By S. A. Abramov, M. A. Barkatou (auth.), Vladimir P. Gerdt, Wolfram Koepf, Ernst W. Mayr, Evgenii V. Vorozhtsov (eds.)

ISBN-10: 3319022962

ISBN-13: 9783319022963

ISBN-10: 3319022970

ISBN-13: 9783319022970

This publication constitutes the complaints of the 14th foreign Workshop on laptop Algebra in clinical Computing, CASC 2013, held in Berlin, Germany, in September 2013. The 33 complete papers offered have been conscientiously reviewed and chosen for inclusion during this ebook.

The papers handle matters equivalent to polynomial algebra; the answer of tropical linear structures and tropical polynomial structures; the idea of matrices; using computing device algebra for the research of varied mathematical and utilized subject matters concerning traditional differential equations (ODEs); functions of symbolic computations for fixing partial differential equations (PDEs) in mathematical physics; difficulties bobbing up on the program of laptop algebra tools for locating infinitesimal symmetries; purposes of symbolic and symbolic-numeric algorithms in mechanics and physics; computerized differentiation; the applying of the CAS Mathematica for the simulation of quantum mistakes correction in quantum computing; the appliance of the CAS hole for the enumeration of Schur earrings over the crowd A5; positive computation of 0 separation bounds for mathematics expressions; the parallel implementation of quickly Fourier transforms through the Spiral library iteration method; using object-oriented languages equivalent to Java or Scala for implementation of different types as sort sessions; a survey of business functions of approximate desktop algebra.

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**Extra info for Computer Algebra in Scientific Computing: 15th International Workshop, CASC 2013, Berlin, Germany, September 9-13, 2013. Proceedings**

**Sample text**

Backelin’s Lemma comes to aid when applying a homotopy to ﬁnd all isolated cyclic n-roots as follows. We must decide at the end of a solution path whether we have reached an isolated solution or a positive dimension solution set. This problem is especially diﬃcult in the presence of isolated singular solutions (such as 4-fold isolated cyclic 9-roots [36]). With the form of the solution set as in Backelin’s Lemma, we solve a triangular binomial system in the parameters t and with as x values the solution found at the end of a path.

Thus {F0 , . . , Fτ −1 } is a triangular set with main variables (b0 , b1 , . . , bτ −1 ) and main degrees (d, 1, . . , 1). d Moreover, we have init(F1 ) = · · · = init(Fτ −1 ) = i=1 i · ai,0 bi−1 0 , which is coprime with F0 .

Then, we deﬁne ord(ϕ) = r . m=n am T Puiseux Theorem. If k has characteristic zero, the ﬁeld k((T ∗ )) is the algebraic closure of the ﬁeld of formal Laurent series over k. Moreover, if k = C, the ﬁeld C( T ∗ ) is algebraically closed as well. From now on, we assume k = C. Puiseux Expansion. Let B = C((X ∗ )) or C( X ∗ ). Let f ∈ B[Y ], where d := deg(f, Y ) > 0. Let h := lc(f, Y ). According to Puiseux Theorem, there exists ϕi ∈ B, i = 1, . . , d, such that fh = (Y − ϕ1 ) · · · (Y − ϕd ). We call ϕ1 , .

### Computer Algebra in Scientific Computing: 15th International Workshop, CASC 2013, Berlin, Germany, September 9-13, 2013. Proceedings by S. A. Abramov, M. A. Barkatou (auth.), Vladimir P. Gerdt, Wolfram Koepf, Ernst W. Mayr, Evgenii V. Vorozhtsov (eds.)

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