+Logarithmic, exponential and roots: log(x) - decimal logarithm; ln(x) - natural logarithm; log_2(x) - binary logarithm; log1p(x) - decimal logarithm of 1 + x, accurate for small x; ln1p(x) - natural logarithm of 1 + x, accurate for small x; exp(x) - natural exponent; sqr(x) or sqrt(x) - square root; cbrt(x) - cubic root; root(x;n) - n-th root;
+Rounding: round(x) - round to the nearest integer; floor(x) - round to the smaller integer (towards -∞); ceiling(x) - round to the greater integer (towards +∞); trunc(x) - round to the smaller integer (towards zero);
+Integer: mod(x;y) - the remainder of an integer division; gcd(x;y;z…) - the greatest common divisor of several integers; lcm(x;y;z…) - the least common multiple of several integers;
+Complex: re(z) - the real part of a complex number; im(z) - the imaginary part of a complex number; abs(x) - absolute value/magnitude; phase(z) - the phase of a complex number; conj(z) - the conjugate of a complex number;
+Vector: Creational: vector(n) - creates an empty vector with length n; vector_hp(n) - creates an empty high performance (hp) vector with length n; range(x1;xn;s) - creates a vector with values spanning from x1 to xn with step s; range_hp(x1;xn;s) - creates a high-performance (hp) vector from the values in the range; Structural: len(⃗v) - returns the length of vector ⃗v; size(⃗v) - the actual size of vector ⃗v (the index of the last non-zero element); resize(⃗v;n) - sets a new length n of vector ⃗v; fill(⃗v;x) - fills vector ⃗v with value x; join(A;⃗b;c…) - creates a vector by joining the arguments: matrices, vectors and scalars; slice(⃗v;i1;i2) - returns the part of vector ⃗v bounded by indexes i1 and i2 inclusive; first(⃗v;n) - the first n elements of vector ⃗v; last(⃗v;n) - the last n elements of vector ⃗v; extract(⃗v;⃗i) - extracts the elements from ⃗v whose indexes are contained in ⃗i; Data: sort(⃗v) - sorts the elements of vector ⃗v in ascending order; rsort(⃗v) - sorts the elements of vector ⃗v in descending order; order(⃗v) - the indexes of vector ⃗v, arranged by the ascending order of its elements; revorder(⃗v) - the indexes of vector ⃗v, arranged by the descending order of its elements; reverse(⃗v) - a new vector containing the elements of ⃗v in reverse order; count(⃗v;x;i) - the number of elements in ⃗v, after the i-th one, that are equal to x; search(⃗v;x;i)- the index of the first element in ⃗v, after the i-th one, that is equal to x; find(⃗v;x;i) or find_eq(⃗v;x;i) - the indexes of all elements in ⃗v, after the i-th one, that are = x; find_ne(⃗v;x;i) - the indexes of all elements in ⃗v, after the i-th one, that are ≠ x; find_lt(⃗v;x;i) - the indexes of all elements in ⃗v, after the i-th one, that are < x; find_le(⃗v;x;i) - the indexes of all elements in ⃗v, after the i-th one, that are ≤ x; find_gt(⃗v;x;i) - the indexes of all elements in ⃗v, after the i-th one, that are > x; find_ge(⃗v;x;i) - the indexes of all elements in ⃗v, after the i-th one, that are ≥ x; lookup(⃗a;⃗b;x) or lookup_eq(⃗a;⃗b;x) - all elements in ⃗b for which the respective elements in ⃗a are = x; lookup_ne(⃗a;⃗b;x) - all elements in ⃗b for which the respective elements in ⃗a are ≠ x; lookup_lt(⃗a;⃗b;x) - all elements in ⃗b for which the respective elements in ⃗a are < x; lookup_le(⃗a;⃗b;x) - all elements in ⃗b for which the respective elements in ⃗a are ≤ x; lookup_gt(⃗a;⃗b;x) - all elements in ⃗b for which the respective elements in ⃗a are > x; lookup_ge(⃗a;⃗b;x) - all elements in ⃗b for which the respective elements in ⃗a are ≥ x; Math: norm_1(⃗v) - L1 (Manhattan) norm of vector ⃗v; norm(⃗v) or norm_2(⃗v) or norm_e(⃗v) - L2 (Euclidean) norm of vector ⃗v; norm_p(⃗v;p) - Lp norm of vector ⃗v; norm_i(⃗v) - L∞ (infinity) norm of vector ⃗v; unit(⃗v) - the normalized vector ⃗v (with L2 norm = 1); dot(⃗a;⃗b) - scalar product of two vectors ⃗a and ⃗b; cross(⃗a;⃗b) - cross product of two vectors ⃗a and ⃗b (with length 2 or 3); polyroots(⃗a) - finds all real roots of the polynomial: a₁ + a₂·x + a₃·x² + ... + aₙ₊₁·xⁿ;
