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/* Generate a polynomial base1 + base2*x + ....*/
ArbPoly(_base,n_IsPositiveInteger) <-- Sum(MakeVector(base,n)*x^(0 .. (n-1)));
/*
SinTaylor and ExpTaylor: direct series for the taylor series expansions
of Sin and Exp.
Examples:
In> Simplify(SinTaylor(10) - Taylor(x,0,10)Sin(x))
Out> 0;
In> Simplify(ExpTaylor(10) - Taylor(x,0,10)Exp(x))
Out> 0;
*/
SinTaylor(n_IsPositiveInteger) <--
[
Local(m);
n:=((n-1)>>1);
m:=(1+2*(0 .. n));
Sum((-1)^(0 .. n)*x^m/(m!));
];
ExpTaylor(n_IsPositiveInteger) <--
[
Sum(x^(0 .. n)/((0 .. n)!));
];
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