load "lvalue.magma";

// K = F_5 ( \theta ), rational function field in variable \theta = th

K< th > := RationalFunctionField( GF( 5 ) ); 

// Kt = K[ t ]

Kt< t > := PolynomialRing( K );	

// We define a rank 2 t-motive M over K by giving a matrix for \sigma

M := Matrix( Kt, 2, 2, [ 1, th-t, 1, 0 ] ); 

// We compute an approximation to the value of L( M, S ) at s = 2
// by multiplying the Euler factors of all primes of degree at most 7

LValue( M, 2, 7 : Precision := 20 ); 

// note that z = t^{-1}.