Section9.33

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## 9.33 HexadecimalExpansion

All rationals have repeating hexadecimal expansions. The operation hexhexHexadecimalExpansion returns these expansions of type HexadecimalExpansion. Operations to access the individual numerals of a hexadecimal expansion can be obtained by converting the value to RadixExpansion(16). More examples of expansions are available in the DecimalExpansionXmpPage , BinaryExpansionXmpPage , and RadixExpansionXmpPage .

This is a hexadecimal expansion of a rational number.

r := hex(22/7)

3. 249‾

Type: HexadecimalExpansion

Arithmetic is exact.

r + hex(6/7)

4

Type: HexadecimalExpansion

The period of the expansion can be short or long ...

[hex(1/i) for i in 350..354]

[0. 0 0BB3EE721A54D88‾,0. 00BAB6561‾,0. 00 BA2E8‾,0. 00B9A7862A0FF465879D5F‾,0. 0 0B92143FA36F5E02E4850FE8DBD78‾]

Type: List HexadecimalExpansion

or very long!

hex(1/1007)

0. 0041149783F0BF2C7D13933192AF6980619EE345E91EC2BB9D5CC‾A5C071E40926E54E8DDAE24196C0B2F8A0AAD60DBA57F5D4C8‾536262210C74F1‾

Type: HexadecimalExpansion

These numbers are bona fide algebraic objects.

p := hex(1/4)*x**2 + hex(2/3)*x + hex(4/9)

0. 4 x 2+0. A‾x+0. 71C‾

Type: Polynomial HexadecimalExpansion
q := D(p, x)

0. 8 x+0. A‾

Type: Polynomial HexadecimalExpansion
g := gcd(p, q)

x+1. 5‾

Type: Polynomial HexadecimalExpansion
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