Convert into an element of a basic domain

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expr(object) converts object into an element of a basic domain, such that all sub-objects are elements of basic domains as well.

expr is a type conversion function, for converting an element of a more complex library domain, such as a polynomial or a matrix, into an element of a basic kernel domain.

expr proceeds recursively, such that all sub-objects of the returned object are elements of basic domains, or infinities, or undefined. See Example 1 and Example 2.

The two special objects infinity and complexInfinity are translated into identifiers with the same name by expr. Evaluating these identifiers yields the original objects. See Example 1.

If object already belongs to a basic domain other than DOM_POLY, then expr is only applied recursively to the operands of object, if any.

If object is a polynomial of domain typeDOM_POLY, then expr is applied recursively to the coefficients of object, and afterwards the result is converted into an identifier, a number, or an expression. See Example 1.

If object belongs to a library domain T with an "expr" slot, then the corresponding slot routine T::expr is called with object as argument, and the result is returned.

This can be used to extend the functionality of expr to elements of user-defined domains. If the slot routine is unable to perform the conversion, it must return FAIL. See Example 6.

If the domain T does not have an "expr" slot, then expr returns FAIL.

The result of expr is not evaluated further. Use eval to evaluate it. See Example 4.


Example 1

expr converts a polynomial into an expression, an identifier, or a number:

expr(poly(x^2 + y, [x])), expr(poly(x)), expr(poly(2, [x]));
map(%, domtype)

expr also works with the objects infinity, complexInfinity, and undefined:

expr(infinity), expr(complexInfinity), expr(undefined);
map(%, domtype)

Example 2

This example shows that expr works recursively on expressions. All subexpressions which are domain elements are converted into expressions. The construction with hold(_plus)(..) is necessary since x + i(1) would evaluate to FAIL:

i := Dom::IntegerMod(7):
hold(_plus)(x, i(1));  expr(%)

Example 3

The function series returns an element of the domain Series::Puiseux, which is not a basic domain:

s := series(sin(x), x);

Use expr to convert the result into an element of domain type DOM_EXPR:

e := expr(s); domtype(e)

Note that the information about the order term is lost after the conversion.

Example 4

expr does not evaluate its result. In this example the polynomial p has a parameter a and the global variable a has a value. expr applied on the polynomial p returns an expression containing a. If you want to insert the value of a use the function eval:

p := poly(a*x, [x]):  a := 2:  expr(p);  eval(%)

Example 5

A is an element of type Dom::Matrix(Dom::Integer):

A := Dom::Matrix(Dom::Integer)([[1, 2], [3, 2]]);  

In this case, expr converts A into an element of type DOM_ARRAY:

a := expr(A); domtype(a)

However, it is not guaranteed that the result is of type DOM_ARRAY in future versions of MuPAD® as well. For example, the internal representation of matrices might change in the future. Use coerce to request the conversion into a particular data type:

coerce(A, DOM_ARRAY)

A nested list is an alternative representation for a matrix:

coerce(A, DOM_LIST)

Example 6

If a sub-object belongs to a domain without an "expr" slot, then expr returns FAIL:

T := newDomain("T"):
d := new(T, 1, 2);

You can extend the functionality of expr to your own domains. We demonstrate this for the domain T by implementing an "expr" slot, which returns a list with the internal operands of its argument:

T::expr := x -> [extop(x)]:

If now expr encounters a sub-object of type T during the recursive process, it calls the slot routine T::expr with the sub-object as argument:

expr(d), expr([d, 3])



An arbitrary object

Return Values

Element of a basic domain.

Overloaded By


See Also

MuPAD Functions