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C++ API

symbolic

The Octave-Forge Symbolic package adds symbolic calculation features to GNU Octave. These include common Computer Algebra System tools such as algebraic operations, calculus, equation solving, Fourier and Laplace transforms, variable precision arithmetic and other features. Internally, the package uses [SymPy](www.sympy.org), but no knowledge of Python is required. Compatibility with other symbolic toolboxes is intended.

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symbolic

assume
Specify assumptions for a symbolic variable (replace existing).
assumptions
List assumptions on symbolic variables.
bernoulli
Return symbolic Bernoulli numbers or Bernoulli polynomials.
catalan
Return Catalan constant.
cell2sym
Convert cell array to symbolic array.
digits
Set/get number of digits used in variable precision arith.
dirac
Compute the Dirac delta (generalized) function.
eulergamma
Return Euler–Mascheroni constant.
evalpy
Run Python code, automatically transferring results.
fibonacci
Return symbolic Fibonacci numbers or Fibonacci polynomials.
findsymbols
Return a list (cell array) of the symbols in an expression.
finiteset
Return a symbolic set containing the inputs without duplicates.
heaviside
Compute the Heaviside unit-step function.
laguerreL
Evaluate Laguerre polynomials.
lambertw
Compute the Lambert W function of Z.
octsympy_tests
Run the OctSymPy tests, log results, and return true if any fail.
poly2sym
Create a symbolic polynomial expression from coefficients.
python_cmd
Run some Python command on some objects and return other objects.
sympref
Preferences for the Symbolic package.
syms
Create symbolic variables and symbolic functions.
vpa
Create a variable-precision floating point number.
vpasolve
Numerical solution of a symbolic equation.
@double/coshint
Numerical coshint function.
@double/cosint
Numerical cosint function.
@double/dilog
Numerical dilogarithm function
@double/fresnelc
Numerical fresnelc function.
@double/fresnels
Numerical fresnels function.
@double/logint
Numerical logint function.
@double/polylog
Numerical polylogarithm function
@double/sinhint
Numerical sinhint function.
@double/sinint
Numerical sinint function.
@double/zeta
Numerical zeta function.
@logical/isAlways
Test if expression is mathematically true.
@sym/abs
Symbolic abs function.
@sym/acos
Symbolic acos function.
@sym/acosd
Symbolic inverse cos function with output in degrees.
@sym/acosh
Symbolic acosh function.
@sym/acot
Symbolic acot function.
@sym/acoth
Symbolic acoth function.
@sym/acsc
Symbolic acsc function.
@sym/acsch
Symbolic acsch function.
@sym/adjoint
Adjoint/Adjugate of a symbolic square matrix.
@sym/airy
Symbolic Airy functions of first/second kind and their derivatives.
@sym/all
Return true if all entries of a symbolic vector are nonzero.
@sym/and
Logical "and" of symbolic arrays.
@sym/angle
Symbolic polar angle.
@sym/any
Return true if any entries of a symbolic vector are nonzero.
@sym/argnames
Return the independent variables in a symfun.
@sym/asec
Symbolic asec function.
@sym/asech
Symbolic asech function.
@sym/asin
Symbolic asin function.
@sym/asind
Symbolic inverse sin function with output in degrees.
@sym/asinh
Symbolic asinh function.
@sym/assume
New assumptions on a symbolic variable (replace old if any).
@sym/assumeAlso
Add additional assumptions on a symbolic variable.
@sym/atan
Symbolic atan function.
@sym/atan2
Return an angle from a point given by symbolic expressions.
@sym/atand
Symbolic inverse tan function with output in degrees.
@sym/atanh
Symbolic atanh function.
@sym/besselh
Symbolic Hankel functions of first/second kind.
@sym/besseli
Symbolic modified Bessel function of the first kind.
@sym/besselj
Symbolic Bessel function of the first kind.
@sym/besseljn
Symbolic Spherical Bessel function of the first kind.
@sym/besselk
Symbolic modified Bessel function of the second kind.
@sym/bessely
Symbolic Bessel function of the second kind.
@sym/besselyn
Symbolic Spherical Bessel function of the second kind.
@sym/beta
Beta function.
@sym/cat
Concatenate symbolic arrays along particular dimension.
@sym/cbrt
Symbolic cbrt function.
@sym/ccode
Convert symbolic expression into C code.
@sym/ceil
Symbolic ceil function.
@sym/char
Return string representation of a symbolic expression.
@sym/charpoly
Characteristic polynomial of symbolic matrix.
@sym/chebyshevT
Find the nth symbolic Chebyshev polynomial of the first kind.
@sym/chebyshevU
Find the nth symbolic Chebyshev polynomial of the second kind.
@sym/children
Return "children" (terms, lhs/rhs, etc) of symbolic expression.
