By Le Bellac M.

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**Extra resources for A short introduction to quantum information and quantum computation: solutions of exercises**

**Sample text**

Two other functions controlling the appearance of real numbers are outputFloating and outputFixed. The former causes Axiom to display floating-point values in exponent notation and the latter causes it to use fixed-point notation. 00345 Note that the semicolon “;” in the examples above allows several expressions to be entered on one line. The result of the last expression is displayed. remember also that the percent symbol “%” is used to represent the result of a previous calculation. To display rational numbers in a base other than 10 the function radix is used.

2. 3 21 Useful Functions To obtain the absolute value of a number the abs function can be used. This takes a single argument which is usually an integer or a floating point value but doesn’t necessarily have to be. The sign of a value can be obtained via the sign function which rturns −1, 0, or 1 depending on the sign of the argument. 42354) 1 NonNegativeInteger 22 CONTENTS Type: PositiveInteger Tests on values can be done using various functions which are generally more efficient than using relational operators such as = particularly if the value is a matrix.

In the example: 4/2 2 Type: Fraction Integer the result is stored as the fraction 2/1 but is displayed as the integer 2. This fraction could be converted to type Integer with no loss of information but Axiom will not do so automatically. 2. 6 Type: Float Although Axiom can convert this back to a fraction it might not be the same fraction you started with as due to rounding errors. For example, the following conversion appears to be without error but others might not: %::Fraction Integer 23 5 Type: Fraction Integer where “%” represents the previous result (not the calculation).