something is *definitely* unhinged here : On 9.8.beta3 running on Debian
testing on core i7 + 16 GB RAM, after running :
a = RR(-4967757600021511 / 2**106)
b = RR(-7769080564883485 / 2**52)
c = RR( 5221315298319565 / 2**53)
m = matrix([[a, b], [c, -a]])
M = matrix([[var("p%d%d"%(u, v), latex_name="p_{%s,%d}"%(u, v))
for v in range(2)]
for u in range(2)])
S = dict(zip(M.list(), [a, b, c, -a]))
MN = M.apply_map(lambda u:u.subs(S))
one gets :
sage: m.parent()
Full MatrixSpace of 2 by 2 dense matrices over Real Field with 53 bits of
precision
sage: m*~m
[ 1.00000000000000 -1.23259516440783e-32]
[ 2.31872978520878 1.00000000000000]
sage: (~m)*m
[ 1.00000000000000 -6.90032969864117]
[6.16297582203915e-33 1.00000000000000]
sage: MN.parent()
Full MatrixSpace of 2 by 2 dense matrices over Symbolic Ring
sage: MN*~MN
[ 1.00000000000000 -1.23259516440783e-32]
[ 2.31872978520878 1.00000000000000]
sage: (~MN)*MN
[ 1.00000000000000 -6.90032969864117]
[6.16297582203915e-33 1.00000000000000]
all being wrong, *wrong*, *wrong*…
However :
sage: (M*~M).apply_map(lambda u:u.subs(S))
[ 1.00000000000000 0]
[-3.54953126192945e-17 1.00000000000000]
sage: ((~M)*M).apply_map(lambda u:u.subs(S))
[ 1.00000000000000 1.05630833481279e-16]
[ 0 1.00000000000000]
both being acceptable.
One also notes that the form of :
sage: ~M
[1/p00 - p01*p10/(p00^2*(p01*p10/p00 - p11))
p01/(p00*(p01*p10/p00 - p11))]
[ p10/(p00*(p01*p10/p00 - p11))
-1/(p01*p10/p00 - p11)]
sage: (~M).apply_map(simplify)
[1/p00 - p01*p10/(p00^2*(p01*p10/p00 - p11))
p01/(p00*(p01*p10/p00 - p11))]
[ p10/(p00*(p01*p10/p00 - p11))
-1/(p01*p10/p00 - p11)]
is somewhat unexpected ; one expects :
sage: (~M).apply_map(lambda u:u.simplify_full())
[-p11/(p01*p10 - p00*p11) p01/(p01*p10 - p00*p11)]
[ p10/(p01*p10 - p00*p11) -p00/(p01*p10 - p00*p11)]
which is also the form returned by maxima :
sage: maxima_calculus.invert(M).sage()
[-p11/(p01*p10 - p00*p11) p01/(p01*p10 - p00*p11)]
[ p10/(p01*p10 - p00*p11) -p00/(p01*p10 - p00*p11)]
giac :
sage: giac.inverse(giac(M)).sage()
[[-p11/(p01*p10 - p00*p11), p01/(p01*p10 - p00*p11)],
[p10/(p01*p10 - p00*p11), -p00/(p01*p10 - p00*p11)]]
fricas :
sage: fricas.inverse(M._fricas_()).sage()
[-p11/(p01*p10 - p00*p11) p01/(p01*p10 - p00*p11)]
[ p10/(p01*p10 - p00*p11) -p00/(p01*p10 - p00*p11)]
mathematica :
sage: mathematica.Inverse(M).sage()
[[-p11/(p01*p10 - p00*p11), p01/(p01*p10 - p00*p11)],
[p10/(p01*p10 - p00*p11), -p00/(p01*p10 - p00*p11)]]
and (somewhat un-backconvertible) :
sage: sympy.sympify(M)^-1._sage_()
Matrix([
[ p11/(p00*p11 - p01*p10), -p01/(p00*p11 - p01*p10)],
[-p10/(p00*p11 - p01*p10), p00/(p00*p11 - p01*p10)]])
This is, IMNSHO, a *critical* bug. Could you open a tichet for this, and
mark it as such ?
Le samedi 5 novembre 2022 à 07:59:27 UTC+1, Håkan Granath a écrit :
> Hi, there seems to be a problem with inverses of matrices with elements in
> RR. It only occurs very sporadically for me, but here is an example:
>
> a = RR(-4967757600021511 / 2**106)
> b = RR(-7769080564883485 / 2**52)
> c = RR( 5221315298319565 / 2**53)
>
> m = matrix([[a, b], [c, -a]])
>
> print(m)
> print()
> print(~m)
>
> On my machines it produces the output
>
> [-6.12323399573677e-17 -1.72508242466029]
> [ 0.579682446302195 6.12323399573677e-17]
>
> [ 4.00000000000000 1.72508242466029]
> [ -0.579682446302195 -6.12323399573676e-17]
>
> Clearly the element 4 is wrong (the correct inverse is -m). Is this a
> known bug?
>
> Some system information:
>
> SageMath version 9.7, using Python 3.10.5
> OS: Ubuntu 20.04.5 LTS
> CPU: Intel(R) Core(TM) i7-7700 CPU @ 3.60GHz
>
> Best regards,
>
> Håkan Granath
>
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