MathematicaWe present a new package, VEST (Vector Einstein Summation Tools), that performs abstract vector calculus computations in Mathematica. Through the use of index notation, VEST is able to reduce three-dimensional scalar and vector expressions of a very general type to a well defined ...
An affine transformation from ℝ2 to ℝ2 defined in two-dimensional matrix notation fx_,y_:=1234×xy+56; MatrixForm[f[{0, 0}]] 56 MatrixForm[f[{3, 4}]] 1631 MatrixForm56+1631==f0,0+f3,4 True ■ An affine transformation defined with the AffineTransform function t = AffineTransfor...
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The following sections are included:Elementary Operations with VectorsScalar and Vector FieldsThe Divergence and the Divergence TheoremStokes' Theorem and CurlGreen's IdentitiesOrthogonal Curvilinear CoordinatesEvaluation of Line and Surface IntegralsSuffix Notation Elementary Operations with Vectors Scalar and Ve...
notation above,\(P(D|{\mathrm {FR}}=3\,{\mathrm {Hz}}) > \! > \,P(D|{\mathrm {FR}}=20\,{\mathrm {Hz}}).\)The main idea behind the method is to systematically move the Gaussian across the real number line (e.g. from FR changes of −10 to 10 Hz in steps of 0...
Spacelike Submanifolds in the De Sitter Space (the particular notation is abbreviated) with Constant Scalar Curvature Let M(superscript n) be a closed spacelike submanifold isometrically immersed in de Sitter space (the particular notation is abbreviated). Denote by R, H a... JF Zhang - Applie...
This has been achieved using exact computations in Mathematica. Here we have slightly abused notation by writing \chi _{\beta } for the coordinate representation of \chi _{\beta } using (x, y)-coordinates in the source and the following coordinates in the target space: ...
and, with a little abuse of notation, when referring to Eq. (2.23), we sometimes drop the\big |_{\delta (s_2)}, to ease the notation. 3Description of the calculation In order to compute the power corrections of the cross section in Eq. (2.23), we follow the path along which we...
We present a new package, VEST (Vector Einstein Summation Tools), that\nperforms abstract vector calculus computations in Mathematica. Through the use\nof index notation, VEST is able to reduce three-dimensional scalar and vector\nexpressions of a very general type to a well defined standard ...
The colon notation can be used in other contexts in MatLab as well. For instance, [1:4] is the row vector [1, 2, 3, 4]. The syntax, 1:4, which omits the square brackets, works fine in MatLab. However, we will usually use square brackets, since they draw attention to the presen...