Computing in $\mathbb {Z}$/p$\mathbb {Z}$ or in $\mathbb {Z}$/p$\mathbb {Z}$[x]

The way to compute over $\mathbb {Z}$/p$\mathbb {Z}$ or over $\mathbb {Z}$/p$\mathbb {Z}$[x] depends on the syntax mode :

• In Xcas mode, an object n over $\mathbb {Z}$/p$\mathbb {Z}$ is written n%p. Some examples of input for
  • an integer n in $\mathbb {Z}$/13$\mathbb {Z}$
    n:=12%13.
  • a vector V in $\mathbb {Z}$/13$\mathbb {Z}$
    V:=[1,2,3]%13 or V:=[1%13,2%13,3%13].
  • a matrix A in $\mathbb {Z}$/13$\mathbb {Z}$
    A:=[[1,2,3],[2,3,4]]%13 or
    A:=[[1%13,2%13,3%13],[[2%13,3%13,4%13]].
  • a polynomial A in $\mathbb {Z}$/13$\mathbb {Z}$[x] in symbolic representation
    A:=(2*x^2+3*x-1)%13 or
    A:=2%13*x^2+3%13*x-1%13.
  • a polynomial A in $\mathbb {Z}$/13$\mathbb {Z}$[x] in list representation
    A:=poly1[1,2,3]%13 or A:=poly1[1%13,2%13,3%13].
  To recover an object o with integer coefficients instead of modular coefficients, input o % 0. For example, input o:=4%7 and o%0,then output is -3.
• In Maple mode, integers modulo p are represented like usual integers instead of using specific modular integers. To avoid confusion with normal commands, modular commands are written with a capital letter (inert form) and followed by the mod command (see also the next section).

Remark

• For some commands in $\mathbb {Z}$/p$\mathbb {Z}$ or in $\mathbb {Z}$/p$\mathbb {Z}$[x], p must be a prime integer.
• The representation is the symetric representation :
  11%13 returns -2%13.