Algebraic K-theory. Proc. Oberwolfach 1980 by R. Keith Dennis

By R. Keith Dennis

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If the operator is evaluated to a polynomial, then the variables are substituted by the operands. • If the operator is a list or set, then each element of the operator is viewed as a function and applied to the operands. The elements are then replaced by the evaluated function calls and the resulting list or set is returned. • If the operator is an array or table, then each entry again is viewed as a function and applied to the operands. The evaluated function calls replace the original entries.

A+-*$# () {} [] < > =: & II! 12. 2 19 Details of Evaluation In MuPAD, evaluation is understood as being the evaluation of an expression or the execution of a statement. This process is carried out by the system's evaluator or interpreter respectively. In this chapter some of the concepts and methods for influencing evaluation shall be introduced. For this it is first necessary to get an overview of the internal mechanisms of evaluation. 1 Expressions An expression is an algebraic object that can be processed by the evaluator.

Example 11 Let us look at the procedure » f := proc() local a; begin a*2; end_proc; which returns a*2. After the assignment >> a:=b; the call » eval(f()+text2expr("a+1")); returns the value a*2+b+1 because the result of the call f (), in contrast to the result of the text2expr call is not subsequently evaluated although it is also in an argument of the eval call. 26 THE LANGUAGE AND ITS FUNCTIONALITY The effect of the function hold is cancelled by a surrounding eval call. In the case of multiple nested hold calls, only one hold call is cancelled independent of the number of surrounding eval calls.

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