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Re: [Axiom-mail] sum()

From: David MENTRE
Subject: Re: [Axiom-mail] sum()
Date: Tue, 22 Jun 2004 18:34:33 +0200
User-agent: Gnus/5.1006 (Gnus v5.10.6) Emacs/21.3 (gnu/linux)

Hello Daniel,

"Daniel Yokomiso" <address@hidden> writes:

>> You tried: 
>>  >    f: Integer -> Integer;
>>  >    f(0)==1; f(1)==2;
>>  >    f(n)==sum(f(i)*f(n-i), i=0..(n-1))
>> Try
>> f: Integer -> Integer;               
>> f(0)==1; f(1)==2;                    
>> f(n)==reduce(+,[f(i)*f(n-i) for i in 1..(n-1)])
>> I have no good explanation why sum won't work.
> "sum" doesn't work because your definition is different. The original
> has "i" ranging from 0 to (n - 1), while yours ranges from 1 to (n -
> 1). Using "i" from 0 makes the definition incorrect.

I don't agree with you. The range of i was one bug (when i=0,
f(n)=...*f(n-0)...=...*f(n)... -> stack overflow).

But there is another type bug.

-> f: Integer -> Integer; f(0)==1; f(1)==2; f(n)==sum(f(i)*f(n-i), i=1..(n-1))

-> f(3)
   Compiling function f with type Integer -> Integer 
   Conversion failed in the compiled user function f .
   Cannot convert from type Variable i to Integer for value

sum expects (rationalFunction, symbolOrSegmentBinding), from Axiom book
p. 683 in its paper form (Operations appendix).

f as defined by Marcus is not a rationalFunction and thus cannot be
defined using sum.

reduce is a program loop and not the mathematical Sum operator, that's
why it works.

David MENTRE <address@hidden> --

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