# Commands

In this page you can find all the commands you can use on CalcMe. They are distributed among fields that typically match the tabs in CalcMe menu. Since this is the first version of the documentation some of the functions might not be available yet. In this case, you can check the following list

#### A

 absolute The absolute value of a number adjoint_element Adjoint element of a finite field quotient a polynomial adjoint_matrix Adjoint matrix computation all_variables All the variables of an expression amplitude The amplitude of an arc angle The angle between two objects annihilating_polynomial Annihilating polynomial of an irrational append Append a vertex to a polygon append Appends an element arc Arc constructor arccos Arccosine function arccot Arccotangent function arccsc Arcosecant function arcosh Inverse hyperbolic cosine function arcsec Arcsecant function arcsin Arcsine function arctan Arctangent function area Area enclosed in a figure argument Argument of a complex number arguments Arguments of an expression arithmetic? Checks if a progression is arithmetic arsinh Inverse hyperbolic sine function artanh Inverse hyperbolic tangent function

#### B

 bar_chart Draw a bar chart barycenter Barycenter of a figure base_change Change of base (decimal, binary...) base Base ring of an extension belongs_to_domain? Checks if a point belongs to domain belongs? Checks if a point belongs to a figure belongs? Checks if an element belongs to a set bernoulli_variable Bernoulli variable bezout Bezout identity bezout Computes the polynomials of the bezout identity binomial_variable Binomial variable binomial Binomial number bisector Bisector constructor bit Bit expression of a number boxplot Draw a boxplot

#### C

 canonic_vector Construct a canonic vector cardinal Cardinality of a set category Category (arithmetic, geometric...) of a progression ceil Ceiling function center Center of a conic central_moment Central moment computation characteristic_matrix Compute the characteristic matrix characteristic_polynomial Characteristic polynomial of a matrix characteristic_polynomial Compute the characteristic polynomial characteristic Characteristic of a ring chi_squared_variable variable chinese_theorem Chinese theorem coefficients circumcenter Circumcenter point circumference Circumference constructor circumradius Circumradius closest_point Closest point of a figure coefficient_domain Coefficient domain of a polynomial coefficient_of_variation Coefficient of variation computation coefficient_si Coefficient of a quantity in the SI coefficient Coefficient of a quantity coefficient Coefficient of a series coefficients Coefficients of a polynomial colinear? Checks if points are colinear collect Collect terms in a polynomial column Column of a matrix combinations_with_repetitions Number of combinations with repetitions combinations Number of combinations compare Compare function compass The mark done with a compass complement Complement of two sets complex_variable_name Change the name of the complex variable components Element components in a ring composition Composition of two permutations conic Conic constructor conjugate Conjugate of a complex number conjugates Conjugate of an element over the base field of an extension conjugates Conjugates of a complex number constant_list Constant list constructor constant_matrix Construct a constant matrix constant_sequence Create a constant sequence constant_vector Construct a constant vector content_and_primitive_part Content and primitive part of a polynomial content Content of a polynomial convergent? Checks if a series is convergent conversion_factor Conversion factor between two units convert Convert one quantity to another one coplanars? Checks if points are coplanar correlation_n Correlation computation, up to a factor correlation Correlation computation cos Cosine function cosh Hyperbolic cosine function cot Cotangent function count_element Number of appearences of an element in a list covariance Covariance computation csc Cosecant function cube Construct a cube curve Construct a curve cycles_representation Representation of a permutation by cycles

#### D

 decimal Decimal part of a number definition Definition of a function degree Degree of a polynomial degree Degree of a unit degrees_minutes_seconds Angle expressed in degrees, minutes and seconds denominator Denominator of a fraction density Density function of a random variable depend Dependencies of an expression determinant Determinant of a matrix diagonal_matrix Construct a diagonal matrix differentiate Differentiation of a function dimensions Dimensions of a matrix directrix Directrix of a parabola discontinuities Discontinuities of a function distance Distance between two figures distribution Distribution function of a random variable distribution Distribution of the elements in a divisor divisor Divisor constructor divisors_mu_moebius Divisors of -Moebius function divisors Divisors of a number dodecahedron Constructs a dodecahedron domain Returns the domain of a function double_factorial Double factorial operation drop Drop a vertex of a polygon

