galgebra.dop

Differential operators, for all sympy expressions

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

Members

class galgebra.dop.Sdop(*args)

Bases: _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: _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).