In the present note a MAPLE subroutine computing Milnor and Tyurina numbers of an isolated algebraic hypersurface singularity is presented and described in detail.

This article describes the subroutine library SLICOT that provides Fortran 77 implementations of numerical algorithms for computations in systems and control theory. Around a nucleus of basic numerical linear algebra subroutines, this library builds methods for the design and analysis of linear control systems. A brief history of the library is given together with a description of the current v...

and Applied Analysis 3 Proof. Since f(x) defined in (2) belongs to the PDGstructured family and by Lemma 2.1 in [16] the Clarke subdifferential of F(x, ρ) at x can be formulated by ∂F (x, ρ) = ∂f (x) + ρ∂G (x) = ∂f (x) + ρ conv { ∇g j (x) | j ∈ J (x) ∪ {0}}

Hoffman and Schwartz [13] developed the Lattice Polyhedron model and proved that it is totally dual integral (TDI), and so has integral optimal solutions. The model generalizes many important combinatorial optimization problems such as polymatroid intersection, cut covering polyhedra, min cost aborescences, etc., but has lacked a combinatorial algorithm. The problem can be seen as the blocking ...

Automated deduction techniques are being used in a system called Amphion to derive, from graphical speci cations, programs composed from a subroutine library. The system has been applied to construct software for the planning and analysis of interplanetary missions. The library for that application is a collection of subroutines written in FORTRAN-77 at JPL to perform computations in solar-syst...

This paper positively solves the quantum subroutine problem for fully quantum oracles. The quantum subroutine problem asks whether a quantum computer with an efficiently computable oracle can be efficiently simulated by a non-oracle quantum computer. We extends the earlier results obtained by Bennett, Bernstein, Brassard, and Vazirani, and by Aharonov, Kitaev, and Nisan to the case where the or...

A number of synthesis applications are made possible by automated tools for synthesis. Recent work has shown that SMT solvers, instead of just acting as subroutines for automated software synthesis tasks, can be instrumented to perform synthesis themselves. This paper focuses on some of the current challenges for developing fast and useful procedures in SMT solvers for the benefit of synthesis ...

Square-root is a function for which numerous numerical methods have been developed. In most math packages for microprocessors, simple iterative methods have been used, as no special demands for speed — nor even for accuracy in some cases are expected: e.g. in [ l ] and [2] the execution time of square-rooting is approx. 2-5 times longer than that of multiplication, and in [3] a quintuple error ...

Variational quantum algorithms are augmented by an additional subroutine that efficiently detects signatures of barren plateaus -- unfavorable parameter regions prevent optimization due to vanishing gradients.