+Matrix: Creational: matrix(m;n) - creates an empty matrix with dimensions m⨯n; identity(n) - creates an identity matrix with dimensions n⨯n; diagonal(n;d) - creates a n⨯n diagonal matrix and fills the diagonal with value d; column(m;c) - creates a column matrix with dimensions m⨯1, filled with value c; utriang(n) - creates an upper triangular matrix with dimensions n⨯n; ltriang(n) - creates a lower triangular matrix with dimensions n⨯n; symmetric(n) - creates a symmetric matrix with dimensions n⨯n; matrix_hp(m;n) - creates an empty high-performance (hp) matrix with dimensions m⨯n; identity_hp(n) - creates a high-performance (hp) identity matrix with dimensions n⨯n; diagonal_hp(n;d) - creates a high-performance (hp) n⨯n diagonal matrix filled with value d; column_hp(m;c) - creates a high-performance (hp) m⨯1 column matrix filled with value c; utriang_hp(n) - creates a high-performance (hp) n⨯n upper triangular matrix; ltriang_hp(n) - creates a high-performance (hp) n⨯n lower triangular matrix; symmetric_hp(n) - creates a high-performance (hp) symmetric matrix with dimensions n⨯n; vec2diag(⃗v) - creates a diagonal matrix from the elements of vector ⃗v; vec2row(⃗v) - creates a row matrix from the elements of vector ⃗v; vec2col(⃗v) - creates a column matrix from the elements of vector ⃗v; join_cols(⃗c1;⃗c2;⃗c3…) - creates a new matrix by joining column vectors; join_rows(⃗r1;⃗r2;⃗r3…) - creates a new matrix by joining row vectors; augment(A;B;C…) - creates a new matrix by appending matrices A;B;C side by side; stack(A;B;C…) - creates a new matrix by stacking matrices A;B;C one below the other; Structural (matrices and tables): n_rows(M) - number of rows in matrix M; n_cols(M) - number of columns in matrix M; mresize(M;m;n) - sets new dimensions m and n for matrix M; mfill(M;x) - fills matrix M with value x; fill_row(M;i;x) - fills the i-th row of matrix M with value x; fill_col(M;j;x) - fills the j-th column of matrix M with value x; copy(A;B;i;j) - copies all elements from A to B, starting from indexes i and j of B; add(A;B;i;j) - adds all elements from A to those of B, starting from indexes i and j of B; row(M;i) - extracts the i-th row of matrix M as a vector; col(M;j) - extracts the j-th column of matrix M as a vector; extract_rows(M;⃗i) - extracts the rows from matrix M whose indexes are contained in vector ⃗i; extract_cols(M;⃗j) - extracts the columns from matrix M whose indexes are contained in vector ⃗j; diag2vec(M) - extracts the diagonal elements of matrix M to a vector; submatrix(M;i1;i2;j1;j2) - extracts a submatrix of M, bounded by rows i1 and i2 and columns j1 and j2, incl.; Data (matrices and tables): sort_cols(M;i) - sorts the columns of M based on the values in row i in ascending order; rsort_cols(M;i) - sorts the columns of M based on the values in row i in descending order; sort_rows(M;j) - sorts the rows of M based on the values in column j in ascending order; rsort_rows(M;j) - sorts the rows of M based on the values in column j in descending order; order_cols(M;i) - the indexes of the columns of M based on the ordering of the values from row i in ascending order; revorder_cols(M;i) - the indexes of the columns of M based on the ordering of the values from row i in descending order; order_rows(M;j) - the indexes of the rows of M based on the ordering of the values in column j in ascending order; revorder_rows(M;j) - the indexes of the rows of M based on the ordering of the values in column j in descending order; mcount(M;x) - number of occurrences of value x in matrix M; msearch(M;x;i;j) - vector with the two indexes of the first occurrence of x in matrix M, starting from indexes i and j; mfind(M;x) or mfind_eq(M;x) - the indexes of all elements in M that are = x; mfind_ne(M;x) - the indexes of all elements in M that are ≠ x; mfind_lt(M;x) - the indexes of all elements in M that are < x; mfind_le(M;x) - the indexes of all elements in M that are ≤ x; mfind_gt(M;x) - the indexes of all elements in M that are > x; mfind_ge(M;x) - the indexes of all elements in M that are ≥ x; hlookup(M;x;i1;i2) or hlookup_eq(M;x;i1;i2) - the values from row i2 of M, for which the elements