Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Dual numbers
Standalone and Geometric Algebra based dual numbers
Dual | constructor for dual numbers |
DualRe | real part |
DualEps | dual part |
XXXX.
Symbolic rule-based dual numbers:
In[41]:=
eps=Dual[0,1]
Out[41]=
ϵ
In[42]:=
eps^2
Out[42]=
0
In[39]:=
Dual[a,b]
Out[39]=
a+bϵ
In[40]:=
Dual[a,b]^2
Out[40]=
2
a
In[43]:=
Exp[Dual[a,b]]
Out[43]=
a
a
In[1542]:=
ArcCos[Dual[a,b,c]]
Out[1542]=
ArcCos[a]---
b
1-
2
a
ϵ
1
c
1-
2
a
ϵ
2
abc
3/2
(1-)
2
a
ϵ
12
In[1546]:=
D[ArcCos[a],{a,2}]
Out[1546]=
-
a
3/2
(1-)
2
a
Multivector dual numbers:
In[1630]:=
MultivectorFunctionArcCos,
[{a,b},{0,0,1}]
 | Multivector |
Out[1630]=
ArcCos[a]+-
b
1-
2
a
e
1
In[1672]:=
 | Multivector |
Out[1672]=
a+b+c
e
3
e
12
In[1670]:=
MultivectorFunctionArcCos,
[{a,0,0,b,c},{1,0,2}]//FullSimplify
 | Multivector |
Out[1670]=
ArcCos[a]+-+-+-
b
1-
2
a
e
3
c
1-
2
a
e
12
abc
3/2
(1-)
2
a
e
123
""