Calculation command of maple tree

Chapter 65438 +0 Chapter No.

1. 1 complex number

Returns the real/imaginary part of a complex expression.

Absolute function

Independent variable-amplitude-angle function of complex number

Conjugate-Returns the complex number of * * * yoke

Symbolic Functions of Real and Complex Expressions

Signum Sign Function of Real and Complex Expressions 5

1.2 maple leaf constant

Known variable name

Exponential constant (based on natural logarithm)

The root of I-x 2 =-1

Infinity is infinite.

1.3 integer function

! Factorial function

Irem, iquo- quotient of remainder/integer

Isprime- prime number test

Isqr free factorization without integer square

Max, min- the maximum/minimum value of a number.

Mod, modp, MODS- calculate the integer modulus of m.

Random number generator

Randomize-Reset Random Number Generator

1.4 prime number

Randpoly, rand Prime- random polynomial/first prime polynomial of finite field

Determine the i-th prime number.

Nextprime, prev prime- Determines the next maximum/minimum prime number.

Binary conversion of 1.5 number

Conversion between radix/radix conversion

Convert/binary- Convert to binary form.

Convert/Decimal-Convert to 10 radix.

Convert/double- Converts a double-precision floating-point number from one form to another.

Convert/float- Convert to floating point number.

Convert/hex- Convert to hexadecimal form

Convert/Metric-Convert to metric units.

Convert/octal-Convert to octal form.

Type check of 1.6 number

Type-number type checking function

Chapter II Elementary Mathematics

2. 1 elementary function

Product deterministic product and uncertain product

exponential function

Sum-deterministic sum and uncertain sum

Sqrt- Calculates the square root

Arithmetic operators+,-,*,/,.

Add/multiply multivalued sequence

2.2 trigonometric function

Ahlsien, Ahlsien. -Inverse trigonometric function/inverse hyperbolic function

Sin, sin. -trigonometric function/hyperbolic function

2.3 Logarithmic function

Double logarithmic function

Ln, log, log 10- natural logarithm/ordinary logarithm, ordinary logarithm

2.4 Type conversion

Convert/` +`, Convert/`* `- Convert to sum/product.

Convert/hypergeom- Converts the sum to a transcendental function.

Convert/degrees- Converts radians to angles.

Convert/expsincos- converts the trig function into exp, sin, cos.

Convert/Ei- Convert to exponential integral.

Convert/exp- Converts the trig function to an exponential function.

Convert/ln- converts arctrig into a logarithmic function.

Polar coordinates-Convert to polar coordinates.

Convert/radian-Converts an angle to radian.

Convert/sincos- converts the trig function into sin, cos, sinh and cosh.

Convert/tan- converts the trig function to tan.

Convert exponential function into trigonometric function and hyperbolic function.

Chapter III Evaluation

3. 1 hypothesis function

3.2 Assessment

Eval- evaluates the expression.

Eval- evaluation

Evala- Evaluates in the algebraic number (or function) field.

Eval B- Calculates based on a Boolean expression.

Evalc- symbolic evaluation on complex field

Evalf- evaluate using floating-point algorithm

Eval HF- evaluates expressions with hardware floating-point operations.

Evalm- calculation matrix expression

Evaln- Calculate a name.

Evalr, shake- Use interval algorithm to find the value and calculation range of the expression.

Calculating expressions with complex interval algorithm

Value inertia function for evaluation

Chapter 4 Seeking Roots and Solving Equations

4. 1 numerical solution

F solve- use floating-point number algorithm to solve

Solve/floats- An expression containing floating-point numbers.

4.2 Optimization

Extreme value-Find the relative extreme value of an expression.

Minimize, Maximize-Calculate the minimum/maximum value.

Maximum norm-a polynomial infinite norm

4.3 Root-seeking

All values- Calculates all possible values of an expression containing RootOfs.

Isqrt, I root- the square root of an integer /n-th root.

Isolation interval of real root-polynomial real root

Root-the nth root of algebraic expression

The representation of the root of the equation

Surd- non-principal root function

Root-the exact root of a polynomial of a variable.