in row i1 are = x; hlookup_ne(M;x;i1;i2) - the values from row i2 of M, for which the elements in row i1 are ≠ x; hlookup_lt(M;x;i1;i2) - the values from row i2 of M, for which the elements in row i1 are < x; hlookup_le(M;x;i1;i2) - the values from row i2 of M, for which the elements in row i1 are ≤ x; hlookup_gt(M;x;i1;i2) - the values from row i2 of M, for which the elements in row i1 are > x; hlookup_ge(M;x;i1;i2) - the values from row i2 of M, for which the elements in row i1 are ≥ x; vlookup(M;x;j1;j2) or vlookup_eq(M;x;j1;j2) - the values from column j2 of M, for which the elements in column j1 are = x; vlookup_ne(M;x;j1;j2) - the values from column j2 of M, for which the elements in column j1 are ≠ x; vlookup_lt(M;x;j1;j2) - the values from column j2 of M, for which the elements in column j1 are < x; vlookup_le(M;x;j1;j2) - the values from column j2 of M, for which the elements in column j1 are ≤ x; vlookup_gt(M;x;j1;j2) - the values from column j2 of M, for which the elements in column j1 are > x; vlookup_ge(M;x;j1;j2) - the values from column j2 of M, for which the elements in column j1 are ≥ x; Math: hprod(A;B) - Hadamard product of matrices A and B; fprod(A;B) - Frobenius product of matrices A and B; kprod(A;B) - Kronecker product of matrices A and B; mnorm_1(M) - L1 norm of matrix M; mnorm(M) or mnorm_2(M) - L2 norm of matrix M; mnorm_e(M) - Frobenius norm of matrix M; mnorm_i(M) - L∞ norm of matrix M; cond_1(M) - condition number of M based on the L1 norm; cond(M) or cond_2(M) - condition number of M based on the L2 norm; cond_e(M) - condition number of M based on the Frobenius norm; cond_i(M) - condition number of M based on the L∞ norm; det(M) - determinant of matrix M; rank(M) - rank of matrix M; trace(M) - trace of matrix M; transp(M) - transpose of matrix M; adj(M) - adjugate of matrix M; cofactor(M) - cofactor matrix of M; eigenvals(M;ne) - the first ne eigenvalues of matrix M (or all if omitted); eigenvecs(M;ne) - the first ne eigenvectors of matrix M (or all if omitted); eigen(M;ne) - the first ne eigenvalues and eigenvectors of matrix M (or all if omitted); cholesky(M) - Cholesky decomposition of a symmetric, positive-definite matrix M; lu(M) - LU decomposition of matrix M; qr(M) - QR decomposition of matrix M; svd(M) - singular value decomposition of M; inverse(M) - inverse of matrix M; lsolve(A;⃗b) - solves the system of linear equations A⃗x = ⃗b using LDLT decomposition for symmetric matrices, and LU for non-symmetric; clsolve(A;⃗b) - solves the linear matrix equation A⃗x = ⃗b with symmetric, positive-definite coefficient matrix A using Cholesky decomposition; slsolve(A;⃗b) - solves the linear matrix equation A⃗x = ⃗b with high-performance symmetric, positive-definite coefficient matrix A using preconditioned conjugate gradient (PCG) method; msolve(A;B) - solves the generalized matrix equation AX = B using LDLT decomposition for symmetric matrices, and LU for non-symmetric; cmsolve(A;B) - solves the generalized matrix equation AX = B with symmetric, positive-definite coefficient matrix A using Cholesky decomposition; smsolve(A;B) - solves the generalized matrix equation AX = B with high-performance symmetric, positive-definite coefficient matrix A using preconditioned conjugate gradient (PCG) method; matmul(A;B) - fast multiplication of square hp matrices using parallel Winograd algorithm. The multiplication operator A*B uses it internally for all square hp matrices of size 10 and larger; fft(M) - performs fast Fourier transform of row-major matrix M. It must have one row for real data and two rows for complex; ift(M) - performs inverse Fourier transform of row-major matrix M. It must have one row for real data and two rows for complex; Double interpolation: take(x;y;M) - returns the element of matrix M at indexes x and y; line(x;y;M) - double linear interpolation from the elements of matrix M based on the values of x and y; spline(x;y;M) - double Hermite spline interpolation from the elements of matrix M based on the values of x and y. Tol - target tolerance for the iterative PCG solver.
