/* This script illustrates the behavior between Maple and arenaireplot */
/* It is meant to be used with arenaireplot version 0.0.2.2-alpha      */

/* WARNING: the parameter diam represents a *relative diameter*:       */
/* To get the absolute maximal diameter of the zero boxes Delta, use   */
/* the formula:     Delta = diam * |I|                                 */
/* where |I| denotes the diameter of the input interval I.             */


filenameMaple="log2Example.mpl";
commandMaple="maple -q < log2Example.mpl";


a=-1b-9;
b=1b-9;
d=[a;b];
f=log2(1+x);
p = x * (117045327009867803036301574157545b-106 + x * ((-58522663504933901606981166592605b-106) + x * (8663094464742397b-54 + x * ((-6497320848515433b-54) + x * (2598928339549937b-53 + x * ((-541446114948727b-51) + x * 3712726891772213b-54))))));



dyadic=powers!;
write > $filenameMaple "restart: Digits := 50: with(numapprox): log1p := x -> log(1+x): expm1 := x -> exp(x)-1: log2 := x -> log[2](x): f := x -> ", f, ": p := x -> ", p, ": a := ", a, ": b:= ", b, ":\n";
write >> $filenameMaple "printf(\"Maple with 50 digits                  :  %a\\n\", infnorm((p(x)-f(x))/f(x),x=a..b)):\n";
write >> $filenameMaple "restart: Digits := 100: with(numapprox): log1p := x -> log(1+x): expm1 := x -> exp(x)-1: log2 := x -> log[2](x): f := x -> ", f, ": p := x -> ", p, ": a := ", a, ": b:= ", b, ":\n";
write >> $filenameMaple "printf(\"Maple with 100 digits                 :  %a\\n\", infnorm((p(x)-f(x))/f(x),x=a..b)):\n";
bashexecute $commandMaple;


verbosity=0!;
dyadic=off!;
r = <dirtyinfnorm (p-f)/f in d>;

taylorrecursions=2!;
rI = <[infnorm (p-f)/f in d, diam=1b-80]>;

print "Arenairetools with dirtyinfnorm       :", r;
print "Arenairetools with infnorm, diam=1b-80:", <rI>_;
write "                                        ", <rI>;