CoCoA:HowTo:Use Modular Numbers: Difference between revisions

Latest revision as of 09:44, 29 October 2020

How can one compute with modular numbers? What's wrong in this?

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

Moreover this command throws an error

  Use R::=Z/(5);

  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 either 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
-------------------------------

The creation of a polynomial ring with no indeterminates has been disabled to highlight this (unexpected?) behaviour.

by Bigatti 17:26, 29 Nov 2005 (CET)

@@ Line 1: / Line 1: @@
-== Modular Numbers ==
+== Question ==
-=== Question ===
+How can one compute with modular numbers?  What's wrong in this?
     Use R::=Z/(5)[x];
 x+2y;
 y
-  ---
+  -------------------------------
 =0;
-  FALSE :-((
+  FALSE
-  ---
+  -------------------------------
+Moreover this command throws an error
+   Use R::=Z/(5);
-Use R::=Z/(5);
+== Answer ==
-=== Answer ===
+   Type(5);
-  Type(5);
+ INT
-INT
+ -------------------------------
--------------------------------
+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)?  ;-)
-e' un intero, e gli interi non dipendono dall'anello corrente (puoi
-immaginarti cosa succederebbe a un ciclo For?)
-per vedere 5 come modulare devi fare:
+If you want to use 5 as a modular number you should either use this syntax (similar to C/C++)
 % 5;
 % 5
--------------------------------
+ -------------------------------
-(analogo al C) oppure immergerlo nell'anello di polinomi
+or embed your integer into the polynomial ring
-  Use R::=Z/(5)[x];
+   Use R::=Z/(5)[x];
-  Poly(5);
+   Poly(5);
--------------------------------
+ -------------------------------
+The creation of a polynomial ring with no indeterminates has been disabled to highlight this (unexpected?) behaviour.
+by [[User:Bigatti|Bigatti]] 17:26, 29 Nov 2005 (CET)
+[[Category:HowTo Old]]
+[[Category:CoCoA4]]