+Special: Gamma and beta functions: gamma(x) - gamma function: Γ(x); gammaln(x) - logarithm of the absolute value of the gamma function ln|Γ(x)|; digamma(x) - digamma function: ψ(x) = Γ′(x)/Γ(x); polygamma(n;x) - polygamma function ψ⁽ⁿ⁾(x), the n-th derivative of the digamma function; gammainc_(s;x) - lower incomplete gamma function γ(s, x); gammainc‾(s;x) - upper incomplete gamma function Γ(s, x); beta(a;b) - beta function B(a, b); betainc(x;a;b) - regularized incomplete beta function Iₓ(a, b); Error function and Fresnel integrals: erf(x) - error function; erfc(x) - complementary error function: erfc(x) = 1 − erf(x); erfinv(x) - inverse error function: erf⁻¹(x); erfcinv(x) - inverse complementary error function: erfc⁻¹(x); dawsonf(x) - Dawson's integral: F(x) = exp(−x²)∫₀ˣ exp(t²) dt; fresnelc(x) - Fresnel cosine integral: C(x) = ∫₀ˣ cos(t²) dt; fresnels(x) - Fresnel sine integral: S(x) = ∫₀ˣ sin(t²) dt; Exponential, logarithmic, sine and cosine integrals: ei(x) - exponential integral: Ei(x); li(x) - logarithmic integral: li(x); si(x) - sine integral: Si(x); ci(x) - cosine integral: Ci(x); shi(x) - hyperbolic sine integral: Shi(x); chi(x) - hyperbolic cosine integral: Chi(x); Elliptic integrals: elliptick(m) - complete elliptic integral of the first kind: K(m); elliptice(m) - complete elliptic integral of the second kind: E(m); ellipticp(n;m) - complete elliptic integral of the third kind: Π(n|m); ellipticf(φ;m) - incomplete elliptic integral of the first kind: F(φ|m); ellipticei(φ;m) - incomplete elliptic integral of the second kind: E(φ|m); ellipticpi(n;φ;m) - incomplete elliptic integral of the third kind: Π(n; φ|m); Jacobi elliptic functions: jacobiam(u;m) - Jacobi amplitude: am(u|m); jacobisn(u;m) - Jacobi elliptic function: sn(u|m); jacobicn(u;m) - Jacobi elliptic function: cn(u|m); jacobidn(u;m) - Jacobi elliptic function: dn(u|m); jacobics(u;m) - Jacobi elliptic function: cs(u|m); jacobicd(u;m) - Jacobi elliptic function: cd(u|m); jacobidc(u;m) - Jacobi elliptic function: dc(u|m); jacobisc(u;m) - Jacobi elliptic function: sc(u|m); jacobisd(u;m) - Jacobi elliptic function: sd(u|m); jacobids(u;m) - Jacobi elliptic function: ds(u|m); jacobins(u;m) - Jacobi elliptic function: ns(u|m); jacobinc(u;m) - Jacobi elliptic function: nc(u|m); jacobind(u;m) - Jacobi elliptic function: nd(u|m); Bessel functions: besselj0(x) - Bessel function of the first kind: J₀(x); besselj1(x) - Bessel function of the first kind: J₁(x); bessely0(x) - Bessel function of the second kind: Y₀(x); bessely1(x) - Bessel function of the second kind: Y₁(x); besseljn(n;x) - Bessel function of the first kind: Jₙ(x) of integer order n; besselyn(n;x) - Bessel function of the second kind: Yₙ(x) of integer order n; besseljv(ν;x) - Bessel function of the first kind: Jν(x) of real order ν; besselyv(ν;x) - Bessel function of the second kind: Yν(x) of real order ν; besseljv′(ν;x) - derivative J′ν(x) of the Bessel function of the first kind; besselyv′(ν;x) - derivative Y′ν(x) of the Bessel function of the second kind; besseljs(n;x) - spherical Bessel function of the first kind: jₙ(x); besselys(n;x) - spherical Bessel function of the second kind: yₙ(x); besseljs′(n;x) - derivative j′ₙ(x) of the spherical Bessel function of the first kind; besselys′(n;x) - derivative y′ₙ(x) of the spherical Bessel function of