Symbolic Functions in MATLAB
MATLAB is a mathematical and statistical analysis software program with a focus on matrix operations. It provides a range of procedures not only to deal with numerical data, but also with symbolic expressions. As well as the built-in functions listed below, MATLAB is compatible with MuPAD, a computer algebra system, and can import and evaluate MuPAD expressions and graphics.
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Basic Functions
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MATLAB can perform the basic operations that would be expected from a primarily mathematical software package, including basic arithmetic and matrix and array operations, including practical functions like sorting and transposing. It can also round toward zero or both positive and negative infinity, perform logarithms to the base of either two or 10, and conduct a variety of integrals and integral transformations. MATLAB can also compute error functions, complementary error functions, Gamma, Heaviside step and Lambert W/Omega.
Calculus and Algebra
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Calculus functions include differentiation of symbolic expression, symbolic integration and the computation of the limit of symbolic expression. MATLAB can also compute Jacobian Matrices and Taylor Series expansions. In terms of algebra, a range of matrix operations are possible, including determination of the symbolic matrix, eigenvalues, diagonals, ranks, polynomials, column space, Jordan forms and both upper and lower triangulars. The gradient vector and Hessian matrix of scalers can also be computed.
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Simplification and Conversion
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A selection of simplification functions are offered in MATLAB. These include factorization, Horner's nested polynomials, symbolic expansion of polynomials, algebraic simplification, simplification of fractions, symbolic substitution and the ability to rewrite expressions based on common subexpressions. In terms of conversions, MATLAB can perform C code representation, Fortran representation and LaTeX representation. It can also convert polynomial coefficients to symbolic polynomials, symbolic expressions to Simscape equations, symbolic matrices to single-precision matrices and symbolic matrices to unsigned 8-bit to 64-bit integers.
Graphics Functions
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Graphical and pedagogical functions are also offered. These include a contour plotter (both filled and unfilled) and 3-D mesh plotters. You also can plot three-dimensional parametric curves, colored surfaces and polar coordinates. Taylor series can be graphed, as can the functions of any given variable and Riemann sums. MATLAB has the ability to combine some of these plotters, namely the mesh and contour plotters and the surface and contour plotters.
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References
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