My goal is to get to the matrix form Ax =b by collecting and combining linear terms while I am parsing the ast tree. Once I get a clean matrix form Ax=b, it is straightforward to call my other routines to solve it.
I also realized that symbolic programming or CLP probably need to so similar things. But no idea what are the algorithms they used. Michael On Sat, Jan 16, 2010 at 4:23 AM, Hans Aberg <hab...@math.su.se> wrote: > On 16 Jan 2010, at 01:40, Michael Chen wrote: > >> The input I have is linear equation like: >> >> 2 * x + ( x - y ) = x + 1 >> >> And I would like to get at end >> >> 2 * x - y = 1 >> >> I studied the calculator example, and be able to build ast tree. >> however I have no way to reduce it. Please give me an example or >> link. Thanks. > > You need methods used in symbolic programming (like Maple), theorem provers, > and CLP like: > http://en.wikipedia.org/wiki/CLP(R) > http://en.wikipedia.org/wiki/Constraint_logic_programming > > One can solve polynomial equations using Buchberger's Groebner Basis > Algorithm. Given an ideal (p_1, ..., p_k) it produces a new set of > generators relative a monomial order on diagonalized form. In the case of > one variable, it reduces to the Euclidean algorithm computing the greatest > common denominator. For a set of equations, just write them as p_1 = 0, ..., > p_k = 0, and apply it to the ideal (p_1, ..., p_k). > > If you want to just solve linear equations, you can use just the ordinary > matrix solution method: write matrices A X = B, and solve it. - Check for > computationally efficient methods doing this. > > When doing it the CLP way, one integrates this algorithm into the > unification process that i Prolog is used to unify the heads of the clauses. > This produces a very elegant way to solve them, as you can see on that link > above, but is somewhat limited if one wants to do more general things. > > Hans > > > -- Best regards, Michael Chen Google Voice Phone.: 847-448-0647 _______________________________________________ help-bison@gnu.org http://lists.gnu.org/mailman/listinfo/help-bison
