HP 40gs hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 236
Multmod, Powmod
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hp40g+.book Page 54 Friday, December 9, 2005 1:03 AM MULTMOD POWMOD Performs a multiplication in Z/pZ or in Z/pZ[X]. Example 1 Typing: MULTMOD(11, 8) gives: -3 Example 2 Typing: MULTMOD(11X + 5, 8X + 6) gives: -(3x2 - 2x - 4) Calculates A to the power of N in Z/pZ[X], and A(X) to the power of N in Z/pZ[X]. Example 1 If p = 13, typing: POWMOD(11, 195) gives: 5 In effect: 1112 = 1 mod 13, so 11195 = 1116×12+3 = 5 mod 13. Example 2 Typing: POWMOD(2X + 1, 5) gives: 6x5 + 2x4 + 2x3 + x2 - 3x + 1 since 32 = 6 (mod 13), 80 = 2 (mod 13), 40 = 1 (mod 13), 10 = -3 (mod 13). 14-54 Computer Algebra System (CAS)
14-54
Computer Algebra System (CAS)
MULTMOD
Performs a multiplication in Z/pZ or in Z/pZ[X].
Example 1
Typing:
MULTMOD(11, 8)
gives:
–3
Example 2
Typing:
MULTMOD(11X + 5, 8X + 6)
gives:
POWMOD
Calculates A to the power of N in Z/pZ[X], and A(X) to
the power of N in Z/pZ[X].
Example 1
If
p
= 13, typing:
POWMOD(11, 195)
gives:
5
In effect: 11
12
= 1 mod 13, so 11
195
= 11
16×12+3
= 5
mod 13.
Example 2
Typing:
POWMOD(2X + 1, 5)
gives:
since 32 = 6 (mod 13), 80 = 2 (mod 13), 40 = 1 (mod
13), 10 = –3 (mod 13).
3
x
2
2
x
–
4
–
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–
6
x
5
2
x
4
2
x
3
x
2
3
x
–
1
+
+
+
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hp40g+.book
Page 54
Friday, December 9, 2005
1:03 AM