Z15 = Integers(15)sage: Z15.multiplication_table('digits')
* 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14
+---------------------------------------------
00| 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
01| 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14
02| 00 02 04 06 08 10 12 14 01 03 05 07 09 11 13
03| 00 03 06 09 12 00 03 06 09 12 00 03 06 09 12
04| 00 04 08 12 01 05 09 13 02 06 10 14 03 07 11
05| 00 05 10 00 05 10 00 05 10 00 05 10 00 05 10
06| 00 06 12 03 09 00 06 12 03 09 00 06 12 03 09
07| 00 07 14 06 13 05 12 04 11 03 10 02 09 01 08
08| 00 08 01 09 02 10 03 11 04 12 05 13 06 14 07
09| 00 09 03 12 06 00 09 03 12 06 00 09 03 12 06
10| 00 10 05 00 10 05 00 10 05 00 10 05 00 10 05
11| 00 11 07 03 14 10 06 02 13 09 05 01 12 08 04
12| 00 12 09 06 03 00 12 09 06 03 00 12 09 06 03
13| 00 13 11 09 07 05 03 01 14 12 10 08 06 04 02
14| 00 14 13 12 11 10 09 08 07 06 05 04 03 02 01
Gerar o anel polinomial \(R_q = \mathbb{Z}_{17}[x]/(x^7-1)\):
PolyRing = PolynomialRing(Integers(17), 'x') # Z_17[x]
x = PolyRing.gen()
Rq = PolyRing.quotient(x^7-1, 'x') # RqR.random_element()