Handling erna objects

The functions for handling erna objects are organized into layers, so that, as much as possible, a function in a superior layer accesses only functions from the layer immediately inferior.

1. The first layer contains primitives for working with floats, including computation of the roundoff errors.
2. The basic layer has the necessary functions for defining an erna object, from a Maple constant.
3. Next layer contains the queries that can be addressed to an erna object.
4. The arithmetic operations with erna objects constitute the next layer.
5. The highest level functions handle polynomials with erna real or complex coefficients, or compute solutions for linear or polynomial equations.

We present in the following some of the most important functions.

• creating an erna object from a Maple constant or vector/matrix:

  symb2real(c)	vect2realVect(v)
  symb2complex(c)	matrix2realMatrix(m)

  The new object will have a name of the form _c$n$, where $n$ is a random number between 1 and 9999. Each such name is chosen to be unique.
• queries:
  • dump(r) for obtaining the known approximation of r;
  • epsint(r,eps) for obtaining an approximation of r of accuracy eps; returns the value of the approximation;
  • refine(r) for getting a better approximation of r; returns a two-element list with the new approximation and its accuracy.
  The last two queries have as side-effect the modification of the known approximation stored by the erna object r.
• arithmetic operations:
  • realAdd, realProd, realMinus, realInverse, realDiv, realPower, etc., with obvious meaning; similarly for erna complex: compAdd, compProd, compMinus, compDiv, compPower, compInverse, and for composite objects: rTranspose, rVectorAdd, rMatrixAdd, rMatrixProd, rMatrixInverse, rSubmatrix, etc.

Figure 1: Using erna objects.