Symbolic array matlab

– Create numbered symbolic variables, symbolic variables in MATLAB functions, or symbolic numbers whose values differ from their names in the MATLAB workspace.syms – Create fresh symbolic variables for interactive symbolic workflows, that is, for symbolic variable creation at the MATLAB command line or in MATLAB live scripts. A fresh symbolic variable does not have any assumptions.The syms command is shorthand for the sym syntax, but the two functions handle assumptions differently. syms clears the assumptions when creating variables. However, recreating a variable using sym does not clear its assumptions. For more details about the differences of these two functions, see Choose syms or sym Function.Create the symbolic variables x and y using syms and sym, respectively.The first command creates a symbolic variable x in the MATLAB workspace with the value x assigned to the variable x. The second command creates a symbolic variable y with the value y.With syms, you can create multiple variables in one command. Create the variables a, b, and c.Create Array of Symbolic VariablesIf you want to create a MATLAB array of numbered symbolic variables, you can use the sym or the syms syntax.Use sym to create an array of many numbered symbolic variables. Clear the workspace. Create a row vector containing the symbolic variables a1,…,a10 and assign it to the MATLAB variable A. Display the variable in the MATLAB workspace.clearA = sym("a",[1 10])A = (a1a2a3a4a5a6a7a8a9a10) Name Size Bytes Class Attributes A 1x10 8 sym A is a 1-by-10 array of 10 automatically generated elements. These generated elements of A do not appear in the MATLAB workspace.Use syms to create many fresh symbolic variables with corresponding variable names in the MATLAB workspace. Clear the workspace. Create the fresh symbolic variables a1, ..., a10. Display the variables in the MATLAB workspace. Name Size Bytes Class Attributes a 1x10 8 sym a1 1x1 8 sym a10 1x1 8 sym a2 1x1 8 sym a3 1x1 8 sym a4 1x1 8 sym a5 1x1 8 sym a6 1x1 8 sym a7 1x1 8 sym a8 1x1 8 sym a9 1x1 8 sym The MATLAB workspace contains 10 MATLAB

Create symbolic variables, expressions, functions, matricesSyntaxDescriptionx = sym("x") creates symbolic scalar variable x.exampleA = sym("a",[n1 ... nM]) creates an n1-by-...-by-nM symbolic array filled with automatically generated elements. For example, A = sym("a",[1 3]) creates the row vector A = [a1 a2 a3]. The generated elements a1, a2, and a3 do not appear in the MATLAB® workspace. For multidimensional arrays, these elements have the prefix a followed by the element’s index using _ as a delimiter, such as a1_3_2.exampleA = sym("a",n) creates an n-by-n symbolic matrix filled with automatically generated elements.examplesym(___,set) creates a symbolic variable or array and sets the assumption that the variable or all array elements belong to set. Here, set can be "real", "positive", "integer", or "rational". You also can combine multiple assumptions by specifying a string array or cell array of character vectors. For example, assume a positive rational value by specifying set as ["positive" "rational"] or {'positive','rational'}.examplesym(___,"clear") clears assumptions set on a symbolic variable or array. You can specify "clear" after the input arguments in any of the previous syntaxes, except combining "clear" and set. You cannot set and clear an assumption in the same function call to sym.sym(num) converts a number or numeric matrix specified by num to a symbolic number or symbolic matrix.examplesym(num,flag) uses the technique specified by flag to convert floating-point numbers to symbolic numbers.example sym(strnum) converts the character vector or string specified by strnum to an accurate symbolic number without approximation.examplesymexpr = sym(h) createsa symbolic expression or matrix symexpr froman anonymous MATLAB function associated with the function handle h.example symexpr = sym(M) converts a symbolic matrix variable M of type symmatrix to an array of symbolic scalar variables symexpr of type sym.exampleExamplescollapse allCreate Symbolic VariablesCreate the symbolic variables x and y.Create Symbolic VectorsCreate a 1-by-4 symbolic vector a with automatically generated elements a1,...,a4.You can specify the format for the element names by using a format operator within the first argument. sym replaces %d with the index of the element to generate the element names.However, these syntaxes do not create symbolic variables a1, ..., a4, x1, ..., x4 in the MATLAB workspace. To access the elements of a and b, use the standard indexing methods.Create Symbolic MatricesCreate a 3-by-4 symbolic matrix with automatically generated elements. The sym function generates matrix elements of the form Ai,j. Here, sym generates the elements A1,1, ..., A3,4.A = (A1,1A1,2A1,3A1,4A2,1A2,2A2,3A2,4A3,1A3,2A3,3A3,4)Create a 4-by-4 matrix with the element names x1,1, ..., x4,4 by using a format operator within the first argument. sym replaces %d with the index of the element to generate the element names.B = (x1,1x1,2x1,3x1,4x2,1x2,2x2,3x2,4x3,1x3,2x3,3x3,4x4,1x4,2x4,3x4,4)These syntaxes do not create symbolic variables A1,1, ..., A3,4, x1,1, ..., x4,4 in the MATLAB workspace. To access an element of a matrix, use parentheses.Create Symbolic Multidimensional ArraysCreate a 2-by-2-by-2 symbolic array with automatically generated elements a1,1,1,…,a2,2,2.A(:,:,1) = (a1,1,1a1,2,1a2,1,1a2,2,1)A(:,:,2) = (a1,1,2a1,2,2a2,1,2a2,2,2)Create Symbolic NumbersConvert numeric values to symbolic numbers or expressions. Use sym on subexpressions instead of the entire expression for better accuracy. Using sym on entire expressions is inaccurate because MATLAB® first converts

