ref: d90515c5036b9c62dedc9895c781c6459c872209
dir: /lib/math/ancillary/KM06-calc.gp/
/*
Implementations of some functions from [KM06]. The exact ranges
were applied by manual fiddling.
*/
{ betap(amin, amax, p, n) = my(l, s);
l = amax^(1/p);
s = amin^(1/p);
return(polroots(l^(1 - 1/(2^(n-1))) * (3/s - (x - s) * (p+1)/(s^2)) * (x - s)^2 - s^(1 - 1/(2^(n-1))) * (3/l - (x - l) * (p+1)/(l^2)) * (x - l)^2));
}
{ betam(amin, amax, p, n) = my(l, s);
l = amax^(1/p);
s = amin^(1/p);
return(polroots(l^(1 - 1/(2^(n-1))) * (3/s - (x - s) * (p+1)/(s^2)) * (x - s)^2 + s^(1 - 1/(2^(n-1))) * (3/l - (x - l) * (p+1)/(l^2)) * (x - l)^2));
}
{ beta(amin, amax, p, n) = my(plus, minus, alsmaller, allarger, l, r);
plus = betap(amin, amax, p, n);
minus = betam(amin, amax, p, n);
alsmaller = min(amax^(1/p), amin^(1/p));
allarger = max(amax^(1/p), amin^(1/p));
l = List();
for(i=1, length(plus), if(imag(plus[i]) < 0.001 && imag(plus[i]) > -0.001, listput(l, real(plus[i])), ));
for(i=1, length(minus), if(imag(minus[i]) < 0.001 && imag(minus[i]) > -0.001, listput(l, real(minus[i])), ));
r=0.0;
for(i=1, length(l), if(l[i] <= allarger && l[i] >= alsmaller, r=l[i], ));
return(r);
}
{ maxerr(amin, amax, p, n) = my(x1, x2, e1, e2);
x1 = List([beta(amin, amax, p, n)]);
x2 = List([beta(amin, amax, p, n)]);
for(i=1, n, listput(x1, x1[i]/p * (p - 1 + amin * x1[i]^(-p))));
for(i=1, n, listput(x2, x2[i]/p * (p - 1 + amax * x2[i]^(-p))));
e1 = abs(amin^(1/p) - x1[n + 1]);
e2 = abs(amax^(1/p) - x2[n + 1]);
return(max(e1, e2));
}