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last edited 17 years ago |
Edit detail for SandBoxPfaffian revision 6 of 7
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Editor: 127.0.0.1
Time: 2007/11/27 05:31:17 GMT-8 |
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| Note: | ||
added:
From unknown Tue Nov 27 05:31:13 -0800 2007
From:
Date: Tue, 27 Nov 2007 05:31:13 -0800
Subject:
Message-ID: <20071127053113-0800@axiom-wiki.newsynthesis.org>
\begin{axiom}
guessPRec [1,2,3,4,5]
\end{axiom}
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axiom-- not allowed: )spool pfaffian.output )sys Your argument list is not valid. )set message test on )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]
Type: Void
axiom--R --R
Type: Void
axiom--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
axiom--R --R
Type: Void
axiom--E 2 --S 3 of 9 pfaffian A == eval(PfChar(l, A), l=0)
Type: Void
axiom--R --R
Type: Void
axiom--E 3 --S 4 of 9 m:Matrix(Integer):=[[0,15],[-15,0]]
 | (1) |
Type: Matrix Integer
axiom--R --R + 0 15+ --R (4) | | --R +- 15 0 + --R
Type: Matrix Integer
axiom--E 4 --S 5 of 9 pfaffian m
axiom
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
axiom--R --R (5) 15 --R
Type: Polynomial Integer
axiom--E 5 --S 6 of 9 (a,b,c,d,e,f):=(3,5,7,11,13,17)
 | (3) |
Type: PositiveInteger?
axiom--R --R (6) 17 --R
Type: PositiveInteger?
axiom--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
axiom--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
axiom--E 7 --S 8 of 9 m1ans:=a*f-b*e+d*c
 | (5) |
Type: PositiveInteger?
axiom--R --R --R (8) 63 --R
Type: PositiveInteger?
axiom--E 8 --S 9 of 9 pfaffian m1
axiom
Compiling function B0 with type PositiveInteger -> Matrix Integer
 | (6) |
Type: Polynomial Integer