@sym/chol
Cholesky factorization of symbolic symmetric matrix.
@sym/coeffs
Return non-zero (or all) coefficients of symbolic polynomial.
@sym/colon
Generate a range of symbolic expressions.
@sym/columns
Return the number of columns in a symbolic array.
@sym/cond
Symbolic condition number of a symbolic matrix.
@sym/conj
Symbolic conjugate function.
@sym/cos
Symbolic cos function.
@sym/cosd
Symbolic cos function with input in degrees.
@sym/cosh
Symbolic cosh function.
@sym/coshint
Symbolic coshint function.
@sym/cosint
Symbolic cosint function.
@sym/cot
Symbolic cot function.
@sym/coth
Symbolic coth function.
@sym/cross
Symbolic cross product.
@sym/csc
Symbolic csc function.
@sym/csch
Symbolic csch function.
@sym/ctranspose
Conjugate (Hermitian) transpose of a symbolic array.
@sym/curl
Symbolic curl of symbolic expression.
@sym/dawson
Symbolic Dawson (scaled imaginary error) function.
@sym/degree
Return the degree of a polynomial expression.
@sym/det
Symbolic determinant of a matrix.
@sym/diag
Make diagonal matrix or extract diagonal of symbolic matrix.
@sym/diff
Symbolic differentiation.
@sym/dilog
Symbolic dilogarithm function.
@sym/dirac
Symbolic dirac function.
@sym/disp
Display the value of a symbolic expression.
@sym/display
Display, on command line, the contents of a symbolic expression.
@sym/divergence
Symbolic divergence of symbolic expression.
@sym/divisors
Get divisors of integer.
@sym/dot
Symbolic dot (scalar) product.
@sym/double
Convert symbolic to doubles.
@sym/dsolve
Solve ordinary differentual equations (ODEs) symbolically.
@sym/ei
Symbolic exponential integral (Ei) function.
@sym/eig
Symbolic eigenvalues/eigenvectors of a matrix.
@sym/end
Overloaded end for symbolic arrays.
@sym/eq
Test for symbolic equality, and/or define equation.
@sym/equationsToMatrix
Convert set of linear equations to matrix form.
@sym/erf
Symbolic erf function.
@sym/erfc
Symbolic erfc function.
@sym/erfcinv
Symbolic erfcinv function.
@sym/erfi
Symbolic erfi function.
@sym/erfinv
Symbolic erfinv function.
@sym/exp
Symbolic exp function.
@sym/expand
Combine parts of a symbolic product.
@sym/expint
Symbolic generalized exponential integral (expint) function.
@sym/expm
Symbolic matrix exponential.
@sym/eye
Return an identity matrix.
@sym/ezplot
Simple plotting of symbolic expressions.
@sym/ezplot3
Simple 3D parametric plotting of symbolic expressions.
@sym/ezsurf
Simple 3D surface plots of symbolic expressions.
@sym/factor
Factor a symbolic polynomial or integer.
@sym/factorial
Symbolic factorial function.
@sym/findsym
Find symbols in expression, return them as comma-separated string.
@sym/fix
Symbolic fix function.
@sym/fliplr
Flip a symbolic matrix horizontally.
@sym/flipud
Flip a symbolic matrix vertically.
@sym/floor
Symbolic floor function.
@sym/formula
Return a symbolic expression for this object.
@sym/fortran
Convert symbolic expression into C code.
@sym/fourier
Symbolic Fourier transform.
@sym/frac
Return the fractional part of a symbolic expression.
@sym/fresnelc
Symbolic Fresnel Cosine function.
@sym/fresnels
Symbolic Fresnel Sine function.
@sym/function_handle
Convert symbolic expression into a standard function.
@sym/gamma
Symbolic gamma function.
@sym/gammainc
Symbolic incomplete gamma function.
@sym/gammaln
Symbolic logarithm of the gamma function.
@sym/ge
Test/define symbolic inequality, greater than or equal to.
@sym/gradient
Symbolic gradient of symbolic expression.
@sym/gt
Test/define symbolic inequality, greater than.
@sym/has
Naively test if an expression contains a subexpression.
@sym/heaviside
Symbolic Heaviside step function.
@sym/hessian
Symbolic Hessian matrix of symbolic scalar expression.
@sym/hilb
Return the symbolic Hilbert matrix.
@sym/horner
Convert a symbolic polynomial to Horner form.
@sym/horzcat
Horizontally concatentate symbolic arrays.
@sym/hypergeom
Symbolic generalized hypergeometric function.
@sym/hypot
Return hypoteneuse (distance) from symbolic expressions.
@sym/ifourier
Symbolic inverse Fourier transform.
@sym/igamma
Symbolic upper incomplete gamma function.
@sym/ilaplace
Inverse Laplace transform.
@sym/imag
Imaginary part of a symbolic expression.
