Monomial Sparsity

Monomial patterns describe the monomial terms a polynomial expression has.

monomials(x,deg)

creates a pattern of the l monomials in x with degree(s) in deg, where x must be a tuple of indeterminate variables (or a corresponding, vector-valed polynomial) and deg is a list of nonnegative integers; where l is the total number of such monomials.

Monomial patterns are defined by the class casos.Sparsity; if multiple patterns are concatenated to a vector or matrix, we call that a monomial sparsity pattern. The previous syntax is equivalent to

casos.Sparsity.scalar(x,deg)

while the following syntaxes can be used to create more complex, matrix-valued monomial sparsity patterns:

casos.Sparsity.dense(...,w)
casos.Sparsity.diag(...,w)
casos.Sparsity.band(...,w)
casos.Sparsity.banded(...,w)
casos.Sparsity.nonzeros(...,w)
casos.Sparsity.triplet(...,w)

where ... denotes arguments to the equivalent function of casadi.Sparsity and w is either a scalar monomial pattern or a monomial sparsity pattern with length equal to the nonzero matrix entries.

Both (scalar) monomial patterns and monomial sparsity patterns can be used to define symbolic polynomials.