# 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

## Browse by category

## Alphabetical index

#### 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

#### K

#### 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 |