@sym/int
Symbolic integration.
@sym/intersect
Return the common elements of two sets.
@sym/interval
Return an interval.
@sym/inv
Symbolic inverse of a matrix.
@sym/invhilb
Return the symbolic inverse of the Hilbert matrix.
@sym/ipermute
Invert a permutation the indices of a symbolic array.
@sym/isAlways
Test if expression is mathematically true.
@sym/isNone
Return true if symbolic expression is Python object None.
@sym/isallconstant
Whether all elements of a symbolic array are constant.
@sym/iscolumn
Return true if symbolic expression is a column vector.
@sym/isconstant
Indicate which elements of symbolic array are constant.
@sym/isempty
Return true a symbolic array is empty (one dimension is zero).
@sym/isequal
Test if contents of two or more arrays are equal.
@sym/isequaln
Test if contents of arrays are equal, even with nan.
@sym/isfinite
Is symbolic expression finite.
@sym/isinf
Return true if a symbolic expression is infinite.
@sym/ismatrix
Return true if this symbolic expression is a matrix.
@sym/ismember
Test if an object is contained within a set or a matrix.
@sym/isna
Symbolic expressions cannot be the Octave/R missing data NA.
@sym/isnan
Return true if a symbolic expression is Not-a-Number.
@sym/isprime
Return true if a symbolic number is prime.
@sym/isrow
Return true if symbolic expression is a row vector.
@sym/isscalar
Return true if this symbolic expression is a scalar.
@sym/isvector
Return true if this symbolic expression is a vector.
@sym/jacobian
Symbolic Jacobian of symbolic expression.
@sym/jordan
Symbolic Jordan canonical form of a matrix.
@sym/kron
Kronecker tensor product of two matrices.
@sym/laguerreL
Symbolic Laguerre polynomials and associated Laguerre polynomials.
@sym/lambertw
Symbolic Lambert W function.
@sym/laplace
Laplace transform.
@sym/laplacian
Symbolic Laplacian of symbolic expression.
@sym/latex
Display or return LaTeX typesetting code for symbolic expression.
@sym/ldivide
Element-wise backslash division of symbolic expressions.
@sym/le
Test/define symbolic inequality, less than or equal to.
@sym/length
Length of a symbolic vector.
@sym/lgamma
Symbolic logarithm of the gamma function.
@sym/lhs
Left-hand side of symbolic expression.
@sym/limit
Evaluate symbolic limits.
@sym/linspace
Return a symbolic vector of equispaced points.
@sym/log
Symbolic log function.
@sym/log10
Symbolic log base 10 function.
@sym/log2
Symbolic log base 2 function.
@sym/logical
Test if expression is "structurally" true.
@sym/logint
Symbolic logint function.
@sym/logspace
Return a symbolic vector of logarithmically-spaced points.
@sym/lt
Test/define symbolic inequality, less than.
@sym/lu
Symbolic LU factorization of a matrix.
@sym/matlabFunction
Convert symbolic expression into a standard function.
@sym/max
Return maximum value of a symbolic vector or vectors.
@sym/min
Return minimum value of a symbolic vector or vectors.
@sym/minus
Subtract one symbolic expression from another.
@sym/mldivide
Symbolic backslash: solve symbolic linear systems.
@sym/mod
Element-wise modular arithmetic on symbolic arrays and polynomials.
@sym/mpower
Symbolic expression matrix exponentiation.
@sym/mrdivide
Forward slash division of symbolic expressions.
@sym/mtimes
Multiply symbolic matrices.
@sym/nchoosek
Symbolic binomial coefficient.
@sym/ne
Test/define symbolic inequality, not equal to.
@sym/nextprime
Return the next prime number.
@sym/nnz
Number of non-zero elements in the symbolic array.
@sym/norm
Symbolic vector/matrix norm.
@sym/not
Logical "not" of a symbolic array.
@sym/null
Basis for the nullspace of a symbolic matrix.
@sym/numden
Extract numerator and denominator of symbolic expression.
@sym/numel
Return number of elements in symbolic array.
@sym/ones
Return a matrix whose elements are all 1.
@sym/or
Logical "or" of symbolic arrays.
@sym/orth
Orthonormal basis for column space (range) of symbolic matrix.
@sym/partfrac
Compute partial fraction decomposition of a rational function.
@sym/permute
Permute the indices of a symbolic array.
@sym/pinv
Symbolic Moore-Penrose pseudoinverse of a matrix.
@sym/plus
Add two symbolic expressions together.
@sym/polylog
Symbolic polylogarithm function.
@sym/potential
Symbolic potential of a vector field.
@sym/power
Symbolic expression componentwise exponentiation.
@sym/pretty
Return/display unicode/ascii-art representation of expression.
@sym/prevprime
Return the previous prime number.
@sym/private_disp_name
A string appropriate for representing the name of this sym.
