Re: Evaluation of 1/(1/a + 1/b + 1/r)

• To: mathgroup at smc.vnet.net
• Subject: [mg70166] Re: [mg70129] Evaluation of 1/(1/a + 1/b + 1/r)
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Fri, 6 Oct 2006 01:58:24 -0400 (EDT)
• References: <200610050732.DAA06072@smc.vnet.net>

```On Oct 5, 2006, at 3:32 AM, Diana wrote:

> Folks,
>
> I am trying to write a program to evaluate the sum of two continued
> fractions, written in polynomials of T.
>
> I would like a short routine to evaluate 1/(1/a + 1/b + 1/r), just
> working with a, b, and r if they are not equal to zero.
>
> So, if a = 0, then evaluate 1/(1/b + 1/r)
>
> If a, b, = 0, then evaluate 1/r
>
> If all of a, b, r = 0, give me 0 as output.
>
> If (1/a + 1/b + 1/r) = 0, give me 0 as output.
>
> Assume that a, b, r are arbitrary polynomials in T.
>
> Can someone help?

You can use pattern matching

sumFractions[a_,b_,r_]:=1/(1/a+1/b+1/r)

sumFractions[0,b_,r_]:=1/(1/b+1/r)

sumFractions[0,0,r_]:=1/r

sumFractions[0,0,0]:=0

As the number of patterns increases the typing can get tedious, you
can write an expression to generate these expressions automatically
but I don't see how 1/(1/a + 1/b + 1/r) -> 1/(1/b + 1/r) when a is
zero or 1/r when a and b are zero.  If you know of an expression that
can generate that sequence you can use it to save some typing.

Regards,

Ssezi

```