Identification analysis - java heap space

Dynare help (legacy posts)
1

Dear all,

I am running into problems when running the identification analysis on my model.
The problem is related to the fact that I have a VAR(1) for the exogenous disturbances
of the type: s_{t+1} = P_0 + Ps_{t} + Qepsilon_{t+1}. The vector P_0 has dimension
6x1 while the matrices P and Q have both dimension 6x6. The steady state of the 6x1
vector of the exogenous disturbances s is given by s=inv(I-P)*(P_0). Since this involves
the inversion of a 6x6 matrix, the expression for the steady state of all six shocks
appearing in the vector s is very very long. This leads to a static_params_derivs file
automatically generated by Dynare whose size is in the order of 4GB. Not surprisingly
I get errors related to the Java heap space being insufficient, Dynare crashes and I
thus cannot run the identification analysis. Increasing the heap space in Dynare did
not help to solve the issue.

In this context, I have two questions:

  1. Does the identification command need the static_params_derivs file?

  2. If static_params_derivs file reports the derivatives of the Jacobian with respect to
    the deep parameters I fear this is the case. I was thus thinking that one possible
    solution to the problem might be to let Dynare create the static_params_derivs
    function file by printing “p” instead of “params” since this would significantly reduce
    the size of the file. Which would be the file in Dynare’s “matlab” folder that I would
    need to change to make this possible?

Any suggestions on how to overcome this problem are greatly appreciated.

Many thanks in advance,
Francis

2

  1. Yes, the file is needed as it contains the derivatives of the static equations with respect to the parameters and is needed to find out, whether a parameter influences the steady state.

  2. I have never seen an issue like this. 6 by 6 should not be an issue. Rather, your model and the number of parameters must be huge.

3

As always, many thanks for replying Mr. Pfeifer.

The problem is that the steady state expression involves the
inversion of a 6x6 matrix, this explains the long expressions.

May I ask you for suggestions on how to proceed?

Best regards,
Francis

4

I am not sure I am understanding your problem. Are you doing a symbolic inversion yourself? I don’t understand why 6 derivatives would blow up to 6GB?

5

Yes, I am doing the symbolic inversion myself.

I am copying below (an excerpt of) the **expression for the unconditional mean of just one the first of the six variables in the VAR **to give an idea of the
length of the expressions that each unconditional mean of the exogenous shocks entails. The elements p_{i,j} denote the i-th row, j-th column element
of the matrix P, whereas the elements [zi,li,xi,gi,bi,mpi] are the elements of the vector P_0 in the VAR(1) representation

The parameters that I am estimating in my model are the elements of the matrices P_0, P and QQ’. Only the elements of P_0 and P appear in the
unconditional mean expressions.

In steady state, variables such as the capital stock and hours depend on the unconditional means of four of the exogenous shocks in the VAR. On top
of that, I have a Taylor rule in which steady state output appears. Steady state output depends on steady state capital and labor and, thus, on the
unconditional means of the exogenous VAR(1) shocks and their long expressions of which I provided one example below. Clearly, when calculating
the Jacobian for Iskrev’s identification tests, the derivatives with respect to the elements of the P_0 and P matrices will have to consider their effect
on the unconditional means which, as just explained, in turn affect steady state output in the Taylor rule via their effect on steady state capital and
labour and this is what, I suspect, is causing the creation of such a big file for the analytical derivatives.

