Implementation details:
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 paper
``Special values of multiple polylogarithms,''
see the References page.
The method was coded in the C language using the
GNU MP multiprecision
library.
EZ-Face has been limited to the precision
of 100 digits. A typical computation will complete within few seconds.
Syntax:
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 ).
The value
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
must
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.
Examples:
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
.
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