## some problem with determinant of a matrix

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jocaps
Messages : 118
Inscription : lun. avr. 17, 2017 4:32 pm

### some problem with determinant of a matrix

Consider the following code

Code : Tout sélectionner

``````m:=matrix[[0,0.425*v2,-0.425,0,0,-d5*l4+d5*l5,d5*l4*v5+d5*v5*l5],[0,0.425,0.425*v2,0,0,-d5*l4*v5-d5*v5*l5,-d5*l4+d5*l5],[0.425,0,0,-0.425*v2,d5*l4*l5*v5-d5*v5,0,0],[-2*v2,0,0,2,2*l4*l5*v5+2*v5,0,0],[0,-2*v2,-2,0,0,2*l4*v5-2*v5*l5,2*l4+2*l5],[0,2,-2*v2,0,0,-2*l4-2*l5,2*l4*v5-2*v5*l5],[-2,0,0,-2*v2,2*l4*l5-2,0,0]];
det(m);
``````
I get Error: Bad Argument Value. I tried very hard to find out why this is happenning. So far I could not find the reason. The same matrix has a determinant in other computer algebra systems. If I replace the first row of the matrix by a zero row I get a determinant. I did not do more experiments to figure out the nature of this problem. But this is very peculiar. Any assistance is much appreciated.

Jose

lukamar
Messages : 297
Inscription : ven. juin 30, 2017 9:55 am
Localisation : Zagreb, Croatia

### Re: some problem with determinant of a matrix

Hello Jose,
I think that mixing approx values with symbols is the problem here, but Bernard will know better. As a workaround, I propose applying "exact" before computing the determinant:

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``det(exact(m))``
Luka

parisse
Messages : 5141
Inscription : mar. déc. 20, 2005 4:02 pm
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### Re: some problem with determinant of a matrix

Yes, running det(exact(m)) is a good workaround. I will avoid interpolation for det of these kinds of matrices in the future...

jocaps
Messages : 118
Inscription : lun. avr. 17, 2017 4:32 pm

### Re: some problem with determinant of a matrix

Thank you Luka and Bernard. I guess I should have known better, I often encounter this and I always forget that at times I should switch to rationals. Maple has similar pecularities when you don't make your float rationals. In case you want to look at this more, I think that when working with less symbols (say only one) I did not get this error. No matter. I am switching to rationals for these kind of computations. Thanks a bunch.

parisse
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Inscription : mar. déc. 20, 2005 4:02 pm
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### Re: some problem with determinant of a matrix

jocaps a écrit :
mar. févr. 19, 2019 4:34 am
In case you want to look at this more, I think that when working with less symbols (say only one) I did not get this error.
There are several algorithms to compute determinants, if you don't select one explicitly, there is an heuristic to determine which one should be used and it depends on the number of variables and degrees.