galgebra.dop

Differential operators, for all sympy expressions

For multivector-customized differential operators, see galgebra.mv.Dop.

Members

class galgebra.dop.Sdop(*args)

Bases: galgebra.dop._BaseDop

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)

Remove zero coefs and consolidate coefs with repeated pdiffs.

class galgebra.dop.Pdop(_Pdop__arg)

Bases: galgebra.dop._BaseDop

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).