Numerics Updates in Maple 12 - Maple Programming Help

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Numerics Updates in Maple 12

 

Compiled Complex Numeric Support

Parametric Polynomial System Solving

Numerical solution of systems of procedures

Interpolation of multidimensional Array data

New MPQS Method and Enhanced Access to Existing Methods for Integer Factorization

Compiled Complex Numeric Support

  

The Maple numeric code compiler (see Compiler) and run-time support library have been updated to support complex numerics. Complex arithmetic and calls to elementary functions of a complex argument are now supported in compiled code.

p := proc( a :: complex, b :: complex ) :: complex;
    arcsinh( a / I / b )
end proc:

cp := Compiler:-Compile( p ):

cp( 2.3 + 3.1 * I, I - 2.0  );

1.31074969024882160+0.151385481262499094I

(1)

Parametric Polynomial System Solving

  

The new package RootFinding[Parametric] has been added for analyzing and solving systems of polynomial equations and inequalities depending on parameters. The package offers the ability to answer questions like the following: for which parameter values does the system have a solution, or a given number of solutions? For examples and details, see RootFinding[Parametric].

Numerical solution of systems of procedures

  

The routine fsolve has been enhanced to handle systems of procedures of more than one argument. This is the procedural equivalent of multivariate expressions.

f := proc(x,y,z) sin(x*y-4)+cos(z); end proc:

g := proc(a,b,c) a+b+c; end proc:

h := proc(q,r,s) (q-r)/s; end proc:

fsolve({f,g,h});

6.7445381681428481,6.7445381681428481,13.489076336285696

(2)

[f,g,h](op((2)));

1.210-9,0.,0.

(3)

Interpolation of multidimensional Array data

  

The new routine CurveFitting[ArrayInterpolation] provides the functionality to perform linear, cubic, spline, lowest, highest, or nearest interpolation and efficient data resampling on multidimensional data.

New MPQS Method and Enhanced Access to Existing Methods for Integer Factorization

  

The ifactor command accepts several new options which add the Multiple Polynomial Quadratic Sieve (MPQS) method and provide enhanced access to the existing methods. The new 'mpqs' option enables direct access to the MPQS method, and the new 'mpqsmixed' and 'mixed' options enable access to a combination of factorization methods. The 'morrbril' option enables direct access to the Morrison-Brillhart method. In addition, the performance of the Pollard factorization method has been enhanced.

See Also

Enhancements to Symbolic Capabilities in Maple 12

Index of New Maple 12 Features