Description

Installation:
Install all ‘8xp’ files from the archive.

QPI.
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HP Prime version - Han Duong. TI-84 Plus CE port - slonechkin.

"This program takes a decimal value and returns a one of the following expressions
that is a "close" rational approximation of the specified decimal value":

a/b; (a*√b)/c or √(a/b), depending on program limitations; (a/b)*⋅π; e^(a/b); or ln(a/b).

Usage:

Run A01QPI.
You can enter an expression or a decimal number.
Or you can make a calculation before running the program and enter the result with Ans.
Press [enter].

QRAC for TI-84 Plus CE by slonechkin.
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QRAC is written to recognise square roots in decimal numbers, for some extension of QPI's capabilities.

QPI squares a decimal number and sends it to subroutine to approximate it into an ordinary fraction.
If the result follows certain rules, the resulting fraction is placed under the root sign.
That is, module deriving the denominator and multiplier from under the root is applied already to the number
in which the root from another number has been ‘recognised’.
QPI has certain ‘working ranges’ and limits the denominators of ‘recognised’ numbers to 1000.
For example, √(21)/71 is √(21/5041). The result falls out of the range and is not treated as a root.
The reasons for the limitations are clear - prioritisation and search depth. Otherwise, the program will find everything and everywhere.
In the case of √(21)/51, if we put the denominator back under the root, we get √(21/2601), which is equal to √(7/867),
and the program ‘recognises’ it.

But QRAC ‘recognises’ √(21)/71. It uses a different methodology.

This program takes a decimal value and returns a one of the following expressions:

a/b, up to the number 1000 in the denominator; (a*√b)/c, up to the number 1000 in the denominator and number "a" not more than 1000;
(a+c*√d)/f, up to the number 21 in the denominator and number "a" not more than 101;
(a*√b+c*√d)/f, up to the number 21 in the denominator and a^2*b not more than 101.

The limitations of the program QRAC are related to the use of the brute force method and not the fastest recognition rate.
However, the limits can be changed in the program.
Now, if the program finds nothing, all cycles up to the ‘NOTHING FOUND’ message are completed in 1 minute 30 seconds.
The larger the denominator, the longer it takes the program to reach it. BASIC is BASIC.
Constructions such as (a+c*√d)/f and (a*√b+c*√d)/f are, most often, roots of quadratic equations.
In the equations themselves, the denominator is immediately visible: 2*a.
Therefore, the restriction to 21 in the denominator can be easily circumvented by multiplying the number
or expression being entered by the denominator. Then the answer will be the exact value of the numerator. And the answer will come quickly.

QRAC Usage:

Run A01QRAC.
You can enter an expression or a decimal number.
Or you can make a calculation before running the program and enter the result with Ans.
Press [enter].

The listing of all programming modules can be found in the archive.

I did it for myself, so as it turned out, so it turned out, and bugs may still appear while using it.

(C) slonechkin, 2025.

Screenshots