puncturedfem.Monomial

Monomial of the form c * x_1 ^ alpha_1 * x_2 ^ alpha_2.

Attributes:

Name	Type	Description
alpha	MultiIndex	Multi-index of the Monomial.
coef	float	Coefficient of the Monomial.

__add__(other)

Define the operation self + other.

Parameters:

Name	Type	Description	Default
other	object	The object to add to self. Must be another Monomial.	required

Returns:

Type	Description
Monomial	The result of the addition.

__eq__(other, tol=1e-12)

Return True iff self == other.

Parameters:

Name	Type	Description	Default
other	object	The object to compare to self. Must be another Monomial.	required

Returns:

Type	Description
bool	True iff self == other.

__gt__(other)

Return True iff self.idx > other.idx.

Parameters:

Name	Type	Description	Default
other	object	The object to compare to self. Must be another Monomial.	required

Returns:

Type	Description
bool	True iff self.idx > other.idx.

__init__(alpha=None, coef=0.0)

Monomial of the form c * x_1 ^ alpha_1 * x_2 ^ alpha_2.

Parameters:

Name	Type	Description	Default
alpha	MultiIndex, optional	Multi-index of the Monomial. Default is None.	None
coef	float, optional	Coefficient of the Monomial. Default is 0.0.	0.0

__mul__(other)

Define the operation self * other.

Parameters:

Name	Type	Description	Default
other	object	The object to multiply by self. Must be a scalar (int or float) or another Monomial.	required

Returns:

Type	Description
Monomial	The result of the multiplication.

__neg__()

Define negation operation: -self.

__repr__()

Return a string representation of self.

Returns:

Type	Description
str	String representation of self.

__rmul__(other)

Define the operation: other * self.

Parameters:

Name	Type	Description	Default
other	object	The object to multiply by self. Must be a scalar (int or float).	required

Returns:

Type	Description
Monomial	The result of the multiplication.

copy()

Return a copy of self.

Returns:

Type	Description
Monomial	A copy of self.

eval(x, y)

Evaluate the Monomial at the point (x, y).

Parameters:

Name	Type	Description	Default
x	FloatLike	x-coordinate of the point at which to evaluate the Monomial.	required
y	FloatLike	y-coordinate of the point at which to evaluate the Monomial.	required

Returns:

Type	Description
FloatLike	Value(s) of the Monomial at the point (x, y). If x and y are arrays, the result is an array of the same shape.

grad()

Compute the gradient of self.

Returns:

Type	Description
tuple[Monomial, Monomial]	The partial derivatives of self with respect to x and y.

is_zero(tol=1e-12)

Return True iff self is the zero Monomial.

Parameters:

Name	Type	Description	Default
tol	float, optional	Tolerance for the comparison. Default is 1e-12.	1e-12

Returns:

Type	Description
bool	True iff self is the zero Monomial.

Notes

This method is deprecated and will be removed in a future release.

partial_deriv(var)

Compute the partial derivative of self with respect to var.

Parameters:

Name	Type	Description	Default
var	str	The variable with respect to which to differentiate. Must be one of the strings "x" or "y".	required

Returns:

Type	Description
Monomial	The partial derivative of self with respect to var.

set_coef(coef)

Set the coefficient of the Monomial to coef.

Parameters:

Name	Type	Description	Default
coef	float	Coefficient of the Monomial.	required

set_multidx(alpha)

Set the multi-index of the Monomial to alpha.

Parameters:

Name	Type	Description	Default
alpha	MultiIndex	Multi-index of the Monomial.	required

See Also

MultiIndex: Class representing a multi-index.

set_multidx_from_idx(idx)

Set the multi-index via lexical ordering using the index idx.

Parameters:

Name	Type	Description	Default
idx	int	Lexical ordering index of the multi-index.	required

See Also

MultiIndex: Class representing a multi-index.