Name:
library
binds an external mathematical function to a variable in Sollya
Library names:
sollya_obj_t sollya_lib_libraryfunction(sollya_obj_t, char *,
int (*)(mpfi_t, mpfi_t, int))
sollya_obj_t sollya_lib_build_function_libraryfunction(sollya_obj_t, char *,
int (*)(mpfi_t,
mpfi_t, int))
Usage:
library(path) : string -> function
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.
Example 1:
> bashexecute("gcc -fPIC -Wall -c libraryexample.c -I$HOME/.local/include");
> bashexecute("gcc -shared -o libraryexample libraryexample.o -lgmp -lmpfr");
> myownlog = library("./libraryexample");
> evaluate(log(x), 2);
0.69314718055994530941723212145817656807550013436024
> evaluate(myownlog(x), 2);
0.69314718055994530941723212145817656807550013436024