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-- not allowed: )spool pfaffian.output
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)sys
Your argument list is not valid.
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)set message test on

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)set message auto off

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)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]
Type: Void
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--R
--R
Type: Void
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--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
Type: Void
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--R
--R
Type: Void
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--E 2
--S 3 of 9
pfaffian A == eval(PfChar(l, A), l=0)
Type: Void
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--R
--R
Type: Void
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--E 3
--S 4 of 9
m:Matrix(Integer):=[[0,15],[-15,0]]
 (1)
Type: Matrix(Integer)
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--R
--R        + 0    15+
--R   (4)  |        |
--R        +- 15  0 +
--R
Type: Matrix Integer
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--E 4
--S 5 of 9
pfaffian m
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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)
Type: Polynomial(Integer)
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--R
--R   (5)  15
--R
Type: Polynomial Integer
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--E 5
--S 6 of 9
(a,b,c,d,e,f):=(3,5,7,11,13,17)
 (3)
Type: PositiveInteger?
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--R
--R   (6)  17
--R
Type: PositiveInteger?
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--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)
Type: Matrix(Integer)
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--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
Type: Matrix Integer
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--E 7
--S 8 of 9
m1ans:=a*f-b*e+d*c
 (5)
Type: PositiveInteger?
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--R
--R
--R   (8)  63
--R
Type: PositiveInteger?
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--E 8
--S 9 of 9
pfaffian m1
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Compiling function B0 with type PositiveInteger -> Matrix(Integer)
 (6)
Type: Polynomial(Integer)

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