The Number and Sequence of Real Roots of Polynomials on Interval

4.4 Solving equations

Elimination-Elimination of some variables in the equation system

Solve the integer solution of the equation

Solve one or more variables of a system of equations.

Isolation-The sub-expression on the left side of the isolation equation.

Singular-find the pole of the expression

Solve/Identify-Solve an expression that contains attributes.

Solve/Inequality-Solve Inequality

Solve/Linear-Solve Linear Equation

Solving the equation of unknown root

Solving/scalar-scalar case (univariate sum equation)

Solving/Series-Solving Equation with General Series

Solve/System-Solve an equation or inequality.

Chapter V Operational Expressions

5. 1 Processing expression

Norm-the standard form of algebraic number (or function)

Power inertia power function

Pow mod- inert power function with remainder

Prime field-primitive element of algebraic field

Find the locus of an algebraic number or function.

Characteristic functions of expressions and sets

Find the parameters of an expression.

Invifunc-reciprocal of function table

Power module power function with remainder

Risidue- Calculates the algebraic remainder of an expression

Combine-expression merge (bad for Tan Tan, cot)

Expand- expression extension

Expand- Expands the lazy form of the expression.

Expand off/expandon- Suppress/Not Suppress Function Expansion

5.2 Factorization

Factor-Inert Form of Absolute Factorization

A factors-the inert form of the decomposition item list of absolute factorization.

Explicitness of berlekamp- factorization

Factorization of multivariate polynomials

Factor decomposition table of multivariate polynomials

Inert form of factor-function factor

Inert form of factor-function factor

Complete factorization of polynomials

Chapter VI Simplification

6. 1 expression simplification 1 18

Simplify- implements simplified rules for expressions.

Simplify/@- Simplify expressions with operators

Simplify/Ei- Simplify the expression by exponential integration.

Simplify/Gamma-Simplify with gamma function.

Simplify/RootOf- Simplify the expression with the root of function.

Simplify/wronskian- simplify the expression with wronskian identifiers.

Simplified/Hypergeometry-Simplified Transcendental Function Expression

Simplify/ln- Simplify the expression with logarithm.

Simplify/Piecewise-Simplify Piecewise Function Expression

Simplify/Polar Coordinates-Simplify complex expressions with polar coordinates.

Simplify/power- simplify the expression with power.

Simplify/Radical-Simplify expressions with roots.

Simplified /rtable- Simplified rtable expression

Simplify/Siders-Simplify using relationships.

Simplification /sqrt- basic simplification

Simplify/Trigger-Simplify the expression of the trigger function.

Simplify/Zero Simplify Complex Expressions Embedded in Real and Imaginary Numbers

6.2 Other simplified operations

Inert form of normal-normal function

Convert- Converts an expression to a different form.

Rad normal- Normalize the expression with the number of root symbols.

Rationalization-the denominator is rational

Chapter VII Operational Polynomials

Introduction of Polynomials in 7.0 MAPLE

7. 1 extraction

Extracting coefficients of polynomials

Extract all the coefficients of multivariate polynomials.

Coefficient of multivariate expression

Lcoeff, tcoeff- Returns the coefficients of the first and last terms of a multivariate polynomial.

7.2 Polynomial Divisor and Root

Gcd, LCM- greatest common divisor/least common multiple of polynomial

Psqrt, the square root and n-th root of proot polynomial

The remainder/quotient of a polynomial

7.3 Manipulation Polynomials

Convert/horner- Converts a polynomial into Horner form.

Collect-Combine coefficients like powers.

Determine the number of possible combinations of a polynomial.

Convert/polynom- converts a sequence into polynomial form.

Convert/mathorner- converts a polynomial into horner matrix form.

Convert/rat poly- converts a series into a rational polynomial.

Sort-Sorts the list of values or polynomials.

Square factorization function without square term

7.4 Polynomial Operation

Discriminant formula of disc polynomial

Fix div- Fixed divisor of calculation polynomial

Standard form of norm polynomial

Calculate the final result of two polynomials.

