Re: Mathematical frameworks

On 6 Oct 2013, at 23:37 , Norbert E. Fuchs <[email protected]> wrote:

> I am about to finish the implementation of the arithmetic component of my reasoner RACE for Attempto Controlled English (http://attempto.ifi.uzh.ch/site/resources/).
> 
> Since RACE is implemented in SWI Prolog it was natural to choose SWI's constraint logic library CLPQR to implement the actual arithmetic operations. So far, this works quite nicely.
> 
> However, CLPQR has limitations for non-linear constraints. For example, the non-linear constraint x^2 -3*x + 2 = 0 can only be solved when a value for x is given, meaning that RACE currently cannot solve quadratic or any other non-linear equations. Thus, eventually I need to replace CLPQR by some other mathematical framework. 
> 
> Which mathematical framework would you suggest that offers more mathematical functionality than CLPQR and is easily accessible from SWI Prolog?


Following a hint by Jordi Saludes (UPC Barcelona), namely "transform the quadratic equation into a form that CLPQR can handle", I can solve quadratic equations in RACE. 

Concretely, I transform the quadratic equation 

X^2 + P*X + Q = 0

into its two solutions

X = -(P/2) + ((P/2)^2 - Q)^(1/2) and X = -(P/2) - ((P/2)^2 - Q)^(1/2)

that do not pose any problem for CLPQR. 

Note: This is not yet implemented.

Since linear and quadratic equations are used more often than other higher-order equations I think that currently I can live with CLPQR's limitations and do not need to look for a more powerful mathematical framework.

   --- nef