;(gen-cyclic-group (map 1#(modulo (* %1 3) 7) (between 1 6))) ;{{3 6 2 5 1 4} {2 4 6 1 3 5} {6 5 4 3 2 1} {4 1 5 2 6 3} {5 3 1 6 4 2} {1 2 3 4 5 6}} (define \$z (rtu 7)) (define \$a11 (+ z z^2 z^4)) (define \$a12 (+ z^6 z^5 z^3)) (define \$b10 (+ a11 a12));-1 (define \$b10' b10) (define \$b11 (- a11 a12)) (define \$b12 (- a12 a11)) (define \$b11' (sqrt (** b11 2))) (define \$a11' (/ (+ b10' b11') 2));(/ (+ -1 (* i (sqrt 7))) 2) (define \$a12' (/ (- b10' b11') 2));(/ (+ -1 (* -1 i (sqrt 7))) 2) (define \$a21 (+ z (* w z^2) (* w^2 z^4))) (define \$a22 (+ z^6 (* w z^5) (* w^2 z^3))) (define \$b20 (+ a21 a22)) (define \$b21 (- a21 a22)) (define \$b22 (- a22 a21)) (define \$b20' (rt 3 (** b20 3))) ;(define \$b21' (rt 3 (** b21 3))) ;(** b21 3) ;(+ (* 8 (rtu 7)) (* 8 (rtu 7)^2) (* -5 (rtu 7)^3) (* 5 (rtu 7)^4) (* -8 (rtu 7)^5) (* -8 (rtu 7)^6) (* 3 (rtu 7) w) (* 3 (rtu 7)^2 w) (* -3 (rtu 7)^5 w) (* -3 (rtu 7)^6 w) (* 3 (rtu 7)^3 w^2) (* -3 (rtu 7)^4 w^2)) (define \$b21' (rt 3 (+ (* 5 a11') (* -5 a12') (* w^2 -3 a11') (* w^2 3 a12'))));Calculate manually (define \$a21' (/ (+ b20' b21') 2)) (define \$a22' (/ (- b20' b21') 2)) (define \$a31 (+ z (* w^2 z^2) (* w z^4))) (define \$a32 (+ z^6 (* w^2 z^5) (* w z^3))) (define \$b30 (+ a31 a32)) (define \$b31 (- a31 a32)) (define \$b32 (- a32 a31)) (define \$b30' (rt 3 (** b30 3))) ;(define \$b31' (rt 3 (** b31 3))) ;(** b31 3) ;(+ (* 5 (rtu 7)) (* 8 (rtu 7)^2) (* -5 (rtu 7)^3) (* 5 (rtu 7)^4) (* -8 (rtu 7)^5) (* -5 (rtu 7)^6) (* -3 (rtu 7) w) (* 3 (rtu 7)^3 w) (* -3 (rtu 7)^4 w) (* 3 (rtu 7)^6 w) (* 3 (rtu 7)^2 w^2) (* -3 (rtu 7)^5 w^2)) (define \$b31' (rt 3 (+ (* 5 a11') (* -5 a12') (* w -3 a11') (* w 3 a12'))));Calculate manually (define \$a31' (/ (+ b30' b31') 2)) (define \$a32' (/ (- b30' b31') 2)) (define \$z1' (/ (+ a11' a21' a31') 3)) (define \$z6' (/ (+ a12' a22' a32') 3)) z1' ;(/ (+ -1 (* i (sqrt 7)) (rt 3 (+ 14 (* 21 w))) (rt 3 (+ (* 5 i (sqrt 7)) (* -3 i (sqrt 7) w^2))) (rt 3 (+ -7 (* -21 w))) (rt 3 (+ (* 5 i (sqrt 7)) (* -3 i (sqrt 7) w)))) 6) (/ (+ -1 (rt 3 (+ 14 (* 21 w))) (rt 3 (+ -7 (* -21 w))) (* i (sqrt 7)) (rt 3 (+ (* 5 i (sqrt 7)) (* -3 i (sqrt 7) w))) (rt 3 (+ (* 5 i (sqrt 7)) (* -3 i (sqrt 7) w^2))) ) 6)