Automatic Deduction in Dynamic Geometry using Sage

We present a symbolic tool that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction. The main prototype has been developed as two different worksheets for the open source computer algebra system Sage, corresponding to two different ways of coding a geometric construction. In one worksheet, diagrams constructed with the open source dynamic geometry system GeoGebra are accepted. In this worksheet, Groebner bases are used to either compute the equation of a geometric locus in the case of a locus construction or to determine the truth of a general geometric statement included in the GeoGebra construction as a boolean variable. In the second worksheet, locus constructions coded using the common file format for dynamic geometry developed by the Intergeo project are accepted for computation. The prototype and several examples are provided for testing. Moreover, a third Sage worksheet is presented in which a novel algorithm to eliminate extraneous parts in symbolically computed loci has been implemented. The algorithm, based on a recent work on the Groebner cover of parametric systems, identifies degenerate components and extraneous adherence points in loci, both natural byproducts of general polynomial algebraic methods. Detailed examples are discussed.Comment: In Proceedings THedu'11, arXiv:1202.453

Enhanced thermoelectric response of hole-doped La2_2NiO4+δ_{4+\delta} by ab initio calculations

Thermoelectric properties of the system La$_2$NiO$_{4+\delta}$ have been studied ab initio. Large Seebeck coefficient values are predicted for the parent compound, and to some extent remain in the hole-doped metallic phase, accompanied of an increase in the conductivity. This system, due to its layered structure would be a suitable candidate for an improvement of its thermoelectric figure of merit by nanostructurization in thin films, that has already been shown to increase the electrical conductivity ($\sigma$). Our calculations show that in the region around La$_2$NiO$_{4.05}$ the system has a large thermopower at high temperatures and also a substantially increased $\sigma$. Films grown with this low-doping concentration will show an optimal relationship between thermopower and $\sigma$. This result is obtained for various exchange-correlation schemes (correlated, uncorrelated and parameter-free) that we use to analyze the electronic structure of the hole-doped compound.Comment: 10 pages, 6 figure

Electronic structure of V4_4O7_7: charge ordering, metal-insulator transition and magnetism

The low and high-temperature phases of V$_4$O$_7$ have been studied by \textit{ab initio} calculations. At high temperature, all V atoms are electronically equivalent and the material is metallic. Charge and orbital ordering, associated with the distortions in the V pseudo-rutile chains, occur below the metal-insulator transition. Orbital ordering in the low-temperature phase, different in V$^{3+}$ and V$^{4+}$ chains, allows to explain the distortion pattern in the insulating phase of V$_4$O$_7$. The in-chain magnetic couplings in the low-temperature phase turn out to be antiferromagnetic, but very different in the various V$^{4+}$ and V$^{3+}$ bonds. The V$^{4+}$ dimers formed below the transition temperature form spin singlets, but V$^{3+}$ ions, despite dimerization, apparently participate in magnetic ordering.Comment: 10 pages, 6 figures, 2 table

Automatic Deduction in (Dynamic) Geometry: Loci Computation

A symbolic tool based on open source software that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction is presented. The prototype has been developed as two different worksheets for the open source computer algebra system Sage, corresponding to two different ways of coding a geometric construction, namely with the open source dynamic geometry system GeoGebra or using the common file format for dynamic geometry developed by the Intergeo project. Locus computation algorithms based on Automatic Deduction techniques are recalled and presented as basic for an efficient treatment of advanced methods in dynamic geometry. Moreover, an algorithm to eliminate extraneous parts in symbolically computed loci is discussed. The algorithm, based on a recent work on the Gröbner cover of parametric systems, identifies degenerate components and extraneous adherence points in loci, both natural byproducts of general polynomial algebraic methods. Several examples are shown in detail

Paralytic Shellfish Toxins Occurrence in Non-Traditional Invertebrate Vectors from North Atlantic Waters (Azores, Madeira, and Morocco)

Paralytic shellfish toxins (PSTs) are potent alkaloids of microalgal and cyanobacterial origin, with worldwide distribution. Over the last 20 years, the number of poisoning incidents has declined as a result of the implementation of legislation and monitoring programs based on bivalves. In the summer of 2012 and 2013, we collected a total of 98 samples from 23 different species belonging to benthic and subtidal organisms, such as echinoderms, crustaceans, bivalves, and gastropods. The sampling locations were Madeira, São Miguel Island (Azores archipelago), and the northwestern coast of Morocco. The samples were analyzed using post-column oxidation liquid chromatography with a fluorescence detection method. Our main goal was to detect new vectors for these biotoxins. After reporting a total of 59 positive results for PSTs with 14 new vectors identified, we verified that some of the amounts exceeded the limit value established in the EU. These results suggest that routine monitoring of saxitoxin and its analogs should be extended to more potential vectors other than bivalves, including other edible organisms, for a better protection of public health.This research was partially funded by the Portuguese Fundation of Science and Technology (FCT) project UID/Multi/04423/2013 and by the projects ALERTOXNET (EAPA_317/2016), funded by the Interreg Atlantic program. The Spanish research leading to these results has received funding from the following European Fund for Economic and Regional Development (FEDER) cofunded-grants: Centro para el Desarrollo Tecnológico Industrial (CDTI) and Technological Funds, supported by Ministerio de Economía y Competitividad, AGL2012-40185-CO2-01, AGL2014-58210-R, and Consellería de Cultura, Educación e Ordenación Universitaria, GRC2013-016; CDTI under India&Spain Innovating Program (ISIP) Programme, Spain, IDI-20130304 APTAFOOD; the European Union’s Seventh Framework Programme managed by REA—Research Executive Agency (FP7/2007-2013) under grant agreement 312184 PHARMASEA. Acknowledment to project EMERTOX (grant 734748), funded by H2020-MSCA-RISE 2016

Using a free open source software to teach mathematics

We present the experience of the authors teaching mathematics to freshmen engineering students with the help of the open source computer algebra system Sage. We describe some teaching resources and present an ad hoc distribution of Sage used by the authors