Basic OperatorΒΆ

A basic operator is an object that can be symbolically applied to a list of arguments from a set, the result being a kernel over that set or an expression.

You create an object of type BasicOperator by using the operator operation. This first form of this operation has one argument and it must be a symbol. The symbol should be quoted in case the name has been used as an identifier to which a value has been assigned.

A frequent application of BasicOperator is the creation of an operator to represent the unknown function when solving a differential equation.

Let y be the unknown function in terms of x.

y := operator 'y
 y
                    Type: BasicOperator

This is how you enter the equation y'' + y' + y = 0.

deq := D(y x, x, 2) + D(y x, x) + y x = 0
  ,,       ,
 y  (x) + y (x) + y(x) =
                    Type: Equation Expression Integer

To solve the above equation, enter this.

solve(deq, y, x)
                                      x     x
                              +-+   - -   - -      +-+
                            x\|3      2     2    x\|3
 [particular= 0,basis= [cos(-----)%e   ,%e   sin(-----)]]
                              2                    2
                    Type: Union(Record(particular: Expression Integer,
                                basis: List Expression Integer),...)

Use the single argument form of BasicOperator (as above) when you intend to use the operator to create functional expressions with an arbitrary number of arguments

Nary means an arbitrary number of arguments can be used in the functional expressions.

nary? y
 true
                    Type: Boolean

unary? y
 false
                    Type: Boolean

Use the two-argument form when you want to restrict the number of arguments in the functional expressions created with the operator.

This operator can only be used to create functional expressions with one argument.

opOne := operator('opOne, 1)
 opOne
                    Type: BasicOperator

nary? opOne
 false
                    Type: Boolean

unary? opOne
 true
                    Type: Boolean

Use arity to learn the number of arguments that can be used. It returns “false” if the operator is nary.

arity opOne
 1
                    Type: Union(NonNegativeInteger,...)

Use name to learn the name of an operator.

name opOne
 opOne
                    Type: Symbol

Use is? to learn if an operator has a particular name.

is?(opOne, 'z2)
 false
                    Type: Boolean

You can also use a string as the name to be tested against.

is?(opOne, "opOne")
 true
                    Type: Boolean

You can attached named properties to an operator. These are rarely used at the top-level of the FriCAS interactive environment but are used with FriCAS library source code.

By default, an operator has no properties.

properties y
 table()
                    Type: AssociationList(String,None)

The interface for setting and getting properties is somewhat awkward because the property values are stored as values of type None.

Attach a property by using setProperty.

setProperty(y, "use", "unknown function" :: None )
 y
                    Type: BasicOperator

properties y
 table("use"=NONE)
                    Type: AssociationList(String,None)

We know the property value has type String.

property(y, "use") :: None pretend String
 "unknown function"
                    Type: String

Use deleteProperty! to destructively remove a property.

deleteProperty!(y, "use")
 y
                     Type: BasicOperator

 properties y
  table()
                     Type: AssociationList(String,None)

See Also

  • )help Expression
  • )help Kernel
  • )show BasicOperator

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