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The basic format for representing mathematical formulae is the algebraic form : an expression is internally encoded as a list with prefix operators:

- the first element of a list is an operator,
- the following elements of a list are the arguments which can be symbols (unknowns), numbers or algebraic forms in prefix notation.

Examples:

x + 1 ⇒ (PLUS X 1)

x + y + 1 ⇒ (PLUS X Y 1)

x + y * z + 1 ⇒ (PLUS X (TIMES Y Z) 1)

x^{∧}(y + 1) ⇒ (EXPT X (PLUS Y 1))

Algebraic forms are used for many purposes, for data input, for transferring data between various system components and for output. To get a feel as to how algebraic forms look like, you can make REDUCE display them for you, e.g. by the following sequence:

u:=(x+y)^3/(log z-sqrt 2);

symbolic reval ’u;

symbolic reval ’u;

The first statement assigns an algebraic expression to a variable as usual in algebraic mode, and the second statement forces REDUCE to print the algebraic form corresponding to this expression in symbolic mode.

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