This command computes the set-theoretic difference of two constructible sets or two semi-algebraic sets, depending on the input type.

A constructible set must be encoded as an constructible_set object; see the type definition in ConstructibleSetTools.

A semi-algebraic set must be encoded by a list of regular_semi_algebraic_system, see the type definition of RealTriangularize.

The command Difference(cs1, cs2, R) returns a constructible set which is the set theoretic difference of two constructible sets. The polynomial ring may have characteristic zero or a prime characteristic.

The command Difference(lrsas1, lrsas2, R) returns a list of regular semi-algebraic systems, encoding the set-theoretic difference of two semi-algebraic sets. The polynomial ring must have characteristic zero.

The output may contain certain redundancy among the defining regular systems.

This command is available once RegularChains[ConstructibleSetTools] submodule or RegularChains[SemiAlgebraicSetTools] submodule have been loaded. It can always be accessed through one of the following long forms: RegularChains:-ConstructibleSetTools:-Difference or RegularChains:-SemiAlgebraicSetTools:-Difference.

The RegularChains[SemiAlgebraicSetTools][Difference] command was introduced in Maple 16.

The lrsas1 and lrsas2 parameters were introduced in Maple 16.

For more information on Maple 16 changes, see Updates in Maple 16.

Chen, C.; Golubitsky, O.; Lemaire, F.; Moreno Maza, M.; and Pan, W. "Comprehensive Triangular Decomposition". Proc. CASC 2007, LNCS, Vol. 4770: 73-101. Springer, 2007.

Chen, C.; Davenport, J.-D.; Moreno Maza, M.; Xia, B.; and Xiao, R. "Computing with semi-algebraic sets represented by triangular decomposition". Proceedings of 2011 International Symposium on Symbolic and Algebraic Computation (ISSAC 2011), ACM Press, pp. 75--82, 2011.