Abstract
Outsourcing algebraic computations in dynamic geometry tools is a possible strategy used when software distribution constraints apply. If the target user machine has hardware limitations, or if the computer algebra system cannot be easily (or legally) packaged inside the geometric software, this approach can solve current shortcomings in dynamic environments.We report the design and implementation of a web service using Singular, a program specialized in ideal theory and commutative algebra. Besides its canonical address, a virtual appliance and a port to a low-cost ARM based computer are also provided. Any interactive geometric environment can then outsource computations where Singular is used, and incorporate their results into the system. In particular, we illustrate the capabilities of the web service by extending current abilities of GeoGebra to deal with algebraic loci and envelopes by means of a recent algorithm for studying parametric polynomial systems.
Highlights
Dynamic geometry (DG) software refers to computer programs where accurate geometric constructions can be done
1 http://cabri.com 2 http://www.keycurriculum.com/products/sketchpad 3 http://www.geogebra.org a recent algorithm for solving parametric polynomial systems, GroebnerCover [8], an existing GeoGebra command for computing the algebraic description of geometric loci is improved and a new one dealing with envelopes of curves is implemented
We described the design and implementation of SingularWS, a web service allowing access to Singular, a computer algebra system for polynomial computations
Summary
Either if the target user machine has hardware limitations, or if the computer algebra system cannot be (or legally) packaged inside the geometric software, this approach can solve current shortcomings in dynamic environments. Any interactive geometric environment can outsource computations where Singular is used, and incorporate their results into the system. We illustrate the capabilities of the web service by extending current abilities of GeoGebra to deal with algebraic loci and envelopes by means of a recent algorithm for studying parametric polynomial systems. Keywords Web services · Dynamic geometry · Parametric polynomial systems · Geometric loci · Envelopes
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