Bernoulli-Bernoulli Numbers and Polynomials

Approximating function with Bernstein polynomial

Contents and main parts of multivariate polynomials.

Degree, L Degree-the highest/lowest power of a polynomial

Precise division of division polynomial

Euler-Euler Numbers and Polynomials

I content- integer part of polynomial

Interpolation polynomial interpolation

Pseudo-remainder and Sparse Pseudo-remainder of prem and sprem Polynomials

Random polynomial generator

Spline computing natural spline function

Chapter VIII Rational Expression

8.0 Introduction to Rational Expressions

8. 1 operate rational polynomials

Numer, denom- Returns the numerator/denominator of the expression.

Treat an ordinary expression into a reasonable expression.

Normal- Normalize a rational expression

Convert to decimal form.

Convert/rational- converts floating-point numbers into approximate rational numbers.

Rational function of Ratrecon reconstruction

Chapter 9 Calculus

9. 1 Limit

Limit, limit-calculation limit

Limit[dir]- calculates the direction limit.

Limit [multiple]-the limit in multiple directions.

Limit[return]- the return value of the limit.

9.2 Continuity test

Discont- Find the discontinuity of a function in the real number field.

Using numerical method to find the discontinuous point of function in real number field

Is cont- tests for continuity over a period of time.

9.3 Difference calculation

D- differential operator

D, diff- operator d and function diff

Differential, differential differential or partial differential

Convert/D- converts an expression with a derivative into a d operator expression.

Convert/diff- converts the expression of D(f)(x) into the form of diff(f(x), x).

Implicit diff- the differential of a function defined by an equation.

9.4 Integral calculation

Si, Ci…- trigonometric and hyperbolic integrals

Dirac function/Dirac function

Exponential integral

Ellipse-ellipse integral

Fresnel, Fresnel sine, cosine integral and auxiliary function

Int, Int- definite integral and indefinite integral

Legendre function and its first and second functions

Lie logarithmic integral

Student [change var]- variable substitution

Dawson-Dawson integral

Ellipsoid-surface area of ellipsoid

Evalf(int)- numerical integration

Intat, Intat- integral calculation of a point

10 differential equation

10. 1 Classification of differential equations

Odeadvisor-ODE- solution analyzer

Describe the data structure of solutions of differential equations.

PDE test- test the partial differential equation (PDEs) solution that pdsolve can find.

The solution of 10.2 ordinary differential equation

Solving ordinary differential equations

Solving ordinary differential equations with given initial conditions.

Solution/Inverse Solution of Ordinary Differential Equation by Integral Transformation Method

Numerical solution of d solve/ numerical-ordinary differential equation

Solutions/Piecewise Solutions of Ordinary Differential Equations with Piecewise Coefficients

D solve- series solution of ordinary differential equation problem

Solving ordinary differential equations

Odetest-Whether the test result of ODE solver is explicit or implicit.

The solution of 10.3 partial differential equation

Finding the Analytic Solution of Partial Differential Equation

Chapter 1 1 Numerical calculation

Numerical computing environment in 1 1. 1 MAPLE

IEEE standard and Maple numerical calculation

data type

Special value

envionment variables

1 1.2 algorithm

Standard algorithm

Complex number algorithm

Algorithms with 0, Infinite and Undefined Numbers

1 1.3 data builder 254

Complex-Complex and Complex Constructors

Floating-point number and its constructor

Fraction-Fraction and Its Constructor

Integer-integer and integer constructors

Introduction of 1 1.4 MATLAB software package

1 1.5 ""interval expression

Chapter 65438 +02 series

12. 1 order of power series

Order-order item function

Order- Determines the truncation order of the sequence.

12.2 Universal Series Extension

Series-General Series Extension

Taylor-Taylor series expansion

Multivariate Taylor series expansion

Poisson-Poisson series expansion

12.3 other series

Euler-Euler-maclaurin summation

Piecewise-piecewise continuous function

Progressive expansion

Chapter 13 Special Functions

AiryAi, AiryBi-Airy wave function

Real zeros of AiryAiZeros, AiryBiZeros-Airy functions

Angle, Veber-Angle function and Weber function.

