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Drake
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Drake
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Implements Graded reverse lexicographic order.
| VariableOrder | VariableOrder{}(v1, v2) is true if v1 < v2. |
| BasisElement | A derived class of PolynomialBasisElement. |
We first compare the total degree of the PolynomialBasisElement; if there is a tie, then we use the graded reverse lexicographical order as the tie breaker.
Take monomials with variables {x, y, z} and total degree<=2 as an example, with the order x > y > z. To get the graded reverse lexicographical order, we take the following steps:
First find all the monomials using the total degree. The monomials with degree 2 are {x², y², z², xy, xz, yz}. The monomials with degree 1 are {x, y, z}, and the monomials with degree 0 is {1}. To break the tie between monomials with the same total degree, first sort them in the reverse lexicographical order, namely x < y < z. The lexicographical order compares two monomials by first comparing the exponent of the largest variable, if there is a tie then go forth to the second largest variable. Thus z² > zy >zx
y² > yx > x². Finally reverse the order as x² > xy > y² > xz > yz > z² > x y > z.
There is an introduction to monomial order in https://en.wikipedia.org/wiki/Monomial_order, and an introduction to graded reverse lexicographical order in https://en.wikipedia.org/wiki/Monomial_order#Graded_reverse_lexicographic_order
#include <drake/common/symbolic/polynomial_basis_element.h>
Public Member Functions | |
| bool | operator() (const BasisElement &m1, const BasisElement &m2) const |
| Returns true if m1 < m2 under the Graded reverse lexicographic order. More... | |
| bool operator() | ( | const BasisElement & | m1, |
| const BasisElement & | m2 | ||
| ) | const |
Returns true if m1 < m2 under the Graded reverse lexicographic order.