resultant modifies input

[gorzel]

If the basering contains parameters as trancedental elements, then the resultant computation modifies the input.

> ring r=0,x,dp;
> poly f = 2/3*x+7/5;
> resultant (x,f,x);   // this is f(0)
7/5
> f;                   // OK
2/3x+7/5

> ring ri = (0,i),x,dp;
> minpoly = i2+1;
> poly f = 2/3*x+7/5;
> resultant (x,f,x);
7/5
> f;                    // OK
2/3*x+7/5


> ring rb =(0,b),x,dp;
> poly f = 2/3*x+7/5;
> resultant (x,f,x);
7/5
> f;                   // Wrong, the input has been modified
10*x+21

// Other example
> f = 2/3x+5;
> g = 7/11x-3/8;
> resultant (f,g,x);    // The result is correct
-151/44
> -7/11*subst(2/3x+5,x,3/8*11/7);  // check by hand (product formula for resultant)
-151/44 

> f;    // BUG
2*x+15
> g;    // BUG
56*x-33

> poly f = x/b+1;
> resultant (x,f,x);
1
> f;    // BUG
x+(b)

Conclusion: resultant can be used as cleardenom.

[hannes]

fixed.