)sys

   Your argument list is not valid.

)set message test on

   Your user access level is compiler and this set option is therefore 
      not available. See the )set userlevel command for more 
      information.

)set message auto off
 

)clear all

   All user variables and function definitions have been cleared.

--S 1 of 9
B0 n == matrix [[(if i=j+1 and odd? j then -1 else _
                  if i=j-1 and odd? i then 1 else 0) _
                    for j in 1..n] for i in 1..n]

--R
--R

--E 1

--S 2 of 9
PfChar(lambda, A) ==
   n := nrows A
   (n = 2) => lambda^2 + A.(1,2)
   M := subMatrix(A, 3, n, 3, n)
   r := subMatrix(A, 1, 1, 3, n)
   s := subMatrix(A, 3, n, 2, 2)

   p := PfChar(lambda, M)
   d := degree(p, lambda)

   B := B0(n-2)
   C := r*B
   g := [(C*s).(1,1), A.(1,2), 1]
   if d >= 4 then
       B := M*B
       for i in 4..d by 2 repeat
           C := C*B
           g := cons((C*s).(1,1), g)
   g := reverse! g

   res := 0
   for i in 0..d by 2 for j in 2..d+2 repeat
       c := coefficient(p, lambda, i)
       for e in first(g, j) for k in 2..-d by -2 repeat
           res := res +  c * e * lambda^(k+i)

   res

--R
--R

--E 2

--S 3 of 9
pfaffian A == eval(PfChar(l, A), l=0)

--R
--R

--E 3

--S 4 of 9
m:Matrix(Integer):=[[0,15],[-15,0]]

(1)

--R
--R        + 0    15+
--R   (4)  |        |
--R        +- 15  0 +
--R

--E 4

--S 5 of 9
pfaffian m

Compiling function B0 with type Integer -> Matrix(Integer) 
   The type of the local variable res has changed in the computation.
   We will attempt to interpret the code.
   Cannot compile map: PfChar 
   We will attempt to interpret the code.

(2)

--R
--R   (5)  15
--R

--E 5

--S 6 of 9
(a,b,c,d,e,f):=(3,5,7,11,13,17)

(3)

--R
--R   (6)  17
--R

--E

--S 7 of 9
m1:Matrix(Integer):=[[0,a,b,c],[-a,0,d,e],[-b,-d,0,f],[-c,-e,-f,0]]

(4)

--R
--R        + 0    3     5    7 +
--R        |                   |
--R        |- 3   0     11   13|
--R   (7)  |                   |
--R        |- 5  - 11   0    17|
--R        |                   |
--R        +- 7  - 13  - 17  0 +
--R

--E 7

--S 8 of 9
m1ans:=a*f-b*e+d*c

(5)

--R
--R
--R   (8)  63
--R

--E 8

--S 9 of 9
pfaffian m1

Compiling function B0 with type PositiveInteger -> Matrix(Integer)

(6)