A simple rational computation throws RuntimeError: ECL says: THROW: The catch RAT-ERR is undefined.

maxima

asked 2022-04-18 21:55:42 +0100

tamandua
11 ●1 ●4

I have two a simple but highly nested (rational) expressions, compute their difference and want to manipulate the output:

sage: x, Y = var('x Y')
sage: xi = function('xi')
sage: phi = function('phi')
sage: e1=1/22*(1/((3993*x**11/((121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) +19216/(x**2*(Y**2/x**4 + 32*Y/x**6 +          256/x**8)))*(55*x**6/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))) - 5*x**3 - 792*x**2/((11*
....: x**3 - 96/(x*(Y/x**2 + 16/x**4)))*(Y/x**2 + 16/x**4)))*(5*x**6/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))) - 72*x**2/((11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))*(Y/x**2 + 16/x**4)))) + 5*Y*x**4/(11*x
....: **3 - 96/(x*(Y/x**2 + 16/x**4))))*x**2) + 16/((33*Y*x**7/((5*x**6/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))) - 72*x**2/((11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))*(Y/x**2 + 16/x**4)))*(11*x**3 - 96/
....: (x*(Y/x**2 + 16/x**4)))) - 80*Y*x**4/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))))*x**2))*phi(Y, x)/(3993*x**7/((3993*x**11/((121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y**2/x**4 + 32*
....: Y/x**6 + 256/x**8)))*(55*x**6/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))) - 5*x**3 - 792*x**2/((11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))*(Y/x**2 + 16/x**4)))*(5*x**6/(11*x**3 - 96/(x*(Y/x**2 + 16/x*
....: *4))) - 72*x**2/((11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))*(Y/x**2 + 16/x**4)))) + 5*Y*x**4/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))))*(121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y**2/x
....: **4 + 32*Y/x**6 + 256/x**8)))*(55*x**6/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))) - 5*x**3 - 792*x**2/((11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))*(Y/x**2 + 16/x**4)))*(5*x**6/(11*x**3 - 96/(x*(Y/x**
....: 2 + 16/x**4))) - 72*x**2/((11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))*(Y/x**2 + 16/x**4)))) - 33*Y*x**3/((33*Y*x**7/((5*x**6/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))) - 72*x**2/((11*x**3 - 96/(x*(Y/ 
....: x**2 + 16/x**4)))*(Y/x**2 + 16/x**4)))*(11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))) - 80*Y*x**4/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))))*(5*x**6/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))) - 72*x**2/((1
....: 1*x**3 - 96/(x*(Y/x**2 + 16/x**4)))*(Y/x**2 + 16/x**4)))*(11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))) + 5*Y/((3993*x**11/((121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y**2/x**4 + 32*Y/
....: x**6 + 256/x**8)))*(55*x**6/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))) - 5*x**3 - 792*x**2/((11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))*(Y/x**2 + 16/x**4)))*(5*x**6/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4
....: ))) - 72*x**2/((11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))*(Y/x**2 + 16/x**4)))) + 5*Y*x**4/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))))*(11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))) + 80*Y/((33*Y*x**7/((5*x
....: **6/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))) - 72*x**2/((11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))*(Y/x**2 + 16/x**4)))*(11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))) - \ 
....: 80*Y*x**4/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))))*(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))))) \ 
....: + xi(Y, x)
 sage: e2=1/22*(1/((363*x**11/((25*x**12/(121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y/x**2 + 16/x**4)**2)) - 720*x**8/((121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y**2/x**4 + 32*Y/x**6 + 256/x**8)))*(Y/x**2 + 16/x**4)) + 5184*x**4/((121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y/x**2 + 16/x**4)**2))*(Y**2/x**4 + 32*Y/x**6 + 256/x**8)))*(121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y**2/x**4 + 32*Y/x**6 + 256/x**8)))) + 5*Y*x**4/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))))*x**2) + 16/((33*Y*x**7/((5*x**6/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))) - 72*x**2/((11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))*(Y/x**2 + 16/x**4)))*(11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))) - 80*Y*x**4/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))))*x**2))*phi(Y, x)/(363*x**7/((25*x**12/(121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y/x**2 + 16/x**4)**2)) - 720*x**8/((121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y**2/x**4 + 32*Y/x**6 + 256/x**8)))*(Y/x**2 + 16/x**4)) + 5184*x**4/((121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y/x**2 + 16/x**4)**2))*(Y**2/x**4 + 32*Y/x**6 + 256/x**8)))*(363*x**11/((25*x**12/(121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y/x**2 + 16/x**4)**2)) - 720*x**8/((121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y**2/x**4 + 32*Y/x**6 + 256/x**8)))*(Y/x**2 + 16/x**4)) + 5184*x**4/((121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y/x**2 + 16/x**4)**2))*(Y**2/x**4 + 32*Y/x**6 + 256/x**8)))*(121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y**2/x**4 + 32*Y/x**6 + 256/x**8)))) + 5*Y*x**4/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))))*(121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y**2/x**4 + 32*Y/x**6 + 256/x**8)))) - 33*Y*x**3/((33*Y*x**7/((5*x**6/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))) - 72*x**2/((11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))*(Y/x**2 + 16/x**4)))*(11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))) - 80*Y*x**4/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))))*(5*x**6/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))) - 72*x**2/((11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))*(Y/x**2 + 16/x**4)))*(11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))) + 5*Y/((363*x**11/((25*x**12/(121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y/x**2 + 16/x**4)**2)) - 720*x**8/((121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y**2/x**4 + 32*Y/x**6 + 256/x**8)))*(Y/x**2 + 16/x**4)) + 5184*x**4/((121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y/x**2 + 16/x**4)**2))*(Y**2/x**4 + 32*Y/x**6 + 256/x**8)))*(121*x**6 - 2112*x**2/(Y/x**2 + 16/x**4) + 9216/(x**2*(Y**2/x**4 + 32*Y/x**6 + 256/x**8)))) + 5*Y*x**4/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))))*(11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))) + 80*Y/((33*Y*x**7/((5*x**6/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))) - 72*x**2/((11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))*(Y/x**2 + 16/x**4)))*(11*x**3 - 96/(x*(Y/x**2 + 16/x**4)))) - 80*Y*x**4/(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))))*(11*x**3 - 96/(x*(Y/x**2 + 16/x**4))))) + xi(Y, x)
sage: v = (e1 - e2).denominator()

This throws a : RuntimeError: ECL says: THROW: The catch RAT-ERR is undefined.

Is there a possible workaround around maxima? This kind of rational expression occur very frequently in my computations.

Sorry for the strange formatting, I have no idea why the copy-paste of e1 gives continuation lines, and that of e2 not.

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I didn't manage to get one of these expressions equal to zero or to cancel out though the program is full of zero checks.

So THX, I'll try to incorporate one more zero check at the correct position

To answer your last question: I'm computing Janet bases. These are like of Groebner bases but for linear PDE systems. As we all know that the Groebner bases calculation can become quite nasty the calculation of Janet bases can become very nasty, too.

tamandua ( 2022-04-19 12:55:52 +0100 )edit

A simple rational computation throws RuntimeError: ECL says: THROW: The catch RAT-ERR is undefined.

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A simple rational computation throws RuntimeError: ECL says: THROW: The catch RAT-ERR is undefined. edit

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