the second kind; Modified Bessel functions: besseli0(x) - modified Bessel function of the first kind: I₀(x); besseli1(x) - modified Bessel function of the first kind: I₁(x); besselk0(x) - modified Bessel function of the second kind: K₀(x); besselk1(x) - modified Bessel function of the second kind: K₁(x); besselin(n;x) - modified Bessel function of the first kind: Iₙ(x) of integer order n; besselkn(n;x) - modified Bessel function of the second kind: Kₙ(x) of integer order n; besseliv(ν;x) - modified Bessel function of the first kind: Iν(x) of real order ν; besselkv(ν;x) - modified Bessel function of the second kind: Kν(x) of real order ν; besseliv′(ν;x) - derivative I′ν(x) of the modified Bessel function of the first kind; besselkv′(ν;x) - derivative K′ν(x) of the modified Bessel function of the second kind; Airy functions: ai(x) - Airy function: Ai(x); bi(x) - Airy function: Bi(x); ai′(x) - derivative Ai′(x) of the Airy function; bi′(x) - derivative Bi′(x) of the Airy function; Zeta and Lambert W functions: zeta(s) - Riemann zeta function ζ(s); eta(s) - Dirichlet eta function η(s); lambertw(x) - Lambert W function - principal branch W₀(x);
+Statistical: Descriptive statistics: median(M;⃗v;x…) - median of multiple values; quantile(M;⃗v;x…;p) - sample quantile for probability p (the last argument), linearly interpolated between the sorted values; stdev(M;⃗v;x…) - sample standard deviation; variance(M;⃗v;x…) - sample variance; skew(M;⃗v;x…) - sample skewness; kurt(M;⃗v;x…) - sample excess kurtosis; Two samples and ranks: covar(⃗a;⃗b) - sample covariance of vectors ⃗a and ⃗b; correl(⃗a;⃗b) - Pearson correlation coefficient of vectors ⃗a and ⃗b. Spearman's rank correlation is correl(ranks(⃗a); ranks(⃗b)); linreg(⃗x;⃗y) - least squares line y = a + b·x, returned as the vector [a; b]; ranks(⃗v) - ranks of the elements of vector ⃗v in ascending order. Equal values get the average of their ranks; frequency(⃗v;⃗b) - counts of the elements of vector ⃗v in the bins with upper bounds in vector ⃗b. The last count is for the values above the last bound; Combinatorics: combin(n;k) - number of combinations of n items taken k at a time; permut(n;k) - number of permutations of n items taken k at a time; Probability distributions: normpdf(x;μ;σ) - probability density function of the normal distribution with mean μ and standard deviation σ; normcdf(x;μ;σ) - cumulative distribution function of the normal distribution with mean μ and standard deviation σ; norminv(p;μ;σ) - quantile (inverse cumulative distribution function) of the normal distribution with mean μ and standard deviation σ; lognpdf(x;μ;σ) - probability density function of the lognormal distribution, where ln x has mean μ and standard deviation σ; logncdf(x;μ;σ) - cumulative distribution function of the lognormal distribution, where ln x has mean μ and standard deviation σ; logninv(p;μ;σ) - quantile (inverse cumulative distribution function) of the lognormal distribution, where ln x has mean μ and standard deviation σ; tpdf(t;ν) - probability density function of Student's t-distribution with ν degrees of freedom; tcdf(t;ν) - cumulative distribution function of Student's t-distribution with ν degrees of freedom; tinv(p;ν) - quantile (inverse cumulative distribution function) of Student's t-distribution with ν degrees of