An interface for evaluation of Euler and related sums. |

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 preprint ``Special values of multidimensional 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.
Standard syntax for computer representation of mathematical expressions (as used by Maple) is assumed. The value
can be computed by typing in The value can be computed by typing in zp( a , b , s.
_{1} , ... , s_{k}
)The value can be computed by typing in m( s.
_{1} , ... , s_{k}
)The value can be computed by typing in mgl( s.
_{1} , ... , s_{k}
)The value can be computed by typing in mcl( s.
_{1} , ... , s_{k}
)These functions can be used within any Maple
expression. Their values are calculated The function _{1} , ...
, x_{n}. These lindep expressions can either be entered
in manually by hand or built by toggling the interface into lindep
entry mode. To enter a lindep expression using the lindep
builder, first toggle the interface into the appropriate mode by selecting
the option labeled Add to Lindep. When the interface is in
this mode, each expression entered into the text box labeled Expression
will be added to the expressions collected in the box labeled Lindep.
Clicking on the button labeled Evaluate Lindep will evaluate the
linear combination of these expressions. In order to edit an expression
already collected in the lindep builder, simply select that expression
and click Delete Expression then re-add the expression into the
lindep builder. Lindep doesn't work on complex numbers, so to discover
a relationship between complex numbers the real and imaginary parts should
be done seperately. Please note that all lindep calculations are
performed with a significance of 100 digits.
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