Docstrings for basic field functions

Field operation functions

These functions implement some basic operations pertaining to fields in general.

curl

sympy.physics.vector.fieldfunctions.curl(vect, frame)

Returns the curl of a vector field computed wrt the coordinate symbols of the given frame.

Parameters

vect : Vector

The vector operand

frame : ReferenceFrame

The reference frame to calculate the curl in

Examples

>>> from sympy.physics.vector import ReferenceFrame
>>> from sympy.physics.vector import curl
>>> R = ReferenceFrame('R')
>>> v1 = R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z
>>> curl(v1, R)
0
>>> v2 = R[0]*R[1]*R[2]*R.x
>>> curl(v2, R)
R_x*R_y*R.y - R_x*R_z*R.z

divergence

sympy.physics.vector.fieldfunctions.divergence(vect, frame)

Returns the divergence of a vector field computed wrt the coordinate symbols of the given frame.

Parameters

vect : Vector

The vector operand

frame : ReferenceFrame

The reference frame to calculate the divergence in

Examples

>>> from sympy.physics.vector import ReferenceFrame
>>> from sympy.physics.vector import divergence
>>> R = ReferenceFrame('R')
>>> v1 = R[0]*R[1]*R[2] * (R.x+R.y+R.z)
>>> divergence(v1, R)
R_x*R_y + R_x*R_z + R_y*R_z
>>> v2 = 2*R[1]*R[2]*R.y
>>> divergence(v2, R)
2*R_z

gradient

sympy.physics.vector.fieldfunctions.gradient(scalar, frame)

Returns the vector gradient of a scalar field computed wrt the coordinate symbols of the given frame.

Parameters

scalar : sympifiable

The scalar field to take the gradient of

frame : ReferenceFrame

The frame to calculate the gradient in

Examples

>>> from sympy.physics.vector import ReferenceFrame
>>> from sympy.physics.vector import gradient
>>> R = ReferenceFrame('R')
>>> s1 = R[0]*R[1]*R[2]
>>> gradient(s1, R)
R_y*R_z*R.x + R_x*R_z*R.y + R_x*R_y*R.z
>>> s2 = 5*R[0]**2*R[2]
>>> gradient(s2, R)
10*R_x*R_z*R.x + 5*R_x**2*R.z

scalar_potential

sympy.physics.vector.fieldfunctions.scalar_potential(field, frame)

Returns the scalar potential function of a field in a given frame (without the added integration constant).

Parameters

field : Vector

The vector field whose scalar potential function is to be calculated

frame : ReferenceFrame

The frame to do the calculation in

Examples

>>> from sympy.physics.vector import ReferenceFrame
>>> from sympy.physics.vector import scalar_potential, gradient
>>> R = ReferenceFrame('R')
>>> scalar_potential(R.z, R) == R[2]
True
>>> scalar_field = 2*R[0]**2*R[1]*R[2]
>>> grad_field = gradient(scalar_field, R)
>>> scalar_potential(grad_field, R)
2*R_x**2*R_y*R_z

scalar_potential_difference

sympy.physics.vector.fieldfunctions.scalar_potential_difference(field, frame, point1, point2, origin)

Returns the scalar potential difference between two points in a certain frame, wrt a given field.

If a scalar field is provided, its values at the two points are considered. If a conservative vector field is provided, the values of its scalar potential function at the two points are used.

Returns (potential at position 2) - (potential at position 1)

Parameters

field : Vector/sympyfiable

The field to calculate wrt

frame : ReferenceFrame

The frame to do the calculations in

point1 : Point

The initial Point in given frame

position2 : Point

The second Point in the given frame

origin : Point

The Point to use as reference point for position vector calculation

Examples

>>> from sympy.physics.vector import ReferenceFrame, Point
>>> from sympy.physics.vector import scalar_potential_difference
>>> R = ReferenceFrame('R')
>>> O = Point('O')
>>> P = O.locatenew('P', R[0]*R.x + R[1]*R.y + R[2]*R.z)
>>> vectfield = 4*R[0]*R[1]*R.x + 2*R[0]**2*R.y
>>> scalar_potential_difference(vectfield, R, O, P, O)
2*R_x**2*R_y
>>> Q = O.locatenew('O', 3*R.x + R.y + 2*R.z)
>>> scalar_potential_difference(vectfield, R, P, Q, O)
-2*R_x**2*R_y + 18

Checking the type of vector field

is_conservative

sympy.physics.vector.fieldfunctions.is_conservative(field)

Checks if a field is conservative.

Parameters

field : Vector

The field to check for conservative property

Examples

>>> from sympy.physics.vector import ReferenceFrame
>>> from sympy.physics.vector import is_conservative
>>> R = ReferenceFrame('R')
>>> is_conservative(R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z)
True
>>> is_conservative(R[2] * R.y)
False

is_solenoidal

sympy.physics.vector.fieldfunctions.is_solenoidal(field)

Checks if a field is solenoidal.

Parameters

field : Vector

The field to check for solenoidal property

Examples

>>> from sympy.physics.vector import ReferenceFrame
>>> from sympy.physics.vector import is_solenoidal
>>> R = ReferenceFrame('R')
>>> is_solenoidal(R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z)
True
>>> is_solenoidal(R[1] * R.y)
False