Hi,
While using sympy-0.7.1.win32 to find the determinant of a 9x9 size
matrix, the following code just gives me []:
from sympy import *
from sympy.matrices import *
x, s = symbols('x,s')
M = Matrix([[1,3*x,2*x,5*x,7*x,7*x,4*x,6*x,5*x],[1/(3*x),1,x/2,3*x,5*x,
3*x,5*x,3*x,3*x],[1/(2*x),2/x,1,3*x,6*x,3*x,6*x,5*x,5*x],[1/(5*x),1/
(3*x),1/(3*x),1,6*x,2*x,4*x,3*x,3*x],[1/(7*x),1/(5*x),1/(6*x),1/(6*x),
1,x/5,x/2,x/3,x/3],[1/(7*x),1/(3*x),1/(3*x),1/(2*x),5/x,1,3*x,2*x,2*x],
[1/(4*x),1/(5*x),1/(6*x),1/(4*x),2/x,1/(3*x),1,x,x/3],[1/(6*x),1/(3*x),
1/(5*x),1/(3*x),3/x,1/(2*x),1/x,1,x],[1/(5*x),1/(3*x),1/(5*x),1/(3*x),
3/x,1/(2*x),3/x,1/x,1]])
s = M.det()
s
solve(s)
The below Matlab code I have actually used both produces the symbolic
determinant and its solution making the determinant = 0:
>> [1 3*x 2*x 5*x 7*x 7*x 4*x 6*x 5*x
1/(3*x) 1 x/2 3*x 5*x 3*x 5*x 3*x 3*x
1/(2*x) 2/x 1 3*x 6*x 3*x 6*x 5*x 5*x
1/(5*x) 1/(3*x) 1/(3*x) 1 6*x 2*x 4*x 3*x 3*x
1/(7*x) 1/(5*x) 1/(6*x) 1/(6*x) 1 x/5 x/2 x/3 x/3
1/(7*x) 1/(3*x) 1/(3*x) 1/(2*x) 5/x 1 3*x 2*x 2*x
1/(4*x) 1/(5*x) 1/(6*x) 1/(4*x) 2/x 1/(3*x) 1 x x/3
1/(6*x) 1/(3*x) 1/(5*x) 1/(3*x) 3/x 1/(2*x) 1/x 1 x
1/(5*x) 1/(3*x) 1/(5*x) 1/(3*x) 3/x 1/(2*x) 3/x 1/x 1]
ans =
[ 1, 3*x, 2*x, 5*x, 7*x, 7*x, 4*x, 6*x, 5*x]
[ 1/3/x, 1, 1/2*x, 3*x, 5*x, 3*x, 5*x, 3*x, 3*x]
[ 1/2/x, 2/x, 1, 3*x, 6*x, 3*x, 6*x, 5*x, 5*x]
[ 1/5/x, 1/3/x, 1/3/x, 1, 6*x, 2*x, 4*x, 3*x, 3*x]
[ 1/7/x, 1/5/x, 1/6/x, 1/6/x, 1, 1/5*x, 1/2*x, 1/3*x, 1/3*x]
[ 1/7/x, 1/3/x, 1/3/x, 1/2/x, 5/x, 1, 3*x, 2*x, 2*x]
[ 1/4/x, 1/5/x, 1/6/x, 1/4/x, 2/x, 1/3/x, 1, x, 1/3*x]
[ 1/6/x, 1/3/x, 1/5/x, 1/3/x, 3/x, 1/2/x, 1/x, 1, x]
[ 1/5/x, 1/3/x, 1/5/x, 1/3/x, 3/x, 1/2/x, 3/x, 1/x, 1]
>> A=ans
A =
[ 1, 3*x, 2*x, 5*x, 7*x, 7*x, 4*x, 6*x, 5*x]
[ 1/3/x, 1, 1/2*x, 3*x, 5*x, 3*x, 5*x, 3*x, 3*x]
[ 1/2/x, 2/x, 1, 3*x, 6*x, 3*x, 6*x, 5*x, 5*x]
[ 1/5/x, 1/3/x, 1/3/x, 1, 6*x, 2*x, 4*x, 3*x, 3*x]
[ 1/7/x, 1/5/x, 1/6/x, 1/6/x, 1, 1/5*x, 1/2*x, 1/3*x, 1/3*x]
[ 1/7/x, 1/3/x, 1/3/x, 1/2/x, 5/x, 1, 3*x, 2*x, 2*x]
[ 1/4/x, 1/5/x, 1/6/x, 1/4/x, 2/x, 1/3/x, 1, x, 1/3*x]
[ 1/6/x, 1/3/x, 1/5/x, 1/3/x, 3/x, 1/2/x, 1/x, 1, x]
[ 1/5/x, 1/3/x, 1/5/x, 1/3/x, 3/x, 1/2/x, 3/x, 1/x, 1]
>> det(A)
ans =
1/68040000/
x^7*(220449600*x^14-1886068800*x^13+8102639520*x^12-22674790980*x^11+44475384828*x^10-65346108188*x^9+79077332921*x^8-83067498684*x^7+71729961960*x^6-46617691095*x^5+22014521575*x^4-7596140900*x^3+1857714250*x^2-284550000*x
+21000000)
>> solve(ans)
ans =
.
49392530579267874366477298620162
.
68607861848591739263438236067199
1.4196246448783615212397879138998
1.9485057898549110972454340032617
1.1340390809741388389995399152253+.
46228008343584832122605447632043*i
.22104987835554992382046134671970+.
14086715024698162643184561077195*i
.
95466432759790434570198072089475+2.0841859632376755920542773940758*i
.86308735644910184513831015409445e-1+.
37573309931082667607442258912743*i
-.
39235142430065989265022385248892+1.0529792538101967691779585678336*i
-.
39235142430065989265022385248892-1.0529792538101967691779585678336*i
.86308735644910184513831015409445e-1-.
37573309931082667607442258912743*i
.
95466432759790434570198072089475-2.0841859632376755920542773940758*i
.22104987835554992382046134671970-.
14086715024698162643184561077195*i
1.1340390809741388389995399152253-.
46228008343584832122605447632043*i
I'd appreciate if you could tell me where I am making a mistake in
Sympy?
Best,
Tll
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