Singular Manual: ideal expressions

| ### 4.5.2 ideal expressions An ideal expression is: an identifier of type ideal a function returning an ideal a combination of ideal expressions by the arithmetic operations `+` or `*` a power of an ideal expression (operator `^` or `**`) Note that the computation of the product `i*i` involves all products of generators of `i` while `i^2` involves only the different ones, and is therefore faster. a type cast to ideal Example:
      ring r=0,(x,y,z),dp;
      ideal m = maxideal(1);
      m;
    ==> m[1]=x
    ==> m[2]=y
    ==> m[3]=z
      poly f = x2;
      poly g = y3;
      ideal i = x*y*z , f-g, g*(x-y) + f^4 ,0, 2x-z2y;
      ideal M = i + maxideal(10);
      timer =0;
      i = M*M;
      timer;
    ==> 0
      ncols(i);
    ==> 505
      timer =0;
      i = M^2;
      ncols(i);
    ==> 505
      timer;
    ==> 0
      i[ncols(i)];
    ==> x20
      vector v = [x,y-z,x2,y-x,x2yz2-y];
      ideal j = ideal(v);

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