Example: h = @(x)sin(x) M — Symbolic matrix variable to convert symbolic matrix variable Symbolic matrix variable to convert, specified as a symbolic matrix variable. Alternatively, you can use symmatrix2sym to convert a symbolic matrix variable to an array of symbolic scalar variables. Example: syms A 2 matrix; M = A^2 + eye(2) Data Types: symmatrixOutput Argumentscollapse allx — Variable symbolic scalar variableVariable, returned as a symbolic scalar variable.A — Vector or matrix with automatically generated elements symbolic vector | symbolic matrixVector or matrix with automatically generated elements, returned as a symbolic vector or matrix of symbolic scalar variables. The elements of this vector or matrix do not appear in the MATLAB workspace.symexpr — Expression or matrix converted from anonymous MATLAB function or symbolic matrix variable symbolic expression | symbolic matrix Expression or matrix converted from an anonymous MATLAB function or a symbolic matrix variable, returned as a symbolic expression or matrix of symbolic scalar variables. Data Types: symTipsStatements like pi = sym(pi) and delta = sym("1/10") create symbolic numbers that avoid the floating-point approximations inherent in the values of pi and 1/10. The pi created in this way stores the symbolic number in a workspace variable named pi, which temporarily replaces the built-in numeric function with the same name. Use clear pi to restore the floating-point representation of pi.sym always treats i incharacter vector input as an identifier. To input the imaginary number i,use 1i instead.clear x does not clear the symbolicobject of its assumptions, such as real, positive, or any assumptionsset by assume, sym, or syms.To remove assumptions, use one of these options:assume(x,"clear") removes all assumptions affecting x.clear all clears all objects inthe MATLAB workspace and resets the symbolic engine.assume and assumeAlso provide more flexibility for setting assumptions on variables.When you replace one or more elements of a numericvector or matrix with a symbolic number, MATLAB converts thatnumber to a double-precision number.A = eye(3);A(1,1) = sym(pi)A = 3.1416 0 0 0 1.0000 0 0 0 1.0000 You cannot replace elements of a numeric vector or matrix with a symbolic variable, expression, or function because these elements cannot be converted to double-precision numbers. For example, A(1,1) = sym("a") throws an error.When you use the syntax A = sym("a",[n1 ... nM]), the sym function assigns only the symbolic array A to the MATLAB workspace. To also assign the automatically generated elements of A, use the syms function instead. For example, syms a [1 3] creates the row vector a = [a1 a2 a3] and the symbolic variables a1, a2, and a3 in the MATLAB workspace.Alternative FunctionalityAlternative Approaches for Creating Symbolic VariablesTo create several symbolic variables in one function call, use syms. Using syms also clears assumptions from the named variables.Version HistoryIntroduced before R2006aexpand allR2022b: Convert symbolic matrix variablesYou can convert a symbolic matrix variable M of type symmatrix to an array of symbolic scalar variables symexpr of type sym by using symexpr = sym(M). For an example, see Convert Hessian Matrix.R2020a: sym("pi") creates symbolic variablesym("pi") now creates a symbolic variable