Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
PeterBurbery`NewLinearAlgebraPaclet`
JacobianMatrix  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
TraditionalForm
[{y,5x+Sin[y]},{x,y}]
 | JacobianMatrix |
2
x
Out[1]//TraditionalForm=
2xy | 2 x |
5 | cos(y) |
In[2]:=
TraditionalFormDet
[{y,5x+Sin[y]},{x,y}]
 | JacobianMatrix |
2
x
Out[2]//TraditionalForm=
2xycos(y)-5
2
x
In[3]:=
TraditionalFormFullSimplifyDet
[{y,5x+Sin[y]},{x,y}]
 | JacobianMatrix |
2
x
Out[3]//TraditionalForm=
x(2ycos(y)-5x)
In[4]:=
TraditionalForm
[{rCos[φ],rSin[φ]},{r,φ}]
| JacobianMatrix |
Out[4]//TraditionalForm=
cos(φ) | -rsin(φ) |
sin(φ) | rcos(φ) |
In[5]:=
TraditionalFormDet
[{rCos[φ],rSin[φ]},{r,φ}]
| JacobianMatrix |
Out[5]//TraditionalForm=
r(φ)+r(φ)
2
sin
2
cos
In[6]:=
TraditionalFormFullSimplifyDet
[{rCos[φ],rSin[φ]},{r,φ}]
| JacobianMatrix |
Out[6]//TraditionalForm=
r
In[7]:=
TraditionalForm
[{ρSin[φ]Cos[θ],ρSin[φ]Sin[θ],ρCos[φ]},{ρ,φ,θ}]
| JacobianMatrix |
Out[7]//TraditionalForm=
cos(θ)sin(φ) | ρcos(θ)cos(φ) | -ρsin(θ)sin(φ) |
sin(θ)sin(φ) | ρsin(θ)cos(φ) | ρcos(θ)sin(φ) |
cos(φ) | -ρsin(φ) | 0 |
In[8]:=
TraditionalFormDet
[{ρSin[φ]Cos[θ],ρSin[φ]Sin[θ],ρCos[φ]},{ρ,φ,θ}]
| JacobianMatrix |
Out[8]//TraditionalForm=
2
ρ
2
sin
3
sin
2
ρ
2
cos
3
sin
2
ρ
2
sin
2
cos
2
ρ
2
cos
2
cos
In[9]:=
TraditionalFormFullSimplifyDet
[{ρSin[φ]Cos[θ],ρSin[φ]Sin[θ],ρCos[φ]},{ρ,φ,θ}]
| JacobianMatrix |
Out[9]//TraditionalForm=
2
ρ
In[10]:=
TraditionalForm
[,5,4-2,Sin[],{,,}]
| JacobianMatrix |
x
1
x
3
2
x
2
x
3
x
3
x
1
x
1
x
2
x
3
Out[10]//TraditionalForm=
1 | 0 | 0 |
0 | 0 | 5 |
0 | 8 x 2 | -2 |
x 3 x 1 | 0 | sin( x 1 |
In[11]:=
TraditionalForm
[5,4-2Sin[],,{,,}]
| JacobianMatrix |
x
2
2
x
1
x
2
x
3
x
2
x
3
x
1
x
2
x
3
Out[11]//TraditionalForm=
0 | 5 | 0 |
8 x 1 | -2 x 3 x 2 x 3 | -2 x 2 x 2 x 3 |
0 | x 3 | x 2 |
In[12]:=
TraditionalFormDet
[5,4-2Sin[],,{,,}]
| JacobianMatrix |
x
2
2
x
1
x
2
x
3
x
2
x
3
x
1
x
2
x
3
Out[12]//TraditionalForm=
-40
x
1
x
2
 |
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 |
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""