Is integration and differentiation code sepparate?

On 11/12/10 04:26 PM, Stavros Macrakis wrote:
> For polynomials, it is highly unlikely that random-coefficient tests will
> find any problems.

I thought that might be the case. But for the purposes of developing some test 
code, it seemed an easy way to start. I've not testing that many - perhaps 
10,000 or so.

If I got some code that I thought was worthwhile, I'd run it overnight. I keep 
my Sun on 24/7, so it might as well compute something.

I am using the time of day to seed the random number generator, but I have the 
option of commenting that out. In fact, the first few lines of my code have

/* Comment out the next line if you want the same output each time */
#define SEED_RANDOM_NUMBER_GENERATOR

In any case, I would save any failed results.

I can however see the point in general of having one set of data, and testing 
new versions against that, to see if there are any regressions.

> By the way, you mention complex powers in your polynomials.  Fractional and
> complex powers are not normally considered polynomials (for lots of good
> reasons).

I was not using fractional powers, but I was using complex ones.

These are the sort of things I'd generated


f1=-10 -5*I*x^1  +0*I*x^2  +0*x^3  +1*x^(I*4)  -5*I*x^5
f1=-2*I -7*x^1  -5*x^2  -7*x^(I*3)  +0*I*x^4  -2*x^5
f1=+5*I -8*x^(I*1)  -2*x^2  -8*I*x^3  -4*x^(I*4)  -10*I*x^5
f1=-7*I +0*I*x^(I*1)  -4*x^(I*2)  -5*I*x^(I*3)  -3*I*x^4  +8*x^(I*5)
f1=+10*I +0*x^1  -2*x^2  -8*x^(I*3)  -10*x^(I*4)  -3*I*x^5
f1=-9*I +5*I*x^(I*1)  +10*I*x^2  -6*x^(I*3)  +4*I*x^4  -7*x^(I*5)
f1=-6 +6*x^1  -2*I*x^2  +9*I*x^(I*3)  -7*x^(I*4)  -4*I*x^(I*5)
f1=+7*I -1*I*x^(I*1)  +3*I*x^(I*2)  -6*I*x^(I*3)  +8*I*x^(I*4)  +0*x^(I*5)
f1=-2 +9*x^(I*1)  -1*I*x^2  -3*x^3  -1*I*x^(I*4)  -8*x^(I*5)
f1=+10 +7*I*x^(I*1)  -2*x^2  +2*I*x^3  +5*I*x^(I*4)  +2*I*x^(I*5)

though I had used much higher powers. In the above the probability of a number 
being complex was 0.5, but I can change that.


> For non-polynomials, it should of course be true that
> Differentiate(Integrate(f)) = f.  However, that does not mean that the
> *form* of Differentiate(Integrate(f)) is the same as f.  And determining
> whether two expressions represent the same function is often difficult (in
> fact unsolvable in
> general<http://books.google.com/books?id=B9tC7DOX_oUC&pg=PA81&lpg=PA81&dq=zero-equivalence+unsolvable&source=bl&ots=rhQBOJvapS&sig=hGndNQi1tohzn7VBGidMeojpv64&hl=en&ei=7WndTJKPO4P58Aa9v8jxDw&sa=X&oi=book_result&ct=result&resnum=5&ved=0CDgQ6AEwBA#v=onepage&q=zero-equivalence%20unsolvable&f=false>;
> ).

OK, thank you for that. I was not aware that was the case. I know I managed to 
get some pretty big expressions from something quite simple.

In which case, substituting x for some real number, should allow the in both my 
original function, and what I've differenced would give a reasonable degree of 
certainty that there was not a bug. If I could get a numerical result, which was 
identical, it is likely the symoblic results were mathematically equal.

Does that make sense?


Dave