freedom; chi2pdf(x;k) - probability density function of the χ² distribution with k degrees of freedom; chi2cdf(x;k) - cumulative distribution function of the χ² distribution with k degrees of freedom; chi2inv(p;k) - quantile (inverse cumulative distribution function) of the χ² distribution with k degrees of freedom; gumbelpdf(x;μ;β) - probability density function of the Gumbel distribution (of maxima) with location μ and scale β; gumbelcdf(x;μ;β) - cumulative distribution function of the Gumbel distribution (of maxima) with location μ and scale β; gumbelinv(p;μ;β) - quantile (inverse cumulative distribution function) of the Gumbel distribution (of maxima) with location μ and scale β; wblpdf(x;λ;k) - probability density function of the Weibull distribution with scale λ and shape k; wblcdf(x;λ;k) - cumulative distribution function of the Weibull distribution with scale λ and shape k; wblinv(p;λ;k) - quantile (inverse cumulative distribution function) of the Weibull distribution with scale λ and shape k; binopdf(k;n;p) - probability of k successes in n trials with success probability p (binomial distribution); binocdf(k;n;p) - probability of at most k successes in n trials with success probability p (binomial distribution); poisspdf(k;λ) - probability of k events with mean number λ (Poisson distribution); poisscdf(k;λ) - probability of at most k events with mean number λ (Poisson distribution);
+String: str(x) - converts x to text, as it is displayed in the output; val(s) - converts the text s to a number with optional units; val(M) - converts the string elements of a vector or matrix M to numbers, e.g. to parse the result of split; len(s) - the number of characters in the text s; join(s₁;s₂;s₃…) - joins texts and values into a single text; join(M;colsep;rowsep) - joins the elements of a vector or matrix into a text, with columns separated by colsep and rows by rowsep; left(s;n) - the first n characters of the text s; right(s;n) - the last n characters of the text s; mid(s;i;n) - n characters of the text s, starting from position i; trim(s) - the text s without leading and trailing spaces; ltrim(s) - the text s without leading spaces; rtrim(s) - the text s without trailing spaces; ucase(s) - the text s in upper case; lcase(s) - the text s in lower case; tcase(s) - the text s in title case (the first letter of each word is capital); scase(s) - the text s in sentence case (the first letter of each sentence is capital); instr(s;t;i) - the position of the text t in s, starting from i, or 0 if not found; replace(s;a;b) - the text s with all occurrences of a replaced by b; split(s;sep) - splits the text s at each sep into a vector of strings; split(s;colsep;rowsep) - splits the text s into a matrix of strings, with columns separated by colsep and rows by rowsep;
+Other: sign(x) - sign of a number; random(x) - a random number between 0 and x; getunits(x) - gets the units of x without the value. Returns 1 if x is unitless; setunits(x;u) - sets the units u to x where x can be scalar, vector or matrix; clrunits(x) - clears the units from a scalar, vector or matrix x; hp(x) - converts x to its high performance (hp) equivalent type; ishp(x) - checks if the type of x is a high-performance (hp) vector or matrix;
Comments: '"Title' or 'text', in single quotes. HTML, CSS, JS and SVG are allowed.
