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`jacobian`

Jacobian matrix of a vector function

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Syntax

```jacobian(`v`, `x`)
```

Description

`jacobian(v, x)` computes the Jacobian matrix of the vector function with respect to .

If `v` is a vector then the component ring of `v` must be a field (i.e., a domain of category `Cat::Field`) for which differentiation with respect to `x` is defined.

If `v` is given as a list of arithmetical expressions, then `jacobian` returns a matrix with the standard component ring `Dom::ExpressionField``()`.

Examples

Example 1

The Jacobian matrix of the vector function is:

```delete x, y, z: jacobian([x^3, x*z, y+z], [x, y, z])```

Parameters

 `v` A list of arithmetical expressions, or a vector (i.e., an n×1 or 1 ×n matrix of a domain of category `Cat::Matrix`) `x` A list of (indexed) identifiers

Return Values

Matrix of the domain `Dom::Matrix``(R)`, where `R` is the component ring of `v` or the domain `Dom::ExpressionField()`.

Algorithms

For a vector function , where G is a subset of the matrix

is the Jacobian matrix of .