18.4 The list of commands

18.4.1 SetMonomialOrder[aListOfListsOfIndeterminates, . . . ]

Aliases: None
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 },...}].
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]

which we now describe.

18.4.2 SetUnknowns[aListOfIndeterminates]

Aliases: None
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.
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]

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.
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[]

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.
Arguments: None
Comments / Limitations: Not available before NCAlgebra 1.2

18.4.5 PrintMonomialOrder[]

Aliases: None
Description: PrintMonomialOrder[] prints the order to the screen.
Arguments: None
Comments / Limitations: See Chapter 18. Not available before NCAlgebra 1.2

18.4.6 NCAutomaticOrder[ aMonomialOrder, aListOfPolynomials ]

Aliases: None
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].
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.
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].