Description:

• The command library lets you extend the set of mathematical functions known to Sollya. By default, Sollya knows the most common mathematical functions such as exp, sin, erf, etc. Within Sollya, these functions may be composed. This way, Sollya should satisfy the needs of a lot of users. However, for particular applications, one may want to manipulate other functions such as Bessel functions, or functions defined by an integral or even a particular solution of an ODE.
• library makes it possible to let Sollya know about new functions. In order to let it know, you have to provide an implementation of the function you are interested in. This implementation is a C file containing a function of the form: int my_ident(sollya_mpfi_t result, sollya_mpfi_t op, int n) The semantic of this function is the following: it is an implementation of the function and its derivatives in interval arithmetic. my_ident(result, I, n) shall store in result an enclosure of the image set of the n-th derivative of the function f over I: f^(n)(I) C result.
• The integer value returned by the function implementation currently has no meaning.
• You do not need to provide a working implementation for any n. Most functions of Sollya requires a relevant implementation only for f, f' and f''. For higher derivatives, its is not so critical and the implementation may just store [-Inf, +Inf] in result whenever n>2.
• Note that you should respect somehow interval-arithmetic standards in your implementation: result has its own precision and you should perform the intermediate computations so that result is as tight as possible.
• You can include sollya.h in your implementation and use library functionnalities of Sollya for your implementation. However, this requires to have compiled Sollya with -fPIC in order to make the Sollya executable code position independent and to use a system on with programs, using dlopen to open dynamic routines can dynamically open themselves.
• To bind your function into Sollya, you must use the same identifier as the function name used in your implementation file (my_ident in the previous example). Once the function code has been bound to an identifier, you can use a simple assignment to assign the bound identifier to yet another identifier. This way, you may use convenient names inside Sollya even if your implementation environment requires you to use a less convenient name.
• The dynamic object file whose name is given to library for binding of an external library function may also define a destructor function int sollya_external_lib_close(void). If Sollya finds such a destructor function in the dynamic object file, it will call that function when closing the dynamic object file again. This happens when Sollya is terminated or when the current Sollya session is restarted using restart. The purpose of the destructor function is to allow the dynamically bound code to free any memory that it might have allocated before Sollya is terminated or restarted. The dynamic object file is not necessarily needed to define a destructor function. This ensure backward compatibility with older Sollya external library function object files. When defined, the destructor function is supposed to return an integer value indicating if an error has happened. Upon success, the destructor functions is to return a zero value, upon error a non-zero value.