# Package org.matheclipse.core.reflection.system

Class Summary Class Description Abs Absolute value of a number.AddTo Operator +=And Apart Evaluate the partial fraction decomposition of a univariate polynomial fraction.ArcCos Arccosine See Inverse_trigonometric functionsArcCosh Inverse hyperbolic cosine See Inverse hyperbolic functionsArcCot Arccotangent See Inverse_trigonometric functionsArcCoth Arccotangent hyperbolic See Inverse hyperbolic functionsArcCsc Inverse hyperbolic tangent See Inverse hyperbolic functionsArcCsch Inverse hyperbolic tangent See Inverse hyperbolic functionsArcSec Inverse hyperbolic tangent See Inverse hyperbolic functionsArcSech Inverse hyperbolic secant See Inverse hyperbolic functionsArcSin Arcsine See Inverse_trigonometric functionsArcSinh Arcsin hyperbolic See Inverse hyperbolic functionsArcTan Arctangent See Inverse_trigonometric functionsArcTanh Inverse hyperbolic tangent See Inverse hyperbolic functionsArg BernoulliB Compute the Bernoulli number of the first kind.Binomial Returns the binomial coefficient of 2 integers.Boole Predicate function Returns`1`

if the 1st argument evaluates to`True`

; returns`0`

if the 1st argument evaluates to`False`

; and`null`

otherwise.BooleanMinimize Minimize a boolean function with the Quine McCluskey algorithm.Cancel Cancel(expr) - cancels out common factors in numerators and denominators.CartesianProduct Cartesian product for multiple lists.CatalanNumber Ceiling Returns the smallest (closest to negative infinity)`ISignedNumber`

value that is not less than`this`

and is equal to a mathematical integer.CharacteristicPolynomial Compute the characteristic polynomial of a matrix.ChessboardDistance ChessboardDistance of two vectorsChop Coefficient CoefficientList Collect Collect expressions.Complement Complex ComplexExpand Exponential definitions for trigonometric functions See Wikipedia - List of trigonometric identitiesComposeList CompoundExpression Conjugate Conjugate the given argument.ConjugateTranspose Conjugate and transpose a matrix.ConstantArray Array structure generator for constant (i,j) value.ConstantArray.ArrayIterator ContinuedFraction ContinuedFraction of a double or fraction number See: Continued fractionCoprimeQ The integers a and b are said to be*coprime*or*relatively prime*if they have no common factor other than 1.Cos Cosine function See Trigonometric functions and Wikipedia - Exact trigonometric constantsCosh Hyperbolic cosine See Hyperbolic functionCot Cotangent function See Trigonometric functionsCoth Hyperbolic cotangent See Hyperbolic functionCount Cross Calculate the cross product of 2 vectors with dimension 3.Csc Cosecant function See Trigonometric functionsCsch Hyperbolic Cosecant function See Hyperbolic functionsCurl See: Wikipedia:Curl (mathematics) Example:`Curl[{f[u,v,w],f[v,w,u],f[w,u,v],f[x]}, {u,v,w}]`

.D Differentiation of a function.Decrement Default Get the default value for a symbol (i.e.Denominator Get the denominator part of an expression See Wikipedia: Fraction (mathematics)Derivative Det Compute the determinant of a matrix See DeterminantDiagonalMatrix Create a diagonal matrix from a listDigitQ Returns`True`

, if the given expression is a string which only contains digits.Dimensions Get the dimensions of an expressionDiscriminant Distribute Divergence See Wikipedia - Divergence Example:`Divergence[{f[u,v,w],f[v,w,u],f[w,u,v]}, {u,v,w}]`

.DivideBy Operator /=Dot Eigenvalues Compute the numerical Eigenvalues of a real symmetric matrix See: Wikipedia - Eigenvalue, eigenvector and eigenspaceEigenvectors Compute the numerical Eigenvectors of a real symmetric matrix See: Eigenvalue, eigenvector and eigenspaceEliminate Try to eliminate a variable in a set of equations (i.e.Equal Erf Returns the error function.EuclidianDistance EuclidianDistance of two vectorsEulerE Euler numberEulerPhi Euler phi function See: Euler\'s totient functionEvenQ Predicate function Returns`True`

if the 1st argument is an even integer number;`False`

otherwiseExp Expand ExpandAll Exponent ExtendedGCD Returns the gcd of two positive numbers plus the bezout relations See Extended Euclidean algorithm and See B\xc3\xa9zout\'s identityExtract Factor Factor a univariate polynomialFactorial Returns the factorial of an integer n See FactorialFactorial2 FactorInteger Return the factors of an integer number FactorInteger[-32536] ==> {{-1,1},{2,3},{7,2},{83,1}}FactorSquareFree Factors out only multiple factors of a univariate polynomialFactorSquareFreeList Factors out only multiple factors of a univariate polynomialFactorTerms Fibonacci FindRoot Function for numerically finding roots of a univariate real function.Fit Polynomial fitting of a given data point set.Floor Returns the largest (closest to positive infinity)`ISignedNumber`

value that is not greater than`this`

and is equal to a mathematical integer.FractionalPart Get the fractional part auf a numberFrobeniusSolve FromCharacterCode FromContinuedFraction Convert a list of numbers to a fraction.FullSimplify Try to simplify a given expressionFunction Gamma Returns the Gamma function value.GCD Greatest common divisor See Wikipedia:Greatest common divisorGeometricMean Greater GreaterEqual GroebnerBasis HarmonicNumber Harmonic number of a given integer value See: Harmonic numberHilbertMatrix Hilbert matrix, defined by A_{i,j}= 1 / (i+j-1).Hold Horner Generate the horner scheme for univariate polynomials.IdentityMatrix Create an identity matrix See Wikipedia - Identity matrixIm Get the imaginary part of an expression See: Imaginary partIncrement Inner IntegerPart IntegerPartitions Generate all integer partitions for a given integer number.IntegerQ Predicate function Returns`True`

if the first argument is an integer;`False`

otherwiseIntegrate Integration of a function.InterpolatingFunction Intersection Intersection of 2 sets See: Intersection (set theory)Inverse Invert a matrix See Invertible matrixInverseErf Returns the inverse erf.InverseFunction JacobiMatrix Create a Jacobian matrix.JacobiSymbol Join KOrderlessPartitions KPartitions LCM Least common multiple See Wikipedia:Least common multipleLess LessEqual LetterQ Returns`True`

