By Dongming Wang

With a software program library incorporated, this ebook presents an effortless creation to polynomial removing in perform. The library Epsilon, carried out in Maple and Java, includes greater than 70 well-documented capabilities for symbolic removing and decomposition with polynomial structures and geometric reasoning. The ebook offers the performance, implementation, and function of Epsilon and demonstrates the usefulness of the removing device via a few chosen purposes, including many examples and illustrations. The reader will locate Epsilon an effective software, appropriate to a variety of difficulties in technological know-how, engineering, and undefined, and this booklet an obtainable exposition and a necessary reference for removal conception, equipment, and perform.

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**Additional info for Elimination Practice: Software Tools and Applications (With CD-Rom)**

**Example text**

Pi4-l + --- + Pd, Po^O, where o r d ^ X p ) < q for each i. We call xpq the lead of P, denoted by lead(F), and Po the initial ofP, denoted by ini(F). The differential polynomial dP/dxpq is called the separant ofP, denoted by sep(P). Let Q be another differential polynomial. Pseudo-dividing Q by P and its derivatives in xp, one may get a differential pseudo-remainder formula of the form dki P dksP sep(F)«ini(F)P e = " 1 ^ - + • • • +HMlp- +R, 36 Chapter 3. The CharSets Package where a, (3,A:y are nonnegative integers and R a differential polynomial with rank (R,xp) -< (q,d) (see [50, 94]).

3 Test Examples Example 0 refers to the polynomial set {x\ + X\x\ — X2X4 — X\X2X4 + X\X2 + 3x2, -*1 M + X3 — Xi^2, X3X4 — 2x\ —X\X2—\) with variable ordering x\ -<•••-< X4 which is taken from [59, 78]. 2. The source of the other test examples are given in Appendices A and B. The examples used to test the functions of dcharsets are listed below. Ex 1. P = {xy' - 2x"y,zz'y" + 6xy,z'y'y" + 3zx"} and Q = {z - 2y,y'} with x -< y -< z; Ex 2. P ~ {x1 — u\x2 — u2x, U2 — x2} with u\ -< U2 < x; Ex3. F = {x" -yxf-y' -u,y"-2xy'-2x'yx-y-2x,z-y} u a parameter independent of t; Ex4.

However, this works well only in some cases. The characteristic sets and thus various related zero decompositions are not unique in general. To avoid redundant or unpleasant output expressions, we have also arranged to tidy up the output (this postprocess may be quite expensive). 3 Test Examples Example 0 refers to the polynomial set {x\ + X\x\ — X2X4 — X\X2X4 + X\X2 + 3x2, -*1 M + X3 — Xi^2, X3X4 — 2x\ —X\X2—\) with variable ordering x\ -<•••-< X4 which is taken from [59, 78]. 2. The source of the other test examples are given in Appendices A and B.