJ→ DROP >> EVAL
output:
1: -.302775637732
2: 3.30277563773
RE: root of a quadratic equation - Thomas Klemm - 08-22-2015 07:01 PM
I was using tri-graphs to write the code. This makes it easy to transfer it to the calculator.
HTH
Thomas
RE: root of a quadratic equation - Gerson W. Barbosa - 08-22-2015 07:28 PM
(08-22-2015 12:03 PM)Thomas Klemm Wrote: Why not using PROOT?
Code:
\<< { 3 } \->ARRY PROOT OBJ\-> DROP \>>
Well, for this example PROOT will give ugly approximations:
1
'-√2-√3'
'√6'
« { 3 } →ARRY PROOT OBJ→ DROP
»
EVAL
-->
1.41421356237
1.73205080757
For exact results, in exact mode I would prefer something like
« ROT NEG SWAP OVER
/ UNROT / 2 / SWAP
OVER SQ + √ DUP2 -
FACTOR UNROT +
FACTOR
»
-->
'√2'
'√3'
Cheers,
Gerson.
RE: root of a quadratic equation - Gerson W. Barbosa - 08-22-2015 07:33 PM
(08-22-2015 09:41 AM)tigger Wrote: There might be any hope and help to rectify these short programs?
While these aren't fixed, you can try
« ROT NEG SWAP OVER / UNROT / 2. / SWAP OVER SQ + √ DUP2 - UNROT + »
Not sure whether this is shorter, though.
Sizewise, Thomas Klemm's suggestion above is a much better option.
Regards,
Gerson.
RE: root of a quadratic equation - Thomas Klemm - 08-22-2015 07:35 PM
(08-22-2015 09:41 AM)tigger Wrote: Is there a sign for SQRT on this page?
- \v/ (tri-code)
- √ (unicode)
- \(\sqrt{}\) (LaTeX)
Quote:When I punched the keys in the calculator itself made a blank between the - and the 2. How could I know that the calculator made this mistake?
Does the HP always makes mistakes like this?
How can I avoid this kind of mistakes?
To enter -2 you have to punch the [2] and then the [±] key.
Cheers
Thomas
RE: root of a quadratic equation - Gerson W. Barbosa - 08-22-2015 08:07 PM
(08-22-2015 09:41 AM)tigger Wrote: These two equations help to solve a root of a quadratic equation:
<< 3 PICK / SWAP ROT -2 * / DUP SQ ROT - SQRT DUP2 * ROT ROT - >>
* and - at the end should be - and +, respectively:
<< 3 PICK / SWAP ROT -2 * / DUP SQ ROT - SQRT DUP2 - ROT ROT + >>
On the HP 50g, we can use
<< PICK3 / SWAP ROT -2 * / DUP SQ ROT - SQRT DUP2 - UNROT + >>
and save a few bytes. This is 50-byte long, 5 bytes shorter than my attempt at this above.
Gerson.
RE: root of a quadratic equation - Thomas Klemm - 08-22-2015 08:18 PM
(08-22-2015 09:41 AM)tigger Wrote: There might be any hope and help to rectify these short programs?
Here's a variant from a previous thread using local variables:
Code:
« → a b c
« b a / -2 /
c a / → p q
« p SQ q - √ → D
« p D -
p D +
»
»
»
»Cheers
Thomas
RE: root of a quadratic equation - Hlib - 08-22-2015 11:06 PM
(08-22-2015 07:28 PM)Gerson W. Barbosa Wrote: Well, for this example PROOT will give ugly approximations:
1
'-√2-√3'
'√6'
« { 3 } →ARRY PROOT OBJ→ DROP
»
EVAL
-->
1.41421356237
1.73205080757
For exact results, in exact mode I would prefer something like
« ROT NEG SWAP OVER
/ UNROT / 2 / SWAP
OVER SQ + √ DUP2 -
FACTOR UNROT +
FACTOR
»
-->
'√2'
'√3'
Cheers,
Gerson.
The simple way to obtain result:
'x²+(-√2-√3)*x+√6=0'
SOLVEVX
SIMPLIFY
=>>
{x=√2 x=√3}
RE: root of a quadratic equation - Gerson W. Barbosa - 08-23-2015 12:43 AM
(08-22-2015 11:06 PM)Hlib Wrote:(08-22-2015 07:28 PM)Gerson W. Barbosa Wrote: Well, for this example PROOT will give ugly approximations:
1
'-√2-√3'
'√6'
« { 3 } →ARRY PROOT OBJ→ DROP
»
EVAL
-->
1.41421356237
1.73205080757
For exact results, in exact mode I would prefer something like
« ROT NEG SWAP OVER
/ UNROT / 2 / SWAP
OVER SQ + √ DUP2 -
FACTOR UNROT +
FACTOR
»
-->
'√2'
'√3'
Cheers,
Gerson.
The simple way to obtain result:
'x²+(-√2-√3)*x+√6=0'
SOLVEVX
SIMPLIFY
=>>
{x=√2 x=√3}
Well, live and learn!