@sym/prod
Product of symbolic expressions.
@sym/psi
Symbolic polygamma function.
@sym/qr
Symbolic QR factorization of a matrix.
@sym/rank
Rank of a symbolic matrix.
@sym/rdivide
Element-wise forward slash division of symbolic expressions.
@sym/real
Real part of a symbolic expression.
@sym/repmat
Build symbolic block matrices.
@sym/reshape
Change the shape of a symbolic array.
@sym/resize
Resize a symbolic array, cropping or padding with zeros.
@sym/rewrite
Rewrite a symbolic expression.
@sym/rhs
Right-hand side of symbolic expression.
@sym/round
Symbolic round function.
@sym/rows
Return the number of rows in a symbolic array.
@sym/rref
Reduced Row Echelon Form of a symbolic matrix.
@sym/sec
Symbolic sec function.
@sym/sech
Symbolic sech function.
@sym/setdiff
Set subtraction.
@sym/setxor
Return the symmetric difference of two sets.
@sym/sign
Symbolic sign function.
@sym/signIm
Return the sign of the imaginary part of a complex expression.
@sym/simplify
Simplify an expression.
@sym/sin
Symbolic sin function.
@sym/sind
Symbolic sin function with input in degrees.
@sym/sinh
Symbolic sinh function.
@sym/sinhint
Symbolic sinhint function.
@sym/sinint
Symbolic sinint function.
@sym/size
Return the size of a symbolic array.
@sym/solve
Symbolic solutions of equations, inequalities and systems.
@sym/sort
Order the elements in increasing order.
@sym/sqrt
Symbolic sqrt function.
@sym/ssinint
Symbolic shifted sine integral function.
@sym/subs
Replace symbols in an expression with other expressions.
@sym/subsasgn
Assign to entries of a symbolic array.
@sym/subsindex
Used to implement indexing by sym.
@sym/subsref
Access entries of a symbolic array.
@sym/sum
Sum of symbolic expressions.
@sym/svd
Symbolic singular value decomposition.
@sym/sym
Define symbols and numbers as symbolic expressions.
@sym/sym2poly
Return vector of coefficients of a symbolic polynomial.
@sym/symprod
Symbolic product.
@sym/sympy
The underlying SymPy representation as a string.
@sym/symreplace
Replace symbols in caller’s workspace or in syms/struct/cells.
@sym/symsum
Symbolic summation.
@sym/symvar
Find symbols in expression and return them as a symbolic vector.
@sym/tan
Symbolic tan function.
@sym/tand
Symbolic tan function with input in degrees.
@sym/tanh
Symbolic tanh function.
@sym/taylor
Symbolic Taylor series.
@sym/times
Return Hadamard product (element-wise multiplication) of matrices.
@sym/toeplitz
Construct a symbolic Toeplitz matrix.
@sym/trace
Trace of symbolic matrix.
@sym/transpose
Structural transpose (not conjugate) of a symbolic array.
@sym/tril
Lower-triangular part of a symbolic matrix.
@sym/triu
Upper-triangular part of a symbolic matrix.
@sym/uminus
Return the negation of a symbolic expression.
@sym/union
Return the union of elements of two sets.
@sym/unique
Return the unique elements of a symbolic matrix.
@sym/uplus
Symbolic unitary minus.
@sym/vertcat
Vertically concatentate symbolic arrays.
@sym/xor
Logical xor of symbolic arrays.
@sym/zeros
Return a matrix whose elements are all 0.
@sym/zeta
Symbolic zeta function.
@symfun/argnames
Return the independent variables in a symfun.
@symfun/diff
Symbolic differentiation of symbolic functions.
@symfun/formula
Return a symbolic expression for this symfun.
@symfun/int
Symbolic integration of a symfun.
@symfun/ldivide
Component-wise backslash division of symbolic functions.
@symfun/minus
Subtract one symbolic function from another.
@symfun/mldivide
Backslash division of symbolic functions.
@symfun/mpower
Symbolic function exponentiation.
@symfun/mrdivide
Forward slash division of symbolic functions.
@symfun/mtimes
Multiply symbolic functions.
@symfun/numel
Number of elements in a symfun.
@symfun/plus
Add two symbolic functions together.
@symfun/power
Symbolic function component-wise exponentiation.
@symfun/private_disp_name
A string appropriate for representing the name of this symfun.
@symfun/rdivide
Forward slash component division of symbolic functions.
@symfun/size
Return the size of a symbolic function.
@symfun/subsref
Evaluate a symfun at a particular value.
@symfun/symfun
Define a symbolic function (not usually called directly).
@symfun/symvar
Find symbols in symfun and return them as a symbolic vector.
@symfun/times
Symbolic function component-wise multiplication.
@symfun/uminus
Return the negation of a symbolic function.

Package: symbolic