kv

-

kernel handle of type MKernelVector

s

-

type ALGEB object

fn

-

Maple FUNCTION object

n

-

number of arguments

args

-

array of n hardware floats

    #include <math.h>

    #include "maplec.h"

    ALGEB M_DECL MyNewton( MKernelVector kv, ALGEB *args )

    {

    M_INT i;

    FLOAT64 guess[2], tolerance;

    ALGEB f, fprime, x;

    if( 3 != MapleNumArgs(kv,(ALGEB)args) ) {

        MapleRaiseError(kv,"three arguments expected");

        return( NULL );

    }

    if( IsMapleProcedure(kv,args[1]) ) {

        f = args[1];

    }

    else {

        ALGEB indets;

        indets = EvalMapleProc(kv,ToMapleName(kv,"indets",TRUE),1,args[1]);

        if( !IsMapleSet(kv,indets) || MapleNumArgs(kv,indets) != 1 ) {

        MapleRaiseError(kv,"unable to find roots");

        return( NULL );

        }

        i = 1;

        f = EvalMapleProc(kv,ToMapleName(kv,"unapply",TRUE),2,args[1],

             MapleSelectIndexed(kv,indets,1,&i));

        if( !f || !IsMapleProcedure(kv,f) ) {

        MapleRaiseError(kv,"unable to convert first arg to a procedure");

        return( NULL );

        }

    }

    x = ToMapleName(kv,"x",FALSE);

    fprime = EvalMapleProc(kv,ToMapleName(kv,"unapply",TRUE),2,

            EvalMapleProc(kv,ToMapleName(kv,"diff",TRUE),2,

            ToMapleFunction(kv,f,1,x),x),x);

    if( !fprime || !IsMapleProcedure(kv,fprime) ) {

        MapleRaiseError(kv,"unable to compute derivative");

        return( NULL );

    }

    guess[1] = MapleEvalhf(kv,args[2]);

    tolerance = MapleEvalhf(kv,args[3]);

    for( i=0; i<500; ++i ) {

        if( fabs(EvalhfMapleProc(kv,f,1,guess)) <= tolerance )

        break;

        guess[1] = guess[1] - EvalhfMapleProc(kv,f,1,guess) /

            EvalhfMapleProc(kv,fprime,1,guess);

    }

    if( i == 500 ) {

        MapleRaiseError(kv,"unable to find root after 500 iterations");

        return( NULL );

    }

    return( ToMapleFloat(kv,guess[1]) );

    }