galgebra.dop¶
Differential operators, for all sympy expressions
For multivectorcustomized differential operators, see galgebra.mv.Dop
.
Members¶

class
galgebra.dop.
Pdop
(_Pdop__arg)[source]¶ Partial derivative operatorp.
The partial derivatives are of the form
\[\partial_{i_{1}...i_{n}} = \frac{\partial^{i_{1}+...+i_{n}}}{\partial{x_{1}^{i_{1}}}...\partial{x_{n}^{i_{n}}}}.\]If \(i_{j} = 0\) then the partial derivative does not contain the \(x^{i_{j}}\) coordinate.

pdiffs
¶ A dictionary where coordinates are keys and key value are the number of times one differentiates with respect to the key.
Type: dict

order
¶ Total number of differentiations. When this is zero (i.e. when
pdiffs
is{}
) then this object is the identity operator, and returns its operand unchanged.Type: int
The partial differential operator is a partial derivative with respect to a set of real symbols (variables).


class
galgebra.dop.
Sdop
(*args)[source]¶ Scalar differential operator is of the form (Einstein summation)
\[D = c_{i}*D_{i}\]where the \(c_{i}\)’s are scalar coefficient (they could be functions) and the \(D_{i}\)’s are partial differential operators (
Pdop
).
terms
¶ the structure \(((c_{1},D_{1}),(c_{2},D_{2}), ...)\)
Type: tuple of tuple
