linsolve sometimes returns incorrect answer

[Wes Loewer]

I was solving a system of equations for physics and I came across what appears to be bug in the linsolve (and solve) function.

Code:

linsolve([t1-m3*g=m3*a3, t2-m1*g=m1*a1, t2-m2*g=m2*a2, t1-2*t2=0, a1=-(a2+a3)/2], [t1,t2,a1,a2,a3]);

xcas (and maxima) both give the results to be

Code:

[8*g*m1*m2*m3/(2*m1*m2+m1*m3+2*m2*m3),4*g*m1*m2*m3/(2*m1*m2+m1*m3+2*m2*m3),(-2*g*m1*m2-g*m1*m3+2*g*m2*m3)/(2*m1*m2+m1*m3+2*m2*m3),(-2*g*m1*m2+3*g*m1*m3-2*g*m2*m3)/(2*m1*m2+m1*m3+2*m2*m3),(6*g*m1*m2-g*m1*m3-2*g*m2*m3)/(2*m1*m2+m1*m3+2*m2*m3)]

but the Prime CAS, HW 2.1.14603 (2021-12-02) and VC 2.1.14596 (2021-10-01), returns exactly twice the correct answers

Code:

[16*g*m1*m2*m3/(2*m1*m2+m1*m3+2*m2*m3),8*g*m1*m2*m3/(2*m1*m2+m1*m3+2*m2*m3),(-4*g*m1*m2-2*g*m1*m3+4*g*m2*m3)/(2*m1*m2+m1*m3+2*m2*m3),(-4*g*m1*m2+6*g*m1*m3-4*g*m2*m3)/(2*m1*m2+m1*m3+2*m2*m3),(12*g*m1*m2-2*g*m1*m3-4*g*m2*m3)/(2*m1*m2+m1*m3+2*m2*m3)]

However, if I change the last equation from a1=-(a2+a3)/2 to the equivalent 2*a1=-(a2+a3), then the answers are correct.

Also, if I plug in numeric values into the original equations, such as

Code:

linsolve([t1-30*10=30*a3, t2-10*10=10*a1, t2-20*10=20*a2, t1-2*t2=0, a1=-(a2+a3)/2], [t1,t2,a1,a2,a3]);

it produces the correct results.

Code:

[4800/19,2400/19,50/19,-70/19,-30/19]

[Wes Loewer]

Seems that this bug was introduced back in 2017.

I can confirm the following:
firmware 11226 (2016-12-08) does not have this bug
firmware 11385 (2017-01-27) has this bug

[Albert Chan]

We have the same bug for XCas 1.5.0-63 (win32), returning twice the correct answer.

[Wes Loewer]

(10-30-2022 03:57 PM)Albert Chan Wrote:  We have the same bug for XCas 1.5.0-63 (win32), returning twice the correct answer.

Since xcas 1.9.0-7 does not have the bug anymore, perhaps it's already been fixed in the Prime CAS which we'll hopefully see it in the next firmware.

[Wes Loewer]

(10-30-2022 05:34 PM)Wes Loewer Wrote:  

(10-30-2022 03:57 PM)Albert Chan Wrote:  We have the same bug for XCas 1.5.0-63 (win32), returning twice the correct answer.

Since xcas 1.9.0-7 does not have the bug anymore, perhaps it's already been fixed in the Prime CAS which we'll hopefully see it in the next firmware.

I'm surprised that this bug which was fixed in xcas quite some time back is still present in the recently released Prime firmware.