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RegularChains[ConstructibleSetTools][RegularSystemDifference] - compute the difference of two regular systems
Calling Sequence
RegularSystemDifference(rs1, rs2, R)
Parameters
rs1, rs2
-
regular systems of R
R
polynomial ring
Description
The command RegularSystemDifference(rs1, rs2, R) returns a constructible set which is the difference of rs1 and rs2.
This command is part of the RegularChains[ConstructibleSetTools] package, so it can be used in the form RegularSystemDifference(..) only after executing the command with(RegularChains[ConstructibleSetTools]). However, it can always be accessed through the long form of the command by using RegularChains[ConstructibleSetTools][RegularSystemDifference](..).
Examples
Define a polynomial ring.
Define a set of polynomials of R.
The command Triangularize (with lazard option) decomposes the common solutions of the polynomial system by means of regular chains.
There are two groups of solutions, each of which is given by a regular chain. To view their equations, use the Equations command.
Let be the first regular chain, and be the second one.
Consider two polynomials and ; regard them as inequations.
To obtain a regular system, first check whether is regular with respect to , and is regular with respect to .
Both of them are regular, thus you can build the following regular systems.
The command RegularSystemDifference computes the set theoretical difference of two sets defined by regular systems. The output is a list of regular systems which forms a constructible set.
To view the output, use the following sequence of commands.
Alternatively, you could use the Info command.
See Also
ConstructibleSet, ConstructibleSetTools, Difference, RegularChains, RegularSystem, RepresentingChain, RepresentingInequations
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