Bessel function, hankel H 1, …-Bessel function and hankel function.

Bessel Zero, …-Real Zero of Bessel Function

β-β function

Elliptic modular function k(q)

GAMMA, ln GAMMA- complete and incomplete GAMMA functions

Geometric average of Gaussian-Gaussian arithmetic

Jacobin. ,-Jacobian amplitude function and elliptic function

Jacobian θ 1, Jacobian θ4- Jacobian θ function

Jacobi Zeta-Jacobi Zeta function

Kevin Bay-Kelvin function

Kummer,-KummerM function and u function

Lambert-Lambert function

Lechphi-universal Lechphi function

LommelS 1, LommelS2-Lommel function

An improved MeijerG function

ψ-Double γ and Multiple γ Functions

Strufve, Strufve-Strufve function

Weierstrassp-Weierstrassp function and its derivatives

Whitcomb-Whitaker function

Zeta-zeta function

Error function, complementary error function and hypothetical error function.

Harmonic-harmonic function

Hypergeometric generalized transcendental function

Poch hammer- universal pochhammer function

Multivariate Logarithm-Universal Multivariate Logarithm Function

Chapter 14 Linear Algebra

14. 1 matrices, vectors and arrays in algebra (algebra)

Brief introduction of 14.2 LINALG software package

14.3 data structure

Matrix Matrix (lowercase)

Vector vector (vector)

Convert arrays, lists and matrices into matrices.

Convert/Vector- Converts a list, array or Vector into a vector.

Linalg[matrix]- generating matrix (lowercase)

Linalg[vector]- generating vector (lowercase)

14.4 inert function

Det- inertia decision operator

Eigenvalues and eigenvectors of numerical matrices

Hermite and Smith canonical form of Hermite-Smith matrix

14.5 linear algebraic function

Matrix definition matrix

Add addition and subtraction matrix

Adjoint adjoint matrix

BackwardSubstitute solves A. X = B, where a is the upper triangular ladder matrix.

Banded matrix

Basis returns a set of bases in a vector space.

SumBasis returns a set of bases of direct sum of vector space.

IntersectionBasis returns a set of bases at the intersection of vector spaces.

Constructing Bezout Matrix of Two Polynomials

Dual diagonalization simplifies the matrix into dual diagonal type.

Construction of characteristic matrix

Characteristic Polynomials Construct the characteristic polynomials of a matrix.

CompanionMatrix constructs the adjoint matrix (bundle) of the first (or non-first) polynomial or matrix polynomial.

ConditionNumber calculates the condition number of the matrix about the norm.

ConstantMatrix constructs constant matrix

ConstantVector constructs constant vector

Construct a copy of a matrix or vector.

CreatePermutation transforms NAG principal component vector into permutation vector or matrix.

Cross product of cross product vector

Cross product of' & ampx' vector

DeleteRow deletes the rows of the matrix.

DeleteColumn deletes the column of the matrix.

Determinant determinant

Diagonal returns the vector sequence obtained from the matrix.

Diagonal Matrix Construction (Block) Diagonal Matrix

Number of rows and columns in the dimension

dot product

Bilinear formal vector in bilinear form

Eigenvalue coding number calculates the eigenvalue condition number of the eigenvalue or eigenvector of the numerical eigenvalue constraint problem.

Eigenvalue Calculates the eigenvalue of a matrix.

Calculate the eigenvector of the matrix.

Compares whether two vectors or matrices are equal.

ForwardSubstitute solves A. X = B, where a is the lower triangular row ladder matrix.

FrobeniusForm simplifies a square matrix to Frobenius type (rational standard form).

Gaussian elimination method performs Gaussian elimination on the matrix.

ReducedRowEchelonForm performs Gaussian-Jordan elimination on the matrix.

GetResultDataType returns the result data type of a matrix or vector operation.

GetResultShape returns the shape of the result of a matrix or vector operation.

