2 research outputs found
Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains
A new algorithm to compute cylindrical algebraic decompositions (CADs) is
presented, building on two recent advances. Firstly, the output is truth table
invariant (a TTICAD) meaning given formulae have constant truth value on each
cell of the decomposition. Secondly, the computation uses regular chains theory
to first build a cylindrical decomposition of complex space (CCD) incrementally
by polynomial. Significant modification of the regular chains technology was
used to achieve the more sophisticated invariance criteria. Experimental
results on an implementation in the RegularChains Library for Maple verify that
combining these advances gives an algorithm superior to its individual
components and competitive with the state of the art
Understanding Branch Cuts of Expressions
We assume some standard choices for the branch cuts of a group of functions
and consider the problem of then calculating the branch cuts of expressions
involving those functions. Typical examples include the addition formulae for
inverse trigonometric functions. Understanding these cuts is essential for
working with the single-valued counterparts, the common approach to encoding
multi-valued functions in computer algebra systems. While the defining choices
are usually simple (typically portions of either the real or imaginary axes)
the cuts induced by the expression may be surprisingly complicated. We have
made explicit and implemented techniques for calculating the cuts in the
computer algebra programme Maple. We discuss the issues raised, classifying the
different cuts produced. The techniques have been gathered in the BranchCuts
package, along with tools for visualising the cuts. The package is included in
Maple 17 as part of the FunctionAdvisor tool.Comment: To appear in: Proceedings of Conferences on Intelligent Computer
Mathematics (CICM '13) - Mathematical Knowledge Management (MKM) stran