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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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Topic review (newest first)

bobbym
2011-04-11 21:49:23

Hi gAr;

gAr
2011-04-11 21:43:26

Hi bobbym,


bobbym
2011-04-11 21:22:45

What did you get, do not forget to hide it?

gAr
2011-04-11 21:21:28

Aha, now both the expressions work fine.
I increased the precision to 100 digits.

bobbym
2011-04-11 21:07:31

Hi gAr;

That expression is extremely difficult for a package to evaluate. We say it is ill conditioned. Adjust your digit command to get higher precision and try again.

gAr
2011-04-11 21:03:31

Hi bobbym,

Ok.
For that expression I get:
-1.18059162071741e21
and 1.18059162071741e21 for those two numbers as integers.


I evaluated this expression and got
-4.38605752237005e29 for a = 77617.0 , b = 33096.0 ; and
-4.38605749875822e29 for a = 77617 , b = 33096

bobbym
2011-04-11 20:45:31

Hi gAr;

With that identity as well as lots of others the best way is to plot (a+b)(a-b) - (a^2 - b^2 ). Instead of getting a flat line on the x axis ( y = 0 ) you should get a crazy graph of undulating spikes.

I meant the expression in post #1.

gAr
2011-04-11 20:39:42

Hi bobbym,

Did you try that expression? What did you get?

Is it the identity you are asking about?
For numbers like a=1.1 and b=2.2, it displays correctly. When digits after decimal places are increased, it fails.

bobbym
2011-04-11 20:19:48

You also do not use the quadratic formula to get roots.

Did you try that expression? What did you get?

gAr
2011-04-11 20:15:26

I agree.

For that identity, yes, real numbers are always a problem!

bobbym
2011-04-11 20:06:54

You should always mistrust an answer a CAS gives. Same way you should mistrust anything a human says. There are basic guidelines and I will be posing them in the future.

There is a big difference between the way human mathematicians do math and the way a CAS does it. One of the funniest examples is

Human math: This is an identity:



Computer math: This is not!

gAr
2011-04-11 19:58:39

So we do not know when to trust the answers and when not to!

bobbym
2011-04-11 19:37:23

That is the point. Sometimes you can tell that an equation is going to give a CAS ( or a calculator ) a lot of problems. But sometimes you cannot. That one came as a surprise to me too.

gAr
2011-04-11 19:32:42

Oh, does he tell what kind of equations suffer like that?

bobbym
2011-04-11 19:15:46

Hi gAr;

That is one of its problems. The guy who designed it wanted to prove there was a big hole in the way numerical people verify digits.

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