"Source: Text/Ring/FldFunRat.text";
"Line: 1345";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/FldFunRat.text, line: 1345
// Example: H45E14 ()
print "Example: H45E14";
ei := GetEchoInput();
SetEchoInput(true);
S<u> := PowerSeriesRing(Rationals());
f := [Vector([1]), Vector([u])];
pade, seq := PadeHermiteApproximant(f,3);
pade;
seq;
mat := Matrix([Eltseq(v): v in f]);
pade*mat;
PadeHermiteApproximant([1,u],5);
g:= [Vector([1,0,0]), Vector([0,1,0]), Vector([1+u,2+u^2,u^3])];
pade := PadeHermiteApproximant(g,5);
pade;
pade*Matrix([Eltseq(v): v in g]);
SetEchoInput(ei);