, if the given expression is a string which only contains lettersLevel Limit Limit of a function.LinearProgramming The LinearProgramming provides an implementation of George Dantzig\'s simplex algorithm for solving linear optimization problems with linear equality and inequality constraints.LinearSolve Determine`x`

for Matrix`A`

in the equation`A.x==b`

Log LowerCaseQ Returns`True`

, if the given expression is a string which only contains lower case charactersLUDecomposition ManhattanDistance The Manhattan distance of two vectors.Map MapAll MapThread MatchQ Match an expression against a given pattern.MatrixPower MatrixQ Predicate function Returns`True`

if the 1st argument is a matrix;`False`

otherwiseMatrixRank Compute the rank of a matrix.Max Mean See Arithmetic meanMedian See MedianMin Mod MoebiusMu The M\xc3\xb6bius function.MonomialList Get the list of monomials of a polynomial expression.Most Multinomial Returns the multinomial coefficient.Negative NextPrime Get the next prime number.NFourierTransform NIntegrate Function for numerical integration of univariate real functions.NonCommutativeMultiply NonNegative Norm Norm of a given argumentNot NRoots Determine the numerical roots of a univariate polynomial See Wikipedia entries for: Quadratic equation , Cubic function and Quartic functionNSolve Try to solve a set of equations (i.e.NullSpace Compute the null space of a matrix.Numerator Get the numerator part of an expression See Wikipedia: Fraction (mathematics)OddQ Predicate function Returns`True`

if the 1st argument is an odd integer number;`False`

otherwiseOr Order Compares the first expression with the second expression for order.OrderedQ Out Get the specified history line fro the`EvalEngine\'s`

history list.Outer Package Package[{<list of public package rule headers>}, {<list of rules in this package>}}PadLeft PadRight Part Partition Pattern Permutations Generate a list of permutations See PermutationPlus Pochhammer Compute Pochhammer\'s symbol (this)_n.PolynomialExtendedGCD Greatest common divisor of two polynomials.PolynomialGCD Greatest common divisor of two polynomials.PolynomialLCM Least common multiple of two polynomials.PolynomialQ Returns`True`

, if the given expression is a polynoomial objectPolynomialQuotient PolynomialQuotientRemainder PolynomialRemainder Positive PossibleZeroQ Predicate function Returns`True`

if the 1st argument is`0`

`False`

otherwisePower PowerExpand Try to simplify a given expressionPowerMod PreDecrement PreIncrement PrimeQ Test if a number is prime.PrimitiveRoots Product Product of expressions.Quotient RandomInteger RandomReal Range Rational Representation for a rational numberRationalize Re Get the real part of an expression See: Real partReplaceAll ReplacePart ReplaceRepeated Resultant Reverse RootIntervals Determine complex root intervals of a univariate polynomialRoots Determine the roots of a univariate polynomial See Wikipedia entries for: Quadratic equation , Cubic function and Quartic functionRound Round a given value to nearest integer.RowReduce Reduce thea matrix to row form.Rule RuleDelayed SameQ Scan Sec Secant function See Trigonometric functionsSech Hyperbolic Secant function See Hyperbolic functionsSelect Set SetDelayed Sign Gets the sign value of a number.SignCmp Gets the signum value of a complex numberSimplify Try to simplify a given expressionSimplify.IsBasicExpressionVisitor Sin Sine function.SingularValueDecomposition Sinh Hyperbolic sine See Hyperbolic functionSolve Try to solve a set of equations (i.e.Sort Sqrt SquaredEuclidianDistance SquaredEuclidianDistance of two vectorsSquareFreeQ Check if a univariate polynomial is square freeStirlingS2 Stirling numbers of the second kind.StringDrop StringJoin StringLength StringTake Subsets Generate a list of all k-combinations from a given list See CombinationSubtractFrom Operator -=Sum Summation of expressions.SyntaxLength SyntaxQ Returns`True`

, if the given expression is a string which has the correct syntaxTable Table structure generator (i.e.Take Tan Tan See Trigonometric functionsTanh Hyperbolic tangent See Hyperbolic functionTaylor Power series expansion with Taylor formulaThread Through Times TimesBy Operator *=Timing Calculate the time needed for evaluating a n expressionToCharacterCode Together ToString Total ToUnicode Tr Trace of a matrix.Trace Trace the evaluation steps for a given expression.Transpose Transpose a matrix.TrigExpand Expands the argument of sine and cosine functions.TrigReduce Transform products of trigonometric functions into "linear form".TrigToExp Exponential definitions for trigonometric functions See List of trigonometric identities - Exponential definitions,

Hyperbolic functionTrueQ Predicate function Returns`True`

if the 1st argument evaluates to`True`

;`False`

otherwiseTuples Unequal Union Union of two sets.UnitStep UnsameQ UpperCaseQ Returns`True`

, if the given expression is a string which only contains upper case charactersUpSet UpSetDelayed VandermondeMatrix Vandermonde matrix, defined by A_{i,j}= vector[i]^(j-1).Variables Determine the variable symbols of an expressionVectorQ Predicate function Returns`True`

if the 1st argument is a vector;`False`

otherwise

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