Built-in functions

Every function below is built into the jmax binary — no packages to install. They run identically in the browser playground, the CLI, and the Rust library. This page mirrors docs.charlot-lang.dev.

Linear Algebra

Signature	Description
`A * B`	Matrix multiply. Use * operator on matrices.
`A \ b`	Solve linear system Ax = b. NxN via LU decomposition.
`eig(A)`	Eigenvalues of a symmetric matrix via QR algorithm.
`svd(A)`	Singular values via eigendecomposition of A'A.
`qr(A)`	QR decomposition via Gram-Schmidt.
`cholesky(A)`	Cholesky decomposition. A must be symmetric positive definite.
`inv(A)`	Matrix inverse via Gauss-Jordan elimination.
`det(A)`	Determinant via LU decomposition.
`trace(A)`	Sum of diagonal elements.
`rank(A)`	Matrix rank via SVD.
`A'`	Matrix transpose. Use postfix apostrophe.
`eye(n)`	Identity matrix.
`zeros(m, n)`	Zero matrix.
`ones(m, n)`	All-ones matrix.
`linspace(start, end, n)`	N evenly spaced values.

Statistics

Signature	Description
`mean(data)`	Arithmetic mean.
`std(data)`	Standard deviation (sample).
`var(data)`	Variance (sample).
`median(data)`	Median value.
`percentile(data, p)`	P-th percentile (0-1).
`correlation(x, y)`	Pearson correlation coefficient.
`covariance(x, y)`	Sample covariance.
`t_test(a, b)`	Welch's two-sample t-test. Returns p-value.
`chi_squared(observed, expected)`	Chi-squared test statistic.
`linear_regression(x, y)`	OLS. Returns [intercept, slope, r_squared].
`normal_cdf(x)`	Standard normal CDF.
`normal_pdf(x)`	Standard normal PDF.

Signal Processing

Signature	Description
`fft(signal)`	Fast Fourier Transform (Cooley-Tukey). Returns magnitude spectrum.
`ifft(spectrum)`	Inverse FFT.
`convolve(a, b)`	Linear convolution.
`fir_filter(signal, coeffs)`	FIR filter.
`spectrogram(signal, win, hop)`	STFT magnitude spectrogram.
`hann(n)`	Hann window of length n.
`hamming(n)`	Hamming window of length n.
`blackman(n)`	Blackman window of length n.

Machine Learning

Signature	Description
`relu(x)`	Rectified linear unit. max(0, x).
`sigmoid(x)`	1 / (1 + exp(-x)).
`tanh_act(x)`	Hyperbolic tangent activation.
`gelu(x)`	Gaussian error linear unit.
`swish(x)`	x * sigmoid(x).
`softmax(logits)`	Softmax over a vector. Numerically stable.
`cross_entropy(pred, target)`	Cross-entropy loss.
`mse_loss(pred, target)`	Mean squared error loss.
`accuracy(pred, target)`	Classification accuracy.

Symbolic Math

Signature	Description
`sin(x)`	Sine.
`cos(x)`	Cosine.
`tan(x)`	Tangent.
`asin(x)`	Arcsine.
`acos(x)`	Arccosine.
`exp(x)`	e^x.
`log(x)`	Natural logarithm.
`log2(x)`	Base-2 logarithm.
`log10(x)`	Base-10 logarithm.
`sqrt(x)`	Square root.
`abs(x)`	Absolute value.
`floor(x)`	Floor.
`ceil(x)`	Ceiling.
`round(x)`	Round to nearest integer.

Finance

Signature	Description
`black_scholes_call(S, K)`	Black-Scholes call option price. T=1yr, r=5%, sigma=20%.
`black_scholes_put(S, K)`	Black-Scholes put option price.
`sma(data, window)`	Simple moving average.
`ema(data, span)`	Exponential moving average.
`sharpe(returns, risk_free)`	Sharpe ratio.
`max_drawdown(prices)`	Maximum drawdown.
`npv(rate, cash_flows)`	Net present value.
`irr(cash_flows)`	Internal rate of return.

Bioinformatics

Signature	Description
`smith_waterman(seq1, seq2)`	Local alignment score.
`needleman_wunsch(seq1, seq2)`	Global alignment score.
`gc_content(seq)`	GC content ratio (0-1).
`reverse_complement(seq)`	DNA reverse complement.
`translate_dna(seq)`	Translate DNA to protein.

Data Analysis

Signature	Description
`sort(data)`	Sort a vector ascending.
`unique(data)`	Remove duplicates.
`cumsum(data)`	Cumulative sum.
`diff(data)`	First differences.
`len(data)`	Length of a vector or array.

Visualization

Signature	Description
`plot line data`	Line chart.
`plot scatter data`	Scatter plot.
`plot bar data`	Bar chart.
`plot histogram data`	Histogram with automatic binning.
`plot heatmap matrix`	Heatmap with Viridis colormap.
`plot surface matrix`	3D surface plot.
`plot contour matrix`	Contour plot with marching squares.
`plot boxplot data`	Box-and-whisker plot.
`plot violin data`	Violin plot with KDE.
`plot radar data`	Radar/spider chart.

Calculus & Autodiff

Signature	Description
`d/dx(f)`	Exact symbolic differentiation.
`integrate(f, x)`	Rule-based symbolic integration (linearity, power rule, standard functions).
`expand(e)`	Distribute products and expand integer powers of sums.
`simplify(e)`	Canonical simplification via equality-saturation (e-graph).
`solve(expr, x)`	Solve polynomial equations exactly (linear, quadratic).
`grad(f, point)`	Gradient by reverse-mode automatic differentiation.
`hessian(f, point)`	Full Hessian by second-order AD.

Optimization

Signature	Description
`minimize(f, x0)`	Unconstrained minimization — gradient descent or Newton (AD Hessian).
`root(f, x0)`	Find a root by Newton's method (AD derivative).
`fit(model, data)`	Levenberg-Marquardt nonlinear least-squares curve fitting.
`lp(c, A, b)`	Linear program by two-phase simplex (Bland anti-cycling).
`qp(G, a, C, d)`	Quadratic program — equality (KKT) or inequality (active-set).

Differential Equations

Signature	Description
`ode("dy/dt", y0)`	Adaptive Dormand-Prince RK45 integrator.
`ode(…, --stiff)`	Implicit backward-Euler for stiff systems; Jacobian via AD.

Hypothesis Tests

Signature	Description
`anova(g1, g2, …)`	One-way ANOVA F-test for equal group means.
`wilcoxon(a, b)`	Wilcoxon signed-rank test (paired, nonparametric).
`mann_whitney(a, b)`	Mann-Whitney U test (independent samples).
`levene(g1, g2, …)`	Levene/Brown-Forsythe test for equal variances.
`friedman(blocks)`	Friedman repeated-measures test.
`ks_two_sample(a, b)`	Two-sample Kolmogorov-Smirnov test.

Dataframes

Signature	Description
`df file.csv`	Typed columnar dataframe from CSV (with type inference).
`groupby(key, value, op)`	Group-by aggregation: sum, mean, count, min, max.
`pivot(index, cols, value)`	Pivot table.
`join(other, on)`	Inner, left, or outer join.
`--to-parquet out`	Write real Parquet (validated against Apache Arrow).

Units

Signature	Description
`convert(v, from, to)`	Dimensional unit conversion with compound units and metric prefixes.
`Quantity{value, dim}`	Dimension-tracked arithmetic (SI base dimensions).