ref: 228b30bfe204fc490e16eec6ba5484991a765074
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)); }