CoCoA:HowTo:Use Modular Numbers

Modular Numbers

Question

What's wrong in this?

  Use R::=Z/(5)[x];
  5x+2y;
2y
-------------------------------
  5=0;
FALSE
-------------------------------

Moreover this throws an error

  Use R::=Z/(5);

Answer

  Type(5);
INT
-------------------------------

5 is an integer, and integers do not depend on the current ring: could you imagine what would happen to a For cycle over Z/(2)? ;-) If you want to use 5 as a modular number you should use this syntax (similar to C/C++)

  5 % 5;
0 % 5
-------------------------------

or embed your integer into the polynomial ring

  Use R::=Z/(5)[x];
  Poly(5);
0
-------------------------------