6.34.4  Multiplication in ℤ/pℤ or in ℤ/pℤ[x]: *

The * operator multiplies two integers in ℤ/pℤ or two polynomials in ℤ/pℤ[x]. (See also Section 6.8.2.) For polynomial expressions, use the normal command to simplify.

Examples.

• For integers in ℤ/pℤ:
  Input:
  31%13*10%13
  Output:

  ⎛ ⎝

  −2

  ⎞ ⎠

  %13

• For polynomials with coefficients in ℤ/pℤ:
  Input:
  normal((11*x+5)%13*(8*x+6 )% 13)
  or:
  normal((11% 13*x+5%13)*(8% 13*x+6%13))
  Output:

  ⎛ ⎝

  ⎛ ⎝

  −3

  ⎞ ⎠

  %13

  ⎞ ⎠

  x2+

  ⎛ ⎝

  ⎛ ⎝

  −24

  ⎞ ⎠

  %13

  ⎞ ⎠

  x+17%13