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Function Repository Resource:

 JacobianDeterminant

Source Notebook

Compute the Jacobian determinant of a vector function with respect to a list of variables

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["JacobianDeterminant"][{f1,f2,…,fn},{x1,x2,…,xm}]

computes the Jacobian matrix of the vector function {f1,f2,…,fn} with respect to the variables xi.

Details and Options

The Jacobian matrix J of a vector mapping {x1,x2,…,xm}⟶{f1,f2,…,fn} is defined as the matrix with components Jij = . ResourceFunction["JacobianDeterminant"] returns the determinant of this matrix.

Examples

Basic Examples (3) 

Compute the Jacobian determinant of a symbolic vector expression in two dimensions:

In[1]:=
ResourceFunction["JacobianDeterminant"][{4 x^2 y, x - y^2}, {x, y}]
Out[1]=

Compute the Jacobian determinant of mappings in three dimensions:

In[2]:=
ResourceFunction["JacobianDeterminant"][{x y z, x^2, z}, {x, y, z}]
Out[2]=
In[3]:=
ResourceFunction[ "JacobianDeterminant"][{r p Sin[t], r p Cos[t], r^2/p}, {r, p, t}]
Out[3]=

Compute the Jacobian determinant of mapping between polar and Cartesian coordinates in the plane:

In[4]:=
ResourceFunction["JacobianDeterminant"][{r Cos[t], r Sin[t]}, {r, t}]
Out[4]=

Properties and Relations (2) 

Compute the Jacobian determinant of an expression:

In[5]:=
ResourceFunction[ "JacobianDeterminant"][{x^3 - 2 x y - y^6, x - y^2}, {x, y}]
Out[5]=

Compare this to the result obtained by taking the determinant of ResourceFunction["JacobianMatrix"] of the same expression:

In[6]:=
Det[ResourceFunction["JacobianMatrix"][{x^3 - 2 x y - y^6, x - y^2}, {x, y}]]
Out[6]=

Publisher

Wolfram|Alpha Math Team

Version History

  • 6.0.0 – 23 March 2023
  • 5.1.0 – 12 May 2021
  • 5.0.0 – 18 February 2020
  • 4.0.0 – 12 February 2020
  • 2.0.0 – 06 September 2019
  • 1.0.0 – 05 August 2019

Related Resources

License Information