#### E

 eccentricity Eccentricity of a conic eigenvalues_and_vectors Eigenvalues and eigenvectors eigenvalues Eigenvalues of a matrix eigenvectors Eigenvectors of a matrix element_of_order Element of a desired order in a ring element Element of a set elements Elements of a set ellipse Constructs an ellipse else_if Else_if statement else Else statement empty_divisor Empty divisor constructor empty_relation Empty relation constructor empty_table Empty table constructor equation_vector Vector with equation coefficients equation Equation of a figure equilateral_triangle Equilateral triangle constructor equilateral? Check if a triangle is equilateral erase Erase a vertex of a polygon erase Erase an element of a list evaluate Evaluates an expression in a given point exp Exponential function expand Expand an expression expansion_point Expansion point of a series exponential_variable Exponential variable expression_to_set Converts an expression to a set syntax expression Expression of a curve extended_gcd Extended greatest common divisor algorithm extended_gcd Extended greatest common divisor algorithm for polynomials extended_quartile Quartiles of a data sample extension Algebraic extension constructor exterior_bisector Exterior bisector lines external? Checks if a point is external to a figure

#### F

 factor_in_square_free_multiplicity Factorization of a polynomial in square free polynomials factor_in_square_free Factorization of a polynomial in square free polynomials factor Factorization of a number factor Factorization of a polynomial factorial Factorial operation fibonacci Fibonacci numbers field? Checks if a set is a field field Field where an element belongs finite? Checks if a ring is finite finite_field Finite field constructor first_vertex First vertex of a segment floor Floor function focal_semidistance Focal semidistance of a conic focus Focus of a conic for For loop statement frobenius Frobenius endomorphism function User function constructor

#### G

 gaussian_elimination Gaussian elimination algorithm gcd Greatest common divisor of integers gcd Greatest common divisor of polynomials geometric_mean Geometric mean computation geometric_progression Geometric progression constructor geometric_variable Geometric variable get_domain Type of object

#### H

 harmonic_mean Harmonic mean computation head First element of a list height_foot Height and base intersection height Height of triangle hermite_basis Hermite decomposition basis hermite Hermite decomposition hessenberg_reduction Hessenberg reduction algorithm histogram Draw a histogram homothecy Constructs an homothecy hyperbola Constructs an hyperbola

#### I

 i Imaginary unit icosahedron Constructs an icosahedron identity? Checks if a permutation is the identity identity_function Identity function identity_matrix Identity matrix constructor identity Constructs the identity permutation if If statement image Image or rank of a matrix imaginary_part Imaginary part of a complex number in Runs an iterator within a range incenter Center of the incircle index_erase Erase elements of a list index Index of appeareances of an element index Position of an element in a set initial_angle Angle of starting point of an arc inradius Radius of the incircle insert Insert a vertex in a polygon insert Insert an element in a list integral_curve Integral curve of an ordinary differential equation integral_curves Integral curves of an ordinary differential equation integrate Integration of a function internal? Checks if a point is internal to a figure interpolate Interpolation of a function interquartile_range Difference between third and first quartiles intersect Intersection of two figures intersect Intersection of two sets intervals Constructor of intervals inverse Inverse of a matrix irreducible? Checks if a polynomial is irreducible irreducible_polynomial Irreducible polynomial of the desired degree irreducible_polynomials Irreducible polynomials of the desired degree is? Checks the type of object

#### J

 jacobi Jacobi symbol join Joins two polygons jordan Jordan form

#### K

 kernel Kernel of a matrix kurtosis Kurtosis computation

#### L

 lcm Least common multiple of integers leading_coefficient Leading coefficient of a polynomial leading_term Leading term of a polynomial lcm Least common multiple of polynomials legendre Legendre symbol length Length of a segment length Size of an object level_curves Level curves of an ordinary differential equation limit Limit and one-sided limit of a function line Line constructor linearly_independents? Check if vectors are independents list List constructor ln Naperian or natural logarithm function local Local variables log Base 10 logarithm function log2 Base 2 logarithm function lu_decomposition LU decomposition of a matrix lucas Lucas numbers