+Options: Plot.Width - width of the drawing area in pixels; Plot.Height - height of the drawing area in pixels; Plot.Title - title of the plot above the drawing area; Plot.Legend - show a legend with the names of the series = 1 | 0; Plot.LabelX - title of the x axis below the plot; Plot.LabelY - title of the y axis left of the plot; Plot.LogX - plot in logarithmic scale along the x axis = 1 | 0; Plot.LogY - plot in logarithmic scale along the y axis = 1 | 0; Plot.ReverseX - reverse the direction of the x axis (horizontal axis) = 1 | 0; Plot.ReverseY - reverse the direction of the y axis (vertical axis) = 1 | 0; Plot.ReverseZ - reverse the direction of the z axis in $Map = 1 | 0; Plot.FlipAxes - swap the places of the x and y axes; Plot.Limits - limits of the visible area of the plot = [MinX; MinY; MaxX; MaxY]; Plot.MinX - lower limit along the x axis; Plot.MaxX - upper limit along the x axis; Plot.MinY - lower limit along the y axis; Plot.MaxY - upper limit along the y axis; Plot.MinZ - lower limit of the z values in $Map; Plot.MaxZ - upper limit of the z values in $Map; Plot.Step - steps of the values along the x and y axes [StepX; StepY] or common for both; Plot.StepX - step of the values along the x axis; Plot.StepY - step of the values along the y axis; Plot.Grid - grid step along the x and y axes [GridX; GridY] or one value for both; Plot.GridX - step between the grid lines along the x axis; Plot.GridY - step between the grid lines along the y axis; Plot.FormatXAxis - format of the numbers along the x axis, as for the results, e.g. "F2", "0.00", "E3" or "_2"; Plot.FormatYAxis - format of the numbers along the y axis, as for the results; Plot.Svg - draw the plots as vector graphics (SVG) = 1 | 0; Plot.Adaptive - adaptive 1D function plots = 1 | 0; Plot.Series1…10.____ - properties of series 1 to 10, as follows: Plot.Series1.Name - series name, shown in the legend; Plot.Series1.Color - line color = Color.Name | "#RRGGBB"; Plot.Series1.Style - line style =
Plot.Series1.Thickness - line thickness; Plot.Palette - color palette for surface isochromes =
Plot.Shadows - draw surfaces with light and shadows; Plot.Smooth - smooth color transitions on surfaces instead of bands; Plot.LightDirection - direction to the light source =
Plot.MapStep - grid step in pixels for interpolation in $Map = 1 … 100; Plot.Stack - stack the series on top of each other for $Line, $Fill, $Smooth, $Bar and $Column; Plot.Dots - show dots on the plots = 1 | 0; Plot.DataTags - show the values at the points = 1 | 0; Plot.DropLines - show vertical lines from the points to the horizontal axis = 1 | 0; Plot.Reset() - resets all plot options to their default values; Auto - automatic or default value for the above options;
+Table: table(M;nhrows;nhcols) - displays the matrix M as a table, with nhrows header rows and nhcols header columns (1 and 0 by default); Table.Style - style of the table =
Table.CellAlign - alignment of the cells, the same for all columns, or a vector with one value per column =
Table.HeadAlign - alignment of the header cells, the same for all columns, or a vector with one value per column =
Table.MergeCells - merges the cells from row i₁, column j₁ to row i₂, column j₂; a matrix with four columns merges several ranges; Table.MergeHeaders - merges the adjacent header cells with equal text = 1 | 0; Table.CellColor - text color of the cells = Color.Name | "#RRGGBB"; Table.CellFill - background color of the cells = Color.Name | "#RRGGBB"; Table.AltColor - text color of the alternate (even) rows; Table.AltFill - background color of the alternate (even) rows; Table.HeadColor - text color of the header cells; Table.HeadFill - background color of the header cells; Table.Reset() - resets all table options to their default values; Auto - automatic or default value for the above options: numbers aligned right, text left, header rows centered and the colors of the style;
+Output control: #hide - hide the report contents; #show - always show the contents (default); #pre - show the next contents only before calculations; #post - show the next contents only after calculations; #val - show only the final result, without the equation; #equ - show complete equations and results (default); #noc - show only equations without results (no calculations); #nosub - do not substitute variables (no substitution); #novar - show equations only with substituted values (no variables); #varsub - show equations with variables and substituted values (default); #split - split equations that do not fit on a single line; #wrap - wrap equations that do not fit on a single line (default); #round n - rounds the output to n digits after the decimal point; #round default - restores rounding to the default settings; #format FFFF - specifies custom format string; #format default - restores the default formatting; #md on - enables markdown in comments; #md off - disables markdown in comments; #phasor - sets output format of complex numbers to polar phasor: A∠φ; #complex - sets output format of complex numbers to Cartesian algebraic: a + bi.
Each of the above commands is effective after the current line until the end of the report or another command that overrides it. #header - insert a page header in the report.
+Breakpoints for step-by-step execution: #pause - calculates down to the current line and waits for the user to resume manually; #input - renders an input form to the current line and waits for user input.
to calculate. The results will appear in the "Output" box on the right.
to print or 
to copy the output, or export it to Html 
, PDF 
, Word 
or LaTeX 
document.