# Lectures on topics in algebraic number theory. Ghorpade

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Extra resources for Lectures on topics in algebraic number theory. Ghorpade

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Normally, with expressions, this begins with the complete evaluation of all children. At the same time, tests are carried out to check if the operand types are valid for the function. Next the operands are processed and the internal normal form is built. This processing can, for instance, be of the addition of the numerical constants in the evaluation of a sum. The normal form is built by the operands being sorted and identical terms being combined. 9 is executed. The sorting of operands is based on an internal order of expressions, which, in general, is not identical with the lexicographical order.

The expressions in the set are enclosed in set brackets { and }. Empty sets are also valid objects. Analogue to lists, during the evaluation of a set all elements are completely evaluated, whereby the amount of elements may change. After evaluation the set contains only one copy of each element. Analogue to lists, elements that evaluate to objects of type DOM_NULL are not taken into account and expression sequences are flattened. For processing sets the operators union, minus and intersect are available.

If an expression of type DOM_NULL occurs as operand of an expression sequence, set or list, this operand is deleted. The occurrence of expressions of type DOM_NULL as one of the arguments of user-defined functions and most system functions leads also to a corresponding deletion. Example 18 The calls » type(op( [])); type(op(f())); return the result DOM_NULL DOM_NULL when f has no value. The list » [a, op([]), b]; evaluates to [a, b] . 3. Some MuPAD functions are exclusively used for user information.