Command Reference

This document serves as a dictionary of the mathematical operations and commands available in Tungsten.

Most commands in Tungsten operate on a Visual Selection. To use them, highlight the relevant LaTeX or mathematical syntax in your buffer and execute the command.

Core & Arithmetic

These commands handle general expression manipulation and evaluation.

Command	Description
:TungstenEvaluate	Evaluates the current selection. This is the primary entry point for arithmetic, calculus (derivatives/integrals), and variable assignment.
:TungstenSimplify	Attempts to simplify the selected algebraic expression.
:TungstenFactor	Computes the factors of the selected polynomial or integer.

Usage Examples

Evaluate

• Signature: :TungstenEvaluate (on selection)
• Input: 3 \cdot 5
• Output: 15
• Note: If the selection contains an assignment operator (e.g., x := 5), it defines a persistent variable.

Simplify

• Signature: :TungstenSimplify (on selection)
• Input: 2x + 3x
• Output: 5x

Factor

• Signature: :TungstenFactor (on selection)
• Input: x^2 + 2x + 1
• Output: (x+1)^2

See Also: Arithmetic Domains, Calculus

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Units

Commands for unit-aware quantities.

Command	Description
:TungstenUnitConvert	Converts a selected quantity or angle to a specified output unit.

Usage Examples

Convert Units

• Signature: :TungstenUnitConvert (on selection)
• Input: \qty{1}{m}
• Prompt: cm
• Output: \qty{100}{cm}

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Linear Algebra

Commands specifically designed for matrix and vector operations.

Command	Description	Note
:TungstenGaussEliminate	Performs Gaussian elimination on a matrix (Row Reduce).	Returns a row-reduced matrix
:TungstenRank	Calculates the rank of a matrix.
:TungstenLinearIndependent	Checks if a set of vectors or a matrix's cols are linearly independent.	Returns True, False, or Undetermined.
:TungstenEigenvalue	Computes the eigenvalues of a matrix.
:TungstenEigenvector	Computes the eigenvectors of a matrix.
:TungstenEigensystem	Computes both eigenvalues and eigenvectors.

Usage Examples

Gauss Eliminate

• Signature: :TungstenGaussEliminate (on matrix selection)
• Input: \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}
• Output: \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}

Linear Independence

• Signature: :TungstenLinearIndependent (on list of vectors or matrix)
• Input: \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}
• Output: True

Eigensystem

• Signature: :TungstenEigensystem (on matrix selection)
• Input: \begin{pmatrix} 2 & 0 \\ 0 & 1 \\ \end{pmatrix}
• Output: \left( \begin{array}{cc} 2 & 1 \\ \{1,0\} & \{0,1\} \\ \end{array} \right)

See Also: Linear Algebra

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Differential Equations

Commands for solving and analyzing Ordinary Differential Equations (ODEs).

Command	Description
:TungstenSolveODE	Solves a single ODE or a system of ODEs.
:TungstenWronskian	Computes the Wronskian determinant of a set of functions.
:TungstenLaplace	Computes the Laplace transform of an expression.
:TungstenInverseLaplace	Computes the Inverse Laplace transform.
:TungstenConvolve	Computes the convolution of two functions.

Usage Examples

Solve ODE

• Signature: :TungstenSolveODE (on equation or system)
• Input: y'' + y = 0
• Output: y(x) = C_1 \sin(x) + C_2 \cos(x)

Laplace Transform

• Signature: :TungstenLaplace (on expression)
• Input: t^2
• Output: \frac{2}{s^3}

See Also: Differential Equations

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Plotting

Commands for generating visualizations.

Command	Description
:TungstenPlot	Generates a standard 2D plot from the selected function.
:TungstenPlotAdvanced	Opens a UI window to configure advanced plot options (ranges, labels, etc).
:TungstenPlotParametric	Opens a UI window specifically for configuring parametric plots.
:TungstenPlotQueue	Displays the status of active and pending plot jobs.
:TungstenPlotCancel	Cancels the most recent or specific plot job.
:TungstenPlotCheck	Checks for required dependencies (Python/Matplotlib or Wolfram).

Usage Examples

Simple Plot

• Signature: :TungstenPlot (on expression)
• Input: \sin(x)
• Output: Plot of \sin(x) inserted into the buffer or shown in an external viewer depending on your Configuration.

Check Dependencies

• Signature: :TungstenPlotCheck
• Output: List of installed backends (Wolfram, Python, Numpy, SymPy, Matplotlib) and version status.

See Also: Plotting