  We propose a method for automatically generating abstract transformers for
static analysis by abstract interpretation. The method focuses on linear
constraints on programs operating on rational, real or floating-point variables
and containing linear assignments and tests. In addition to loop-free code, the
same method also applies for obtaining least fixed points as functions of the
precondition, which permits the analysis of loops and recursive functions. Our
algorithms are based on new quantifier elimination and symbolic manipulation
techniques. Given the specification of an abstract domain, and a program block,
our method automatically outputs an implementation of the corresponding
abstract transformer. It is thus a form of program transformation. The
motivation of our work is data-flow synchronous programming languages, used for
building control-command embedded systems, but it also applies to imperative
and functional programming.
