Singular Manual: minpoly

  | ### 5.3.3 minpoly `Type:` number `Purpose:` describes the coefficient field of the current basering as an algebraic extension with the minimal polynomial equal to `minpoly`. Setting the `minpoly` should be the first command after defining the ring. `Note:` The minimal polynomial has to be specified in the syntax of a polynomial. Its variable is not one of the ring variables, but the algebraic element which is being adjoined to the field. Algebraic extensions in SINGULAR are only possible over the rational numbers or over Z/p, p a prime number. SINGULAR does not check whether the given polynomial is irreducible! It can be checked in advance with the function `factorize` (see factorize). `Example:`
        //(Q[i]/(i^2+1))[x,y,z]:
        ring Cxyz=(0,i),(x,y,z),dp;
        minpoly=i^2+1;
        i2;  //this is a number, not a poly
      ==> -1
See factorize; ring.

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