Notes on Sollya computed basis

Basis

The basis is a structure made of two elements:

• an integer: the number of elements of the basis;
• an array of Sollya function objects that are the actual elements of the list.

Evaluation of the basis at  some point

For a given point, the evaluation returns a vector of MPFR numbers that are the result of the evaluation of each element of the basis at this point.

Needed functions

Read a text file and create a basis

The idea is to give the basis as a text file holding the basis:

• one basis element per line;
• the text can be converted to a Sollya function object.

We leave the check of the file (existence, creating a handle over the file) to the calling program. The file is given a handle which makes the function more flexible. This is the input argument.

Nevertheless, the function reads the file (and deals with all the problems related to the file contents) and tries to compute a basis from the contents.

The function returns:

• NULL: if something goes wrong (e.g. when reading the file, when trying to create Sollya function objects from the contents);
• a pointer on a basis struture (allocated and assigned in the function body).

Evaluation a some point

We use the evaluate Sollya function.