Addition in $\mathbb {Z}$/p$\mathbb {Z}$ or in $\mathbb {Z}$/p$\mathbb {Z}$[x] : +

+ adds two integers in $\mathbb {Z}$/p$\mathbb {Z}$, or two polynomials in $\mathbb {Z}$/p$\mathbb {Z}$[x]. For polynomials expressions, use the normal command to simplify.
For integers in $\mathbb {Z}$/p$\mathbb {Z}$, input :

3%13+10%13

Output :

0%13

For polynomials with coefficients in $\mathbb {Z}$/p$\mathbb {Z}$, input :

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

or

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

Output :

(6%13)*x+-2%13