# CtcCartProd: $$\mathcal{C}_{\mathcal{C}_1\times \mathcal{C}_2}$$¶

The $$\mathcal{C}_{\mathcal{C}_1\times \mathcal{C}_2}$$ contractor is the Cartesian product of two other contractors $$\mathcal{C}_{\mathcal{C}_1}$$ and $$\mathcal{C}_{\mathcal{C}_2}$$. This contractor is useful in the case where the state vector of the system is composed of two parts subject to independent constraints.

## Definition¶

Important

$\mathcal{C}_{\mathcal{C}_1\times\mathcal{C}_2}\left([\mathbf{x}]\right) = \left(\mathcal{C}_1\left(\Pi_1\right) \times \mathcal{C}_2\left(\Pi_2\right)\right)\left([\mathbf{x}]\right)$
c = CtcCartProd([c1, c2])
c.contract(x)

CtcCartProd c(c1, c2);
c.contract(x);


Optimality

This contractor is optimal as it is based on the optimality of other contractors.

Example incoming