### 11.8.4 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 7.3.2.) For polynomial expressions, use the normal command to simplify.

#### Examples

For integers in ℤ/pℤ:

31%13*10%13

| ⎛ ⎝ | −2 | ⎞ ⎠ | %13

For polynomials with coefficients in ℤ/pℤ:

normal((11*x+5)%13*(8*x+6)%13)

or:

normal((11%13*x+5%13)*(8%13*x+6%13))

| ⎛ ⎝ | ⎛ ⎝ | −3 | ⎞ ⎠ | %13 | ⎞ ⎠ | x2+ | ⎛ ⎝ | ⎛ ⎝ | −24 | ⎞ ⎠ | %13 | ⎞ ⎠ | x+17%13