#### M

 maclaurin Maclaurin series expansion matrix_range Matrix dimensions range matrix Conic matrix matrix Matrix from polynomial max Maximum of a set mean Mean computation median_line Median line of a triangle median Median computation Metric prefixes List of supported metric prefixes midpoint Midpoint of a segment or arc min Minimum of a set minor Minor computation mod Modulo operator mode Mode computation moment Moment computation monic? Checks if a polynomial is monic monic Transformation to a monic polynomial möbius_function Möbius function multiplicity Multiplicity of a root

#### N

 n_columns Number of columns of a matrix n_rows Number of rows of a matrix n_terms Number of terms of an expression n_variables Number of variables of an expression negative? Checks if a number is negative norm_1 1-norm of a polynomial norm_2 2-norm of a polynomial norm_infinity -norm of a polynomial norm Norm of a vector normal_variable Normal variable normal_vector Normal vector of a plane not_belongs? Checks if an element not belongs to a set not_null? Checks if an object is not null not Logical negation operator null? Checks if an object is null number_of_arguments Number of arguments of an operation number_of_irreducible_polynomials Amount of irreducible polynomials numerator Numerator of a fraction numerical_differentiation Numerical differentiation of a function numerical_integration Numerical integration of a function numerical_solve Numerical solve of a system of equations

#### O

 octahedron Constructor of an octahedron order Order of a permutation order Order of an element over a field oriented_angle Oriented angle between two vectors oriented_area Oriented area between two figures orthocenter Orthocenter of a triangle

#### P

 parabola Constructs a parabola parallel? Checks if two lines are parallel parallel Parallel line constructor partial_fractions Partial fractions decomposition perimeter Perimeter computation permutation Constructs a permutation permutations_with_repetitions Permutations with repetitions of a set permutations Permutations of a set perpendicular_bisector Perpendicular bisector line perpendicular? Checks if two lines are perpendicular perpendicular_vector Perpendicular vector perpendicular Perpendicular line or plane phi_euler -Euler function pie_chart Draw a pie chart plane Plane constructor plot Plots an object point Point constructor poisson_variable Poisson variable polar_curve Polar curve constructor polar Polar form of a complex number polar Polar line of a conic polo Polo of a conic polygon Polygon constructor polygonal Polygonal constructor polygonals Polygonals constructor polyhedra_cone_with_lid Polyhedra cone with base constructor polyhedra_cone Polyhedra cone constructor polyhedra_cylinder_with_lids Polyhedra cylinder with bases constructor polyhedra_cylinder Polyhedra cylinder constructor polyhedra_sphere Polyhedra sphere constructor polyhedra_torus Polyhedra torus constructor polyhedra Polyhedra constructor polynomial_to_companion_matrix Companion matrix constructor polynomic? Checks if a progression is polynomic positive? Checks if a number is positive power_modulo Power of a polynomial modulo another polynomial power Power of circumference precedent Precedent algebraic structure of an extension prepend Prepend a vertex in a polygon prepend Prepend an element prime? Checks if a number is prime prime_power Prime power of a number prime A prime number primitive_element Primitive element of a field primitive_part Primitive part of a polynomial prism Prism constructor progression Constructs a progression projection Projection of a point projectivity Image for a projectivity pseudoremainder Pseudoremainder of two polynomials pyramid Constructs a pyramid

#### Q

 qr_decomposition QR decomposition of a matrix quadric Quadric constructor quantile Inverse of cumulative distribution quantity Constructs a quantity quartile Quartile computation quotient_and_remainder Quotient and remainder of euclidean division quotient_and_remainder Quotient and remainder of euclidean division quotient Quotient of euclidean division quotient Quotient of euclidean division

