EZ-Face is based on our fast method for computing Euler sums by
turning them into convolutions of geometrically converging nested sums.
This method is described in our preprint
``Special values of multidimensional polylogarithms,''
see the References page.
The method was coded in the C language using the
GNU MP multiprecision
EZ-Face has been limited to the precision
of 100 digits. A typical computation will complete within few seconds.
Standard syntax for computer representation of mathematical expressions
(as used by Maple) is assumed.
The value can be computed by typing in
z( s1 , ... , sk ).
can be computed by typing in
zp( p , s1 , ... , sk ).
The z() and zp() functions
can be used within any Maple expression. Their
values are calculated before being passed to
Maple. So, the arguments of z or zp are not evaluated and
be non-zero integers (syntactically!),
the only exception being the value of p,
i.e. the first argument of zp(...), which must be an integer
or a floating-point number.
The function lindep( [ x1 , ... , xn ] )
can be used to discover a vanishing linear combination
(with integer coefficients) of the values
x1 , ... , xn.
Input Pi^6 / z(6) evaluates to 945.00000....
Instance of Euler's formula for .
Input z(3,1,3,1,3,1) - 2 * Pi^12 / 14! evaluates to 0
Instance of the now proven Zagier conjecture.
Input lindep( [ z(-1,2) , log(2)*Pi^2 , z(3) ] ) evaluates to 12. , -1. , 3.
Discovery of the relation