difforms
d
exterior differentiation
Calling Sequence
Parameters
Description
Examples
d(expr)
d(expr, forms)
expr
-
expression or list of expressions
forms
(optional) list of 1-forms, i.e. wdegree=one
The function d computes the exterior derivative of an expression. If the expression is a list, then d is applied to each element in the list.
When d is called with an expression and a list of 1-forms, any name of type scalar in the expression will be expanded in these 1-forms. It is assumed that the 1-forms are independent. For each 1-form, a new scalar is created to be the component for that 1-form.
The command with(difforms,d) allows the use of the abbreviated form of this command.
withdifforms:
defformf=0,w1=1,w2=1,w3=1,v=1,x=0,y=0,z=0
dx2y
2xydx+x2dy
dfx,y,z
∂∂xfx,y,zdx+∂∂yfx,y,zdy+∂∂zfx,y,zdz
df,w1,w2,w3
fw1w1+fw2w2+fw3w3
df,dx,dy1,v1
fxdx+fy1dy1+fv1v1
dfw1&ˆw2
&^df,w1,w2+fdw1&ˆw2−fw1&ˆdw2
dxy,y2,w2
ydx+xdy,2ydy,dw2
See Also
D
diff
difforms[mixpar]
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