Symbols

A symbol is an identifier representing a named mathematical object. It belongs to a domain and it may hold a value. A symbol without a value represents a mathematical unknown in an expression.

To change the value or domain of a symbol, use the value and domain properties of the symbol.

A symbol does not have to be declared before it can be used. A previously unknown symbol has a domain of ce.defaultDomain and no value.

const n = ce.box("n"); n.value = 5; console.log("n =", n.value.json);

To get a list of all the symbols in an expression use expr.symbols.

Read more about adding definitions for symbols and functions

Scope

Symbols are defined within a scope.

Read more about scopes

Unknowns and Constants

A symbol that has been declared, but has no values associated with it, is said to be an unknown.

A symbol whose value cannot be changed is a constant. Constants are identified by a special flag in their definition.

The property expr.isConstant is true if a symbol is a constant.

console.log(ce.box("x").isConstant);
// ➔ false

console.log(ce.box("Pi").isConstant);
// ➔ true

The value of constants may depend on settings of the Compute Engine. For example, the value of Pi is determined based on the value of the precision property. The values of constants in scope when the precision setting is changed will be updated.

ce.precision = 4;
const smallPi = ce.box("Pi"); // π with 4 digits
console.log(smallPi.latex);
// ➔ 3.1415

ce.precision = 10;
const bigPi = ce.box("Pi"); // π with 10 digits
console.log(bigPi.latex);
// ➔ 3.1415926535

ce.precision = 100; // Future computations will be done with 100 digits

console.log("pi = ", smallPi.numericValue, "=", bigPi.numericValue);
// ➔ pi  = 3.1415 = 3.1415926535

Automatic Declaration of Symbols

If ce.defaultDomain is not null, an unknown symbol is automatically declared when it is first used in an expression.

The new definition has a domain of ce.defaultDomain and no value associated with it, so the symbol will be an unknwon.

By default, defaultDomain is "ExtendedRealNumbers" so any unknown variable is automatically assumed to be a real number. Use ce.declare() to explictly specify the domain of a symbol.

const symbol = ce.box("m"); // m for mystery
console.log(symbol.domain.symbol);
// ➔ "ExtendedRealNumbers"
symbol.value = 5;
console.log(symbol.numericValue);
// ➔ 5

If ce.defaultDomain is null, and no definition exist for the symbol, the symbol is unbound (no name binding). This will limit the usefulness of the symbol and the symbol will evaluate to an ["Error"] expression.

Forgetting a Symbol

To reset what is known about a symbol use the ce.forget() function.

The ce.forget() function will remove the definition associated with a symbol, including its domain and value, and any assumptions about the symbol.

To forget about a specific symbol, pass the name of the symbol as an argument to ce.forget().

To forget about all the symbols in the current scope, use ce.forget() without any arguments.

Note that only symbols in the current scope are forgotten. If a definition for the symbol existed in a previous scope, that definition will now be in effect.