16 replies to this topic

[genesis]

I have written a program that works just like RUN mode, but gives answers in exact values, that is displaying surds (in simplest form) and fractions (rationalised) simultaneously (even for trigonometry!) Here it is, please give me your opinions, feedback... so far I haven't found any errors, but it's slow for large numbers:

ClrText
?->A:A:Rnd
Frac Ans=0=>Stop:0->B
Do
Isz B:A?B?:Rnd
LpWhile Frac Ans≠0
If Frac √Ans=0
Then 1->C:√Ans->D
Else Ans->C:1->D
While Frac C/4=0
2D->D:C/4->C
WhileEnd
For 3->E To √C Step 2
While Frac C/E?=0
DE->D:C/E?->C
WhileEnd
Next
IfEnd
If B=1
Then If A<0
Then If D=1
Then Locate 19-Int log C,3,"-"
Else Locate 19-Int log D,3,"-"
IfEnd
IfEnd
D≠1=>Locate 19-Int log C-Int log D,3,D
Locate 20-Int log C,3,"√"
Locate 21-Int log C,3,C
Else If C=1
Then A<0=>Locate 18-Int log B-Int log D,3,"-"
Locate 19-Int log B-Int log D,3,D
Else If A<0
Then If D=1
Then Locate 17-Int log B-Int log C,3,"-"
Else Locate 16-Int log B-Int log C-Int log D,3,"-"
IfEnd
IfEnd
D≠1=>Locate 17-Int log B-Int log C-Int log D,3,D
Locate 18-Int log B-Int log C,3,"√"
Locate 19-Int log B-Int log C,3,C
IfEnd
Locate 20-Int log B,3,"/"
Locate 21-Int log B,3,B
IfEnd

NOTE: ?-squared √-root ≠-does not equal /-fraction "-"-"negative sign"
- The first and second Frac tests skip straight to the answer for rational numbers.
- The inputted number is rounded to the specified number of significant figures (10 in normal mode) to account for errors accumulated when multiplying surds.
- The first While loop (While is better than Do, as Do must always be run once) rationalises the denominator.
- The next two While loops simplify the surd in the numerator.
- Logs are used to position the numbers perfectly in place.
- I am currently working on logarithm, trigonometry and radian display.

[dscoshpe]

Hey this is pretty cool! Back before I got my AFX I always wished for some more precision so this would have been welcome, the fraction display is also convenient. But for AFX users the CAS meets the need...

- dscoshpe -

[genesis]

The code has been updated to fix rounding errors. Please continue to test it, I think there may be more...
Points to consider:
- There is currently ambiguity between √(a/b) and (√a)/b, what symbol should I use, fraction, "/", or the division sign?
- Is there a faster way to find the denominator than trying out numbers starting from 1?
- Any ideas for logarithm, trigonometry and radian display? I'm not sure how I should display answers... a single exact value, one over another etc?

[Andy.Davies]

you know it would be helpful to put the link in, rather than an underlined piece of text....

[octobclrnts]

The only problem with converting this code is that TI basic doesn't have a locate command (at least not that I know of). That may present a problem...

[CrimsonCasio]

yes, but the X and Y values are reversed as i recall.

[huhn_m]

you are funny ... how?

Your calc is really slow. Make it faster ...

There IS no way to make Casio Basic faster - you could just replace the
processor.

[genesis]

You know, thats WHY I'm asking for people's opinions because I KNOW its not perfect... If it was perfect, I wouldn't be asking!

The trouble is separating the numerator from the denominator, is there a better way than just testing all the numbers starting from 1? Also, I'm squaring the surds, which is causing problems, is there a way to test surds for divisibility? I could make it that you input each separately, but that defeats the purpose of a all-purpose calculator.

[TacoFred]

i was testing this, and put in sqrt(48), and it printed 8 sqrt(0)...
so...what is this exactly supposed to do?

[liquid]

Yea there seem to be some errors. I entered sqrt(2) and it gives 2sqrt(0)?
But still this is a great program as my 9750 obviously has no cas capability.

I was just thinking that you should edit the program to show the number in decimal from as well beneath it, and then show the decimal form of what it thnks the anwer is. This way you can tell how accurate the answer is and obviouly if its giving a bogus result.

Tip: change start to

ClrText
?->A:A:Rnd
" "
Frac Ans=0=>Stop:0->B
Do

then change end to:

IfEnd
Locate 20-Int log B,3,"/"
Locate 21-Int log B,3,B
IfEnd
A

just adding that A on the end shows the original number in decimal and those " " at the start stops it writing over the Locate stuff.
Can you change it so that it gives another decimal answer that is interpreted from the anwer that the program gives as i explained above?

[genesis]

Sorry for bringing this up again, but what calc are you using? I've tested the program thoroughly, and it produces no such results (your results are also impossible given the code). Remember, it was originally intended for displaying exact values for trigonometic functions, and it is obviously slower for rational numbers (common sense states that you just use the RUN menu...), so don't compare my program's speed to the calculators!

And yes, my program does give bogus results for large numbers, as the calculator doesn't store surds or large numbers to a great deal of accuracy... I don't think its possible to fix it without removing the user interface.

As for the tip, perhaps it would be faster to show the raw value first and the calculated value at the end.