#### R

 radius Radius of a circumference random Random number following a distribution random Random number generator rank Rank of a matrix ratio Ratio of a geometric progression rationalize Rationalize a fraction with square roots real_part Real part of a complex number region Region between two curves regression_exponential Regression following an exponential function regression_line Regression following a linear function regression_logarithm Regression following a logarithm function regression_power Regression following a power law regular_polygon Constructs a regular polygon relation Creates a relation object relative_degree Relative degree of an extension remainder Remainder of euclidean division remainder Remainder of euclidean division repeat Repeat statement replace Replace an element of a vector, list, matrix by another one represent Represents an object and its interesting points resultant_matrix Resultant matrix of two polynomials resultant Resultant of two polynomials reverse Reverses the order of an object ring? Checks if a set is a ring root Root of a number roots_to_polynomial Polynomial with given roots roots Roots of a number roots Roots of a polynomial rotation_matrix Construct a rotation matrix rotation Rotates a figure round Rounding to the nearest integer

#### S

 sec Secant function second_vertex Second vertex of a segment segment Constructs a segment semimajor_axis Semimajor axis of a conic semiminor_axis Semiminor axis of a conic sequence Constructs a sequence sequence Sequence of vertices of a polygon series Series of a function set Set constructor sign Sign function sign Sign of a permutation sign0 Sign function similar? Checks if two triangles are similar simplify_radical Simplify an expression with radicals simplify Simplify an expression sin Sine function sinh Hyperbolic sine function skewness Skewness computation slope Slope of a line smith_normal_form_basis Smith normal form smith_normal_form Smith normal form invariant factors solve Solve linear system solve_inequation Solve an inequation solve Solve a set of equations sort Sort a set split Split a string sqrt Square root of a number sqrts Square roots of a number square_free? Checks if exists a square-free factorization square? Square of a number standard_deviation_n Standard deviation computation, up to a factor standard_deviation Standard deviation computation standardize Standardization of a random variable step Step of a sequence string_substitution Substitute strings in an expression string String constructor student_t_variable -student variable subextension? Checks if an extension is a subextension subset? Checks if a set is a subset of another one subspace_intersection Intersection of subspaces subspace_sum Sum of subspaces substitute Substitute a variable by an expression substring Get substrings from a larger string supplement Supplement of an space support Support (different from zero) of a relation, divisor... surface Constructs a surface symmetric? Check if a matrix is symmetric symmetry_matrix Construct the symmetry matrix symmetry Symmetry of an object

#### T

 table Table constructor tail Tail of a list tail Tail of a polynomial take The first or last elements of a list tan Tangent function tangent_axle Tangent axle tangent_line Tangent line of a figure tangent_lines Tangent lines of a figure tangent_points Tangent points of a figure tanh Hyperbolic tangent function tartaglia Tartaglia triangle's row taylor_series Taylor series of a function taylor Taylor expansion of a function term_list List of term of a series term Term of a series terms_list List of terms of a series terms Terms of a series tetrahedron Tetrahedron constructor to_decimal To decimal form total_degree Total degree of a field extension tower Tower of an extension trace Trace of a matrix translation_matrix Translation matrix translation Translation of a figure transpose Transpose of a matrix transposition Transposition permutation triangle Constructs a triangle trunc Trunc a number truncate Truncate a series

#### U

 uniform_variable Uniform variable union Union of sets unit_si Unit of a quantity in the SI Units List of supported units

#### V

 variable Variable of an expression variables Variables of an expression variance_n Variance computation, up to a factor variance Variance computation variations_with_repetition Variations with repetitions of a set variations Variations of a set vector_field Vector field of an ordinary differential equation vector Constructs a vector vector Permutation to vector converter vectorial_product Vectorial or cross product versor Versor computation vertex Vertex of a parabola or polygon vertices Vertices of a 3D triangle, polygonal or polygon volume Volume of a figure

#### W

 where Where statement while While statement with With statement write Write text in a point

#### Z

 zero? Checks if the elements in a set are different from zero zero0 Zero function zeros Sequence of zeros Zn constructor