GivensRotationMatrix to construct the matrix of Givens rotation

GramSchmidt calculates orthogonal vector sets.

Hankel Matrix Construct a Hankel Matrix

Hermite canonical form of computing matrix

HessenbergForm transforms the square matrix into upper Hessenberg type.

Hilbert Matrix Constructing Generalized Hilbert Matrix

Head of household matrix to construct head of household reflection matrix

IdentityMatrix constructs a identity matrix.

IsDefinite tests whether the matrix is positive, negative or uncertain.

Equal orthogonality tests whether the matrix is orthogonal.

Test whether the matrix is unitary.

IsSimilar determines whether the two matrices are similar.

JordanBlockMatrix constructs Jordan block matrix

JordanForm simplifies the matrix into Jordan form.

Kronecker product to construct Kronecker tensor product of two matrices

Least square solution of least square equation

Solve the linear equation A. x = b

LUDecomposition calculation matrix of Cholesky, PLU or PLU 1R decomposition.

Map maps programs to expressions, and handles matrices and vectors in their original positions.

MatrixAdd calculates the linear combination of two matrices.

VectorAdd calculates the linear combination of two vectors.

MatrixExponential determines matrix exponent exp(A) of matrix A.

MatrixFunction determines the function F(A) of square matrix a.

MatrixInverse calculates the inverse of a square matrix or the Moore-Penrose pseudo-inverse of a matrix.

MatrixMatrixMultiply calculates the product of two matrices.

Matrix Matrix calculates the product of matrix and column vector.

VectorMatrixMultiply calculates the product of a row vector and a matrix.

Power matrix of matrix

Minimal Polynomial The minimal polynomial of a matrix is constructed.

Sub-formula of secondary calculation matrix

Multiplication matrix multiplication

Norm calculates the p norm of a matrix or vector.

MatrixNorm calculates the p norm of a matrix.

VectorNorm calculates the p norm of a vector.

Standardized vector standardization

NullSpace calculates the zero-degree zero space of a matrix.

Outer product of two vectors of OuterProductMatrix

Invariant of permanent square matrix

Principal component elimination method of principal component matrix elements

Popov paradigm

QR decomposition

RandomMatrix constructs random matrix

RandomVector Constructs Random Vector

Rank calculates the rank of a matrix.

Row returns a sequence of row vectors of a matrix.

Column returns the column vector sequence of a matrix.

RowOperation performs elementary row transformation on the matrix.

ColumnOperation performs equicolumn transformation on the matrix.

RowSpace returns a set of bases of a matrix row space.

ColumnSpace returns a set of bases of a matrix column space.

ScalarMatrix constructs several identity matrix.

ScalarVector constructs multiples of the unit vector.

Product of scalar multiplication matrix and number

MatrixScalarMultiply calculates the product of a matrix and a number.

VectorScalarMultiply calculates the product of a vector and a number.

SchurForm transforms the square matrix into Schur type.

SingularValues calculates the singular value of a matrix.

Smith form simplifies matrix to Smith normal form.

Strongly connected block calculates the strongly connected block of a square matrix.

Submatrix The submatrix of a construction matrix.

Construct a subvector of a vector.

Constructing Sylvester Matrix of Two Polynomials

Constructing Toeplitz Matrix with Toeplitz Matrix

Calculate the trace of square matrix

transpose of a matrix

Hermite transposed yoke transposed matrix

Tridiagonalization transforms a square matrix into a tridiagonal type.

Unit vector construction unit vector

Vandermonde Matrix Construct a Vandermonde Matrix

VectorAngle calculates the angle between two vectors.

Construct a zero matrix.

Construct a zero vector.

Zip applies a program with two parameters to a pair of matrices or vectors.

LinearAlgebra[Generic] subfunction package [Generic] subfunction package provides linear algebraic algorithms for fields, Euclidean fields, whole fields and rings. See the help system for a list of commands and details.

LinearAlgebra[Modular] sub-function package [Modular] sub-function package provides a set of tools to complete the calculation in Z/m dense linear algebra, integer module m.