Projects per year
Abstract
In considering the reliability of numerical programs,
it is normal to “limit our study to the semantics
dealing with numerical precision” (Martel, 2005). On the other
hand, there is a great deal of work on the reliability of
programs that essentially ignores the numerics. The thesis
of this paper is that there is a class of problems that fall
between these two, which could be described as “does the lowlevel
arithmetic implement the highlevel mathematics”. Many
of these problems arise because mathematics, particularly
the mathematics of the complex numbers, is more difficult
than expected: for example the complex function log is not
continuous, writing down a program to compute an inverse
function is more complicated than just solving an equation,
and many algebraic simplification rules are not universally
valid.
The good news is that these problems are theoretically
capable of being solved, and are practically close to being solved,
but not yet solved, in several realworld examples. However,
there is still a long way to go
it is normal to “limit our study to the semantics
dealing with numerical precision” (Martel, 2005). On the other
hand, there is a great deal of work on the reliability of
programs that essentially ignores the numerics. The thesis
of this paper is that there is a class of problems that fall
between these two, which could be described as “does the lowlevel
arithmetic implement the highlevel mathematics”. Many
of these problems arise because mathematics, particularly
the mathematics of the complex numbers, is more difficult
than expected: for example the complex function log is not
continuous, writing down a program to compute an inverse
function is more complicated than just solving an equation,
and many algebraic simplification rules are not universally
valid.
The good news is that these problems are theoretically
capable of being solved, and are practically close to being solved,
but not yet solved, in several realworld examples. However,
there is still a long way to go
Original language  English 

Title of host publication  Proceedings of SYNASC 2012: 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing 
Place of Publication  Piscataway 
Publisher  IEEE 
Pages  8388 
Number of pages  6 
ISBN (Print)  9781467350266 
DOIs  
Publication status  Published  2012 
Event  SYNASC 2012: 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing  Timisoara, Romania Duration: 25 Sep 2012 → 28 Sep 2012 
Conference
Conference  SYNASC 2012: 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing 

Country/Territory  Romania 
City  Timisoara 
Period  25/09/12 → 28/09/12 
Projects
 1 Finished

Real Geometry and Connectedness via Triangular Description
Davenport, J., Bradford, R., England, M. & Wilson, D.
Engineering and Physical Sciences Research Council
1/10/11 → 31/12/15
Project: Research council