galgebra.dop¶

Differential operators, for all sympy expressions

For multivector-customized 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
static consolidate_coefs(sdop)[source]

Remove zero coefs and consolidate coefs with repeated pdiffs.