20.1 Simplification
Before using these commands, a monomial order must be specified. See the section after this for
information on how to set the monomial order.
20.1.1 NCSimplifyAll[expressions, startRelations, iterations]
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- Aliases: GroebnerSimplify, NCGroebnerSimplify
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- Description: NCSimplifyAll[expressions, startRelations, iterations] calls
NCMakeGB[startRelations, iterations] and uses the result to reduce the expressions in
expressions. This is useful when the form the Gröbner Basis is irrelevant and is only
used to simplify some set of predetermined equations.
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- Arguments: exprs can be either an expression or a list of expressions. startRelations is a list
of polynomials. iterations is a positive integer.
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- Comments / Limitations: Not available before NCAlgebra 1.2
20.1.2 NCSimplifyRationalX1[expressions, startRelations, iterations]
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- Aliases: None
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- Description: NCSimplifyRationalX1[expressions, startRelations, iterations] is (essentially)
equivalent to
NCSimplifyAll[expressions, Join[startRelations, inverses], iterations]
where inverses is a list of polynomials. inverses consists of the defining
relations of all inverses (elements with inv[...]) in expressions and startRelations.
NCSimplifyRationalX1 simplifies expressions with startRelations together with some
additional innocuous relations.
NCSimplifyRationalX1 is different from NCSimplifyAll with the following adjustment:
first all instances of inv are converted to Inv before calling NCSimplifyAll, and are
converted back afterwards. This overrides NCAlgebra’s automatic handling of inverses.
For example, the command
NCSimplifyRationalX1[{inv[x] **inv[1 - x] + y},{z **inv[y] - a}, 10]
equals
NCSimplifyAll[{Inv[x]**Inv[1-x]+y},{z**Inv[y]-a,y**Inv[y]-1,Inv[y]**y-
1,Inv[x]**x-1,x**Inv[x]-1, (1-x)**Inv[1-x]-1,Inv[1-x]**(1-x)-1}, 10].
This call to NCSimplifyAll returns Inv[x] + Inv[1-x] + y. The call to
NCSimplifyRationalX1 returns inv[x] + inv[1-x] + y.
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- Arguments: expressions is a list of polynomials. startRelations is a list of polynomials.
iterations is a natural number.
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- Comments / Limitations: Not available before NCAlgebra 1.2.