18.4 The list of commands
18.4.1 SetMonomialOrder[aListOfListsOfIndeterminates, . . . ]
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- Aliases: None
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- Description: SetMonomialOrder[a,b,c,...] sets the graded lex order a < b < c < … with
a < b < c <
. If one uses a list of variables rather than a single variable as
one of the arguments, then multigraded lex order is used. It is synonomous with
SetMonomialOrder[{a,b,c,...}]. Pure lex order a << b << c << … on these variables
is set by SetMonomialOrder[{{a}, {b}, {c },...}].
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- Arguments: A multigraded lex order a < b << c < … on these variables is set by
SetMonomialOrder[{ {a, b }, {c },...}]. aListOfListsOfIndeterminates is a list of
Mathematica variable or a list of Mathematica variables.
-
- Comments / Limitations: Not available before NCAlgebra 1.2.
Equivalent to SetMonomialOrder[{a,b }, {c , A }] is SetMonomialOrder[{{a,b }, {c , A }}]. Or
alternatively this is equivalent the following two commands
SetKnowns[a,b]
SetUnKnowns[c, A]
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which we now describe.
18.4.2 SetUnknowns[aListOfIndeterminates]
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- Aliases: None
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- Description: SetUnknowns[aListOfVariables] records the variables in the list of variables
aListOfIndeterminates to be corresponding to unknown quantities. This and
SetUnknowns prescribe a monomial order with the knowns at the the bottom and the
unknowns at the top.
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- Arguments: aListOfIndeterminates is a list of Mathematica variables.
-
- Comments / Limitations: Not available before NCAlgebra 1.2. This is equivalent to
Do[SetMonomialOrder[aListOfVariables[[i]],i+1], {i, 1,Length[aListOfV ariables]}]
18.4.3 SetUnKnowns[aListOfVariables]
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- Aliases: None
-
- Description: SetUnKnowns[aListOfVariables] records the variables in the list of variables
aListOfVariables to be corresponding to unknown quantities. This and SetUnknowns
prescribe a monomial order with the knowns at the the bottom and the unknowns at
the top.
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- Arguments: aListOfVariables is a list of Mathematica variables.
-
- Comments / Limitations: Not available before NCAlgebra 1.2. This is equivalent to
Do[SetMonomialOrder[aListOfVariables[[i]],i+1], {i, 1,Length[aListOfV ariables]}]
18.4.4 ClearMonomialOrder[]
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- Aliases: None
-
- Description: After ClearMonomialOrder[] is called, there are no indeterminates which are
considered ordered. The monomial order can be retrieved by using the ReinstallOrder[]
command.
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- Arguments: None
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- Comments / Limitations: Not available before NCAlgebra 1.2
18.4.5 PrintMonomialOrder[]
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- Aliases: None
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- Description: PrintMonomialOrder[] prints the order to the screen.
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- Arguments: None
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- Comments / Limitations: See Chapter 18. Not available before NCAlgebra 1.2
18.4.6 NCAutomaticOrder[ aMonomialOrder, aListOfPolynomials ]
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- Aliases: None
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- Description: This command assists the user in specifying a monomial order. It inserts
all of the indeterminants found in aListOfPolynomials into the monomial order.
If x is an indeterminant found in aMonomialOrder then any indeterminant whose
symbolic representation is a function of x will appear next to x. For example,
NCAutomaticOrder[{{a},{b}},{ a**Inv[a]**tp[a] + tp[b]}] would set the order to be
a < tp[a] < Inv[a] ≪ b < tp[b].
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- Arguments: A list of indeterminants which specifies the general order. A list of polynomials
which will make up the input to the Gröbner basis command.
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- Comments / Limitations: If tp[Inv[a]] is found after Inv[a] NCAutomaticOrder[ ] would
generate the order a < tp[Inv[a]] < Inv[a]. If the variable is self-adjoint (the input
contains the relation tp[Inv[a]] == Inv[a]) we would have the rule, Inv[a] → tp[Inv[a]],
when the user would probably prefer tp[Inv[a]] → Inv[a].