Thank you for your help,
Francis

6

z = -(zi + gip14 + mpip16 + p15bi + p12li + p13xi - p44zi - p66zi - p55zi - p22zi - p33zi - gip66p14 - gip14p55 - gip14p22 + gip64p16 - gip14p33 + gip54p15 + gip24p12 + gip34p13 - mpip44p16 + mpip14p46 - mpip16p55 - mpip16p22 - mpip16p33 + mpip15p56 + mpip12p26 + mpip13p36 - p44p15bi - p44p12li - p44p13xi + p14p45bi - p66p15bi + p14p42li - p66p12li + p14p43xi - p66p13xi - p22p15bi + p16p65bi - p55p12li - p33p15bi + p16p62li - p33p12li - p55p13xi - p22p13xi + p16p63xi + p15p52li + p12p25bi + p15p53xi + p13p35bi + p12p23xi + p13p32li + p44p66zi + p44p55zi + p44p22zi + p44p33zi - p46p64zi + p66p55zi + p66p22zi + p66p33zi + p55p22zi + p55p33zi + p22p33zi - p45p54zi - p42p24zi - p43p34zi - p65p56zi - p62p26zi - p63p36zi - p52p25zi - p53p35zi - p23p32zi + gip66p14p55 + gip66p14p22 + gip66p14p33 + gip14p55p22 - gip64p16p55 + gip14p55p33 - gip64p16p22 + gip14p22p33 - gip64p16p33 - gip66p54p15 - gip66p24p12 - gip66p34p13 - gip22p54p15 - gip14p65p56 + gip64p15p56 + gip16p54p65 - gip55p24p12 - gip33p54p15 - gip14p62p26 + gip64p12p26 + gip16p24p62 - gip33p24p12 - gip55p34p13 - gip22p34p13 - gip14p63p36 + gip64p13p36 + gip16p34p63 - gip14p52p25 + gip54p12p25 + gip24p15p52 - gip14p53p35 + gip54p13p35 + gip15p34p53 - gip14p23p32 + gip24p13p32 + gip34p12p23 + mpip44p16p55 + mpip44p16p22 +mpip44p16p33 - mpip14p46p55 - mpip14p46p22 - mpip14p46p33 + mpip16p55p22 + mpip16p55p33 + mpip16p22p33 - mpip44p15p56 - mpip44p12p26 - mpip44p13p36 + mpip14p45p56 + mpip46p54p15 - mpip16p45p54 + mpip14p42p26 + mpip46p24p12 - mpip16p42p24 + mpip14p43p36 + mpip46p34p13 - mpip16p43p34 - mpip22p15p56 - mpip55p12p26 - mpip33p15p56 - mpip33p12p26 - mpip55p13p36 - mpip22p13p36 - mpip16p52p25 + mpip15p26p52 + mpip12p56p25 - mpip16p53p35 + mpip15p36p53 + mpip13p56p35 - mpip16p23p32 + mpip12p36p23 + mpip13p26p32 + p44p66p15bi + p44p66p12li + p44p66p13xi - p66p14p45bi - p66p14p42li - p66p14p43xi + p44p22p15bi - p44p16p65bi + p44p55p12li + p44p33p15bi - p44p16p62li + p44p33p12li + p44p55p13xi + p44p22p13xi - p44p16p63xi - p14p22p45bi + p14p46p65bi - p46p64p15bi + p64p16p45bi - p14p55p42li - p14p33p45bi + p66p22p15bi + p14p46p62li - p46p64p12li + p64p16p42li + p66p55p12li + p66p33p15bi - p14p33p42li - p14p55p43xi - p14p22p43xi + p66p33p12li + p14p46p63xi - p46p64p13xi + p64p16p43xi + p66p55p13xi + p66p22p13xi - p16p22p65bi + p22p33p15bi - p16p55p62li - p16p33p65bi + p55p33p12li + p55p22p13xi - p16p33p62li - p16p55p63xi - p16p22p63xi - p44p15p52li - p44p12p25bi - p44p15p53xi - p44p13p35bi - p44p12p23xi - p44p13p32li + p14p45p52li + p14p42p25bi - p45p54p12li + p45p24p12bi + p54p42p15li - p42p24p15bi - p66p15p52li - p66p12p25bi + p14p45p53xi + p14p43p35bi - p45p54p13xi + p45p34p13bi + p54p15p43xi - p15p43p34bi - p66p15p53xi - p66p13p35bi + p14p42p23xi + p14p43p32li - p42p24p13xi + p42p34p13li + p24p43p12xi - p43p34p12li - p66p12p23xi - p66p13p32li + p16p65p52li + p16p62p25bi + p15p56p62li - p15p62p26bi - p12p65p56li + p12p65p26bi - p33p15p52li - p33p12p25bi - p22p15p53xi - p22p13p35bi + p16p65p53xi + p16p63p35bi + p15p56p63xi - p15p63p36bi - p13p65p56xi + p13p65p36bi - p55p12p23xi - p55p13p32li + p16p62p23xi + p16p63p32li + p12p26p63xi - p12p63p36li - p13p62p26xi + p13p62p36li + p15p52p23xi + p15p53p32li - p15p23p32bi + p12p25p53xi - p12p53p35li + p12p35p23bi - p13p52p25xi + p13p52p35li + p13p25p32bi - p44p66p55zi - p44p66p22zi - p44p66p33zi - p44p55p22zi - p44p55p33zi - p44p22p33zi + p46p64p55zi + p46p64p22zi - p66p55p22zi + p46p64p33zi - p66p55p33zi - p66p22p33zi + p66p45p54zi + p66p42p24zi - p55p22p33zi + p66p43p34zi + p44p65p56zi + p44p62p26zi + p44p63p36zi + p22p45p54zi - p46p54p65zi - p64p45p56zi + p55p42p24zi + p33p45p54zi - p46p24p62zi - p64p42p26zi + p33p42p24zi + p55p43p34zi + p22p43p34zi - p46p34p63zi - p64p43p36zi + p22p65p56zi + p55p62p26zi + p33p65p56zi + p33p62p26zi + p55p63p36zi + p22p63p36zi + p44p52p25zi + p44p53p35zi + p44p23p32zi - p45p24p52zi - p54p42p25zi + p66p52p25zi - p45p34p53zi - p54p43p35zi + p66p53p35zi - p42p34p23zi - p24p43p32zi + p66p23p32zi - p65p26p52zi - p56p62p25zi + p33p52p25zi + p22p53p35zi - p65p36p53zi - p56p63p35zi + p55p23p32zi - p62p36p23zi - p26p63p32zi - p52p35p23zi - p25p53p32zi - gip66p14p55p22 - gip66p14p55p33 - gip66p14p22p33 + gip64p16p55p22 - gip14p55p22p33 + gip64p16p55p33 + gip64p16p22p33 + gip66p22p54p15 + gip66p55p24p12 + gip66p33p54p15 + gip66p33p24p12 + gip66p55p34p13 + gip66p22p34p13 + gip14p22p65p56 - gip64p22p15p56 - gip16p22p54p65 + gip22p33p54p15 + gip14p55p62p26 - gip64p55p12p26 - gip16p55p24p62 + gip14p33p65p56 - gip64p33p15p56 - gip16p33p54p65 + gip55p33p24p12 + gip55p22p34p13 + gip14p33p62p26 - gip64p33p12p26 - gip16p33p24p62 + gip14p55p63p36 - gip64p55p13p36 - gip16p55p34p63 + gip14p22p63p36 - gip64p22p13p36 - gip16p22p34p63 + gip66p14p52p25 - gip66p54p12p25 - gip66p24p15p52 + gip66p14p53p35 - gip66p54p13p35 - gip66p15p34p53 + gip66p14p23p32 - gip66p24p13p32 - gip66p34p12p23 - gip14p65p26p52 - gip14p56p62p25 - gip64p16p52p25 + gip64p15p26p52 + gip64p12p56p25 + gip16p54p62p25 + gip16p24p65p52 - gip54p15p62p26 + gip54p12p65p26 + gip24p15p56p62 - gip24p12p65p56 + gip14p33p52p25 - gip33p54p12p25 - gip33p24p15p52 + gip14p22p53p35 - gip22p54p13p35 - gip22p15p34p53 - gip14p65p36p53 - gip14p56p63p35 - gip64p16p53p35 + gip64p15p36p53 + gip64p13p56p35 + gip16p54p63p35 + gip16p34p65p53 - gip54p15p63p36 + gip54p13p65p36 + gip15p34p56p63 - gip34p13p65p56 + gip14p55p23p32 - gip55p24p13p32 - gip55p34p12p23 - gip14p62p36p23 - gip14p26p63p32 - gip64p16p23p32 + gip64p12p36p23 + gip64p13p26p32 + gip16p24p63p32 + gip16p34p62p23 - gip24p12p63p36 + gip24p13p62p36 + gip34p12p26p63 - gip34p13p62p26 - gip14p52p35p23 - gip14p25p53p32 - gip54p15p23p32 + gip54p12p35p23 + gip54p13p25p32 + gip24p15p53p32 - gip24p12p53p35 + gip24p13p52p35 + gip15p34p52p23 + gip34p12p25p53 - gip34p13p52p25 - mpip44p16p55p22 - mpip44p16p55p33 - mpip44p16p22p33 + mpip14p46p55p22 + mpip14p46p55p33 + mpip14p46p22p33 - mpip16p55p22p33 + mpip44p22p15p56 + mpip44p55p12p26 + mpip44p33p15p56 + mpip44p33p12p26 + mpip44p55p13p36 + mpip44p22p13p36 - mpip14p22p45p56 - mpip46p22p54p15 + mpip16p22p45p54 - mpip14p55p42p26 - mpip46p55p24p12 + mpip16p55p42p24 - mpip14p33p45p56 - mpip46p33p54p15 + mpip16p33p45p54 - mpip14p33p42p26 - mpip46p33p24p12 + mpip16p33p42p24 - mpip14p55p43p36 - mpip46p55p34p13 + mpip16p55p43p34 - mpip14p22p43p36 - mpip46p22p34p13 + mpip16p22p43p34 + mpip22p33p15p56 + mpip55p33p12p26 + mpip55p22p13p36 + mpip44p16p52p25 - mpip44p15p26p52 - mpip44p12p56p25 + mpip44p16p53p35 - mpip44p15p36p53 - mpip44p13p56p35 + mpip44p16p23p32 - mpip44p12p36p23 - mpip44p13p26p32 - mpip14p46p52p25 + mpip14p45p26p52 + mpip14p42p56p25 + mpip46p54p12p25 + mpip46p24p15p52 - mpip16p45p24p52 - mpip16p54p42p25 - mpip45p54p12p26 + mpip45p24p12p56 + mpip54p42p15p26 - mpip42p24p15p56 - mpip14p46p53p35 + mpip14p45p36p53 + mpip14p43p56p35 + mpip46p54p13p35 + mpip46p15p34p53 - mpip16p45p34p53 - mpip16p54p43p35 - mpip45p54p13p36 + mpip45p34p13p56 + mpip54p15p43p36 - mpip15p43p34p56 - mpip14p46p23p32 + mpip14p42p36p23 + mpip14p43p26p32 + mpip46p24p13p32 + mpip46p34p12p23 - mpip16p42p34p23 - mpip16p24p43p32 - mpip42p24p13p36 + mpip42p34p13p26 + mpip24p43p12p36 - mpip43p34p12p26 + mpip16p33p52p25 - mpip33p15p26p52 - mpip33p12p56p25 + mpip16p22p53p35 - mpip22p15p36p53 - mpip22p13p56p35 + mpip16p55p23p32 - mpip55p12p36p23 - mpip55p13p26p32 - mpip16p52p35p23 - mpip16p25p53p32 - mpip15p56p23p32 + mpip15p26p53p32 + mpip15p36p52p23 + mpip12p56p35p23 - mpip12p26p53p35 + mpip12p36p25p53 + mpip13p56p25p32 + mpip13p26p52p35 - mpip13p36p52p25 - p44p66p22p15bi - p44p66p55p12li - p44p66p33p15bi - p44p66p33p12li - p44p66p55p13xi - p44p66p22p13xi + p66p14p22p45bi + p66p14p55p42li + p66p14p33p45bi + p66p14p33p42li + p66p14p55p43xi + p66p14p22p43xi + p44p16p22p65bi - p44p22p33p15bi + p44p16p55p62li + p44p16p33p65bi - p44p55p33p12li - p44p55p22p13xi + p44p16p33p62li + p44p16p55p63xi + p44p16p22p63xi - p14p46p22p65bi + p46p64p22p15bi - p64p16p22p45bi + p14p22p33p45bi - p14p46p55p62li + p46p64p55p12li - p64p16p55p42li - p14p46p33p65bi + p46p64p33p15bi - p64p16p33p45bi + p14p55p33p42li - p66p22p33p15bi + p14p55p22p43xi - p14p46p33p62li + p46p64p33p12li - p64p16p33p42li - p66p55p33p12li - p14p46p55p63xi + p46p64p55p13xi - p64p16p55p43xi - p14p46p22p63xi + p46p64p22p13xi - p64p16p22p43xi - p66p55p22p13xi + p44p66p15p52li + p44p66p12p25bi + p44p66p15p53xi + p44p66p13p35bi + p44p66p12p23xi + p44p66p13p32li - p66p14p45p52li - p66p14p42p25bi + p66p45p54p12li - p66p45p24p12bi - p66p54p42p15li + p66p42p24p15bi - p66p14p45p53xi - p66p14p43p35bi + p66p45p54p13xi - p66p45p34p13bi - p66p54p15p43xi + p66p15p43p34bi + p16p22p33p65bi + p16p55p33p62li - p66p14p42p23xi - p66p14p43p32li + p66p42p24p13xi - p66p42p34p13li - p66p24p43p12xi + p66p43p34p12li + p16p55p22p63xi - p44p16p65p52li - p44p16p62p25bi - p44p15p56p62li + p44p15p62p26bi + p44p12p65p56li - p44p12p65p26bi + p44p33p15p52li + p44p33p12p25bi + p44p22p15p53xi + p44p22p13p35bi - p44p16p65p53xi - p44p16p63p35bi - p44p15p56p63xi + p44p15p63p36bi + p44p13p65p56xi - p44p13p65p36bi + p44p55p12p23xi + p44p55p13p32li - p44p16p62p23xi - p44p16p63p32li - p44p12p26p63xi + p44p12p63p36li + p44p13p62p26xi - p44p13p62p36li + p14p46p65p52li + p14p46p62p25bi + p14p45p56p62li - p14p45p62p26bi - p14p42p65p56li + p14p42p65p26bi - p46p64p15p52li - p46p64p12p25bi + p46p54p15p62li - p46p54p12p65li - p46p24p15p62bi + p46p24p12p65bi + p64p16p45p52li + p64p16p42p25bi - p64p45p12p56li + p64p45p12p26bi + p64p42p15p56li - p64p42p15p26bi - p16p45p54p62li + p16p45p24p62bi + p16p54p42p65li - p16p42p24p65bi - p14p33p45p52li - p14p33p42p25bi + p33p45p54p12li - p33p45p24p12bi - p33p54p42p15li + p33p42p24p15bi - p14p22p45p53xi - p14p22p43p35bi + p22p45p54p13xi - p22p45p34p13bi - p22p54p15p43xi + p22p15p43p34bi + p66p33p15p52li + p66p33p12p25bi + p14p46p65p53xi + p14p46p63p35bi + p14p45p56p63xi - p14p45p63p36bi - p14p43p65p56xi + p14p43p65p36bi - p46p64p15p53xi - p46p64p13p35bi + p46p54p15p63xi - p46p54p13p65xi - p46p15p34p63bi + p46p34p13p65bi + p64p16p45p53xi + p64p16p43p35bi - p64p45p13p56xi + p64p45p13p36bi + p64p15p43p56xi - p64p15p43p36bi - p16p45p54p63xi + p16p45p34p63bi + p16p54p43p65xi - p16p43p34p65bi - p14p55p42p23xi - p14p55p43p32li + p55p42p24p13xi - p55p42p34p13li - p55p24p43p12xi + p55p43p34p12li + p66p22p15p53xi + p66p22p13p35bi + p14p46p62p23xi + p14p46p63p32li + p14p42p26p63xi - p14p42p63p36li - p14p43p62p26xi + p14p43p62p36li - p46p64p12p23xi - p46p64p13p32li + p46p24p12p63xi - p46p24p13p62xi - p46p34p12p63li + p46p34p13p62li + p64p16p42p23xi + p64p16p43p32li - p64p42p13p26xi + p64p42p13p36li + p64p43p12p26xi - p64p43p12p36li - p16p42p24p63xi + p16p42p34p63li + p16p24p43p62xi - p16p43p34p62li + p66p55p12p23xi + p66p55p13p32li - p16p33p65p52li - p16p33p62p25bi - p33p15p56p62li + p33p15p62p26bi + p33p12p65p56li - p33p12p65p26bi - p16p22p65p53xi - p16p22p63p35bi - p22p15p56p63xi + p22p15p63p36bi + p22p13p65p56xi - p22p13p65p36bi - p16p55p62p23xi - p16p55p63p32li - p55p12p26p63xi + p55p12p63p36li + p55p13p62p26xi - p55p13p62p36li - p44p15p52p23xi - p44p15p53p32li + p44p15p23p32bi - p44p12p25p53xi + p44p12p53p35li - p44p12p35p23bi + p44p13p52p25xi - p44p13p52p35li - p44p13p25p32bi + p14p45p52p23xi + p14p45p53p32li - p14p45p23p32bi + p14p42p25p53xi - p14p42p53p35li + p14p42p35p23bi - p14p43p52p25xi + p14p43p52p35li + p14p43p25p32bi - p45p54p12p23xi - p45p54p13p32li + p45p24p12p53xi - p45p24p13p52xi + p45p24p13p32bi - p45p34p12p53li + p45p34p12p23bi + p45p34p13p52li + p54p42p15p23xi - p54p42p13p25xi + p54p42p13p35li + p54p15p43p32li + p54p43p12p25xi - p54p43p12p35li - p42p24p15p53xi - p42p24p13p35bi + p42p15p34p53li - p42p15p34p23bi + p42p34p13p25bi + p24p15p43p52xi - p24p15p43p32bi + p24p43p12p35bi - p15p43p34p52li - p43p34p12p25bi - p66p15p52p23xi - p66p15p53p32li + p66p15p23p32bi - p66p12p25p53xi + p66p12p53p35li - p66p12p35p23bi + p66p13p52p25xi - p66p13p52p35li - p66p13p25p32bi + p16p65p52p23xi + p16p65p53p32li - p16p65p23p32bi + p16p62p25p53xi - p16p62p53p35li + p16p62p35p23bi - p16p63p52p25xi + p16p63p52p35li + p16p63p25p32bi + p15p56p62p23xi + p15p56p63p32li - p15p62p26p53xi + p15p62p36p53li - p15p62p36p23bi + p15p26p63p52xi - p15p26p63p32bi - p15p63p36p52li - p12p65p56p23xi + p12p65p26p53xi - p12p65p36p53li + p12p65p36p23bi + p12p56p63p25xi - 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p46p64p55p33p12li + p64p16p55p33p42li + p14p46p55p22p63xi - p46p64p55p22p13xi + p64p16p55p22p43xi - p44p66p33p15p52li - p44p66p33p12p25bi - p44p66p22p15p53xi - p44p66p22p13p35bi - p44p66p55p12p23xi - p44p66p55p13p32li + p66p14p33p45p52li + p66p14p33p42p25bi - p66p33p45p54p12li + p66p33p45p24p12bi + p66p33p54p42p15li - p66p33p42p24p15bi + p66p14p22p45p53xi + p66p14p22p43p35bi - p66p22p45p54p13xi + p66p22p45p34p13bi + p66p22p54p15p43xi - p66p22p15p43p34bi + p66p14p55p42p23xi + p66p14p55p43p32li - p66p55p42p24p13xi + p66p55p42p34p13li + p66p55p24p43p12xi - p66p55p43p34p12li + p44p16p33p65p52li + p44p16p33p62p25bi + p44p33p15p56p62li - p44p33p15p62p26bi - p44p33p12p65p56li + p44p33p12p65p26bi + p44p16p22p65p53xi + p44p16p22p63p35bi + p44p22p15p56p63xi - p44p22p15p63p36bi - p44p22p13p65p56xi + p44p22p13p65p36bi + p44p16p55p62p23xi + p44p16p55p63p32li + p44p55p12p26p63xi - p44p55p12p63p36li - p44p55p13p62p26xi + p44p55p13p62p36li - p14p46p33p65p52li - p14p46p33p62p25bi - p14p33p45p56p62li + p14p33p45p62p26bi + p14p33p42p65p56li - p14p33p42p65p26bi + p46p64p33p15p52li + p46p64p33p12p25bi - p46p33p54p15p62li + p46p33p54p12p65li + p46p33p24p15p62bi - p46p33p24p12p65bi - p64p16p33p45p52li - p64p16p33p42p25bi + p64p33p45p12p56li - p64p33p45p12p26bi - p64p33p42p15p56li + p64p33p42p15p26bi + p16p33p45p54p62li - p16p33p45p24p62bi - p16p33p54p42p65li + p16p33p42p24p65bi - p14p46p22p65p53xi - p14p46p22p63p35bi - p14p22p45p56p63xi + p14p22p45p63p36bi + p14p22p43p65p56xi - p14p22p43p65p36bi + p46p64p22p15p53xi + p46p64p22p13p35bi - p46p22p54p15p63xi + p46p22p54p13p65xi + p46p22p15p34p63bi - p46p22p34p13p65bi - p64p16p22p45p53xi - p64p16p22p43p35bi + p64p22p45p13p56xi - p64p22p45p13p36bi - p64p22p15p43p56xi + p64p22p15p43p36bi + p16p22p45p54p63xi - p16p22p45p34p63bi - p16p22p54p43p65xi + p16p22p43p34p65bi - p14p46p55p62p23xi - p14p46p55p63p32li - p14p55p42p26p63xi + p14p55p42p63p36li + p14p55p43p62p26xi - p14p55p43p62p36li + p46p64p55p12p23xi + p46p64p55p13p32li - p46p55p24p12p63xi + p46p55p24p13p62xi + p46p55p34p12p63li - p46p55p34p13p62li - p64p16p55p42p23xi - p64p16p55p43p32li + p64p55p42p13p26xi - p64p55p42p13p36li - p64p55p43p12p26xi + p64p55p43p12p36li + p16p55p42p24p63xi - p16p55p42p34p63li - p16p55p24p43p62xi + p16p55p43p34p62li + p44p66p15p52p23xi + p44p66p15p53p32li - p44p66p15p23p32bi + p44p66p12p25p53xi - p44p66p12p53p35li + p44p66p12p35p23bi - p44p66p13p52p25xi + p44p66p13p52p35li + p44p66p13p25p32bi - p66p14p45p52p23xi - p66p14p45p53p32li + p66p14p45p23p32bi - p66p14p42p25p53xi + p66p14p42p53p35li - p66p14p42p35p23bi + p66p14p43p52p25xi - p66p14p43p52p35li - p66p14p43p25p32bi + p66p45p54p12p23xi + p66p45p54p13p32li - p66p45p24p12p53xi + p66p45p24p13p52xi - p66p45p24p13p32bi + p66p45p34p12p53li - p66p45p34p12p23bi - p66p45p34p13p52li - p66p54p42p15p23xi + p66p54p42p13p25xi - p66p54p42p13p35li - p66p54p15p43p32li - p66p54p43p12p25xi + p66p54p43p12p35li + p66p42p24p15p53xi + p66p42p24p13p35bi - p66p42p15p34p53li + p66p42p15p34p23bi - p66p42p34p13p25bi - p66p24p15p43p52xi + p66p24p15p43p32bi - p66p24p43p12p35bi + p66p15p43p34p52li + p66p43p34p12p25bi - p44p16p65p52p23xi - p44p16p65p53p32li + p44p16p65p23p32bi - p44p16p62p25p53xi + p44p16p62p53p35li - p44p16p62p35p23bi + p44p16p63p52p25xi - p44p16p63p52p35li - p44p16p63p25p32bi - p44p15p56p62p23xi - p44p15p56p63p32li + p44p15p62p26p53xi - p44p15p62p36p53li + p44p15p62p36p23bi - p44p15p26p63p52xi + p44p15p26p63p32bi + p44p15p63p36p52li + p44p12p65p56p23xi - p44p12p65p26p53xi + p44p12p65p36p53li - p44p12p65p36p23bi - p44p12p56p63p25xi + p44p12p56p63p35li - p44p12p26p63p35bi + p44p12p63p36p25bi + p44p13p65p56p32li + p44p13p65p26p52xi - p44p13p65p26p32bi - p44p13p65p36p52li + p44p13p56p62p25xi - p44p13p56p62p35li + p44p13p62p26p35bi - p44p13p62p36p25bi + p14p46p65p52p23xi + p14p46p65p53p32li - p14p46p65p23p32bi + p14p46p62p25p53xi - p14p46p62p53p35li + p14p46p62p35p23bi - p14p46p63p52p25xi + p14p46p63p52p35li + p14p46p63p25p32bi + p14p45p56p62p23xi + p14p45p56p63p32li - p14p45p62p26p53xi + p14p45p62p36p53li - p14p45p62p36p23bi + p14p45p26p63p52xi - p14p45p26p63p32bi - p14p45p63p36p52li - p14p42p65p56p23xi + p14p42p65p26p53xi - p14p42p65p36p53li + p14p42p65p36p23bi + p14p42p56p63p25xi - p14p42p56p63p35li + p14p42p26p63p35bi - p14p42p63p36p25bi - p14p43p65p56p32li - p14p43p65p26p52xi + p14p43p65p26p32bi + p14p43p65p36p52li - p14p43p56p62p25xi + p14p43p56p62p35li - p14p43p62p26p35bi + p14p43p62p36p25bi - p46p64p15p52p23xi - p46p64p15p53p32li + p46p64p15p23p32bi - p46p64p12p25p53xi + p46p64p12p53p35li - p46p64p12p35p23bi + p46p64p13p52p25xi - p46p64p13p52p35li - p46p64p13p25p32bi + p46p54p15p62p23xi + p46p54p15p63p32li - p46p54p12p65p23xi + p46p54p12p63p25xi - p46p54p12p63p35li - p46p54p13p65p32li - p46p54p13p62p25xi + p46p54p13p62p35li - p46p24p15p62p53xi + p46p24p15p63p52xi - p46p24p15p63p32bi + p46p24p12p65p53xi + p46p24p12p63p35bi - p46p24p13p65p52xi + p46p24p13p65p32bi - p46p24p13p62p35bi + p46p15p34p62p53li - p46p15p34p62p23bi - p46p15p34p63p52li - p46p34p12p65p53li + p46p34p12p65p23bi - p46p34p12p63p25bi + p46p34p13p65p52li + p46p34p13p62p25bi + p64p16p45p52p23xi + p64p16p45p53p32li - p64p16p45p23p32bi + p64p16p42p25p53xi - p64p16p42p53p35li + p64p16p42p35p23bi - p64p16p43p52p25xi + p64p16p43p52p35li + p64p16p43p25p32bi - p64p45p12p56p23xi + p64p45p12p26p53xi - p64p45p12p36p53li + p64p45p12p36p23bi - p64p45p13p56p32li - p64p45p13p26p52xi + p64p45p13p26p32bi + p64p45p13p36p52li + p64p42p15p56p23xi - p64p42p15p26p53xi + p64p42p15p36p53li - p64p42p15p36p23bi - p64p42p13p56p25xi + p64p42p13p56p35li - p64p42p13p26p35bi + p64p42p13p36p25bi + p64p15p43p56p32li + p64p15p43p26p52xi - p64p15p43p26p32bi - p64p15p43p36p52li + p64p43p12p56p25xi - p64p43p12p56p35li + p64p43p12p26p35bi - p64p43p12p36p25bi - p16p45p54p62p23xi - p16p45p54p63p32li + p16p45p24p62p53xi - p16p45p24p63p52xi + p16p45p24p63p32bi - p16p45p34p62p53li + p16p45p34p62p23bi + p16p45p34p63p52li + p16p54p42p65p23xi - p16p54p42p63p25xi + p16p54p42p63p35li + p16p54p43p65p32li + p16p54p43p62p25xi - p16p54p43p62p35li - p16p42p24p65p53xi - p16p42p24p63p35bi + p16p42p34p65p53li - p16p42p34p65p23bi + p16p42p34p63p25bi + p16p24p43p65p52xi - p16p24p43p65p32bi + p16p24p43p62p35bi - p16p43p34p65p52li - p16p43p34p62p25bi - p45p54p12p26p63xi + p45p54p12p63p36li + p45p54p13p62p26xi - p45p54p13p62p36li + p45p24p12p56p63xi - p45p24p12p63p36bi - p45p24p13p56p62xi + p45p24p13p62p36bi - p45p34p12p56p63li + p45p34p12p26p63bi + p45p34p13p56p62li - p45p34p13p62p26bi + p54p42p15p26p63xi - p54p42p15p63p36li - p54p42p13p65p26xi + p54p42p13p65p36li - p54p15p43p62p26xi + p54p15p43p62p36li + p54p43p12p65p26xi - p54p43p12p65p36li - p42p24p15p56p63xi + p42p24p15p63p36bi + p42p24p13p65p56xi - p42p24p13p65p36bi + p42p15p34p56p63li - p42p15p34p26p63bi - p42p34p13p65p56li + p42p34p13p65p26bi + p24p15p43p56p62xi - p24p15p43p62p36bi - p24p43p12p65p56xi + p24p43p12p65p36bi - p15p43p34p56p62li + p15p43p34p62p26bi + p43p34p12p65p56li - p43p34p12p65p26bi - p44p66p55p22p33zi + p46p64p55p22p33zi + p66p22p33p45p54zi + p66p55p33p42p24zi + p66p55p22p43p34zi + p44p22p33p65p56zi + p44p55p33p62p26zi + p44p55p22p63p36zi - p46p22p33p54p65zi - p64p22p33p45p56zi - p46p55p33p24p62zi - p64p55p33p42p26zi - p46p55p22p34p63zi - p64p55p22p43p36zi + p44p66p33p52p25zi + p44p66p22p53p35zi + p44p66p55p23p32zi - p66p33p45p24p52zi - p66p33p54p42p25zi - p66p22p45p34p53zi - p66p22p54p43p35zi - p66p55p42p34p23zi - p66p55p24p43p32zi - p44p33p65p26p52zi - p44p33p56p62p25zi - p44p22p65p36p53zi - p44p22p56p63p35zi - p44p55p62p36p23zi - p44p55p26p63p32zi - p46p64p33p52p25zi + p46p33p54p62p25zi + p46p33p24p65p52zi + p64p33p45p26p52zi + p64p33p42p56p25zi - p33p45p54p62p26zi + p33p45p24p56p62zi + p33p54p42p65p26zi - p33p42p24p65p56zi - p46p64p22p53p35zi + p46p22p54p63p35zi + p46p22p34p65p53zi + p64p22p45p36p53zi + p64p22p43p56p35zi - p22p45p54p63p36zi + p22p45p34p56p63zi + p22p54p43p65p36zi - p22p43p34p65p56zi - p46p64p55p23p32zi + p46p55p24p63p32zi + p46p55p34p62p23zi + p64p55p42p36p23zi + p64p55p43p26p32zi - p55p42p24p63p36zi + p55p42p34p26p63zi + p55p24p43p62p36zi - p55p43p34p62p26zi - p44p66p52p35p23zi - p44p66p25p53p32zi - p66p45p54p23p32zi + p66p45p24p53p32zi + p66p45p34p52p23zi + p66p54p42p35p23zi + p66p54p43p25p32zi - p66p42p24p53p35zi + p66p42p34p25p53zi + p66p24p43p52p35zi - p66p43p34p52p25zi - p44p65p56p23p32zi + p44p65p26p53p32zi + p44p65p36p52p23zi + p44p56p62p35p23zi + p44p56p63p25p32zi - p44p62p26p53p35zi + p44p62p36p25p53zi + p44p26p63p52p35zi - p44p63p36p52p25zi + p46p64p52p35p23zi + p46p64p25p53p32zi + p46p54p65p23p32zi - p46p54p62p35p23zi - p46p54p63p25p32zi - p46p24p65p53p32zi + p46p24p62p53p35zi - p46p24p63p52p35zi - p46p34p65p52p23zi - p46p34p62p25p53zi + p46p34p63p52p25zi + p64p45p56p23p32zi - p64p45p26p53p32zi - p64p45p36p52p23zi - p64p42p56p35p23zi + p64p42p26p53p35zi - p64p42p36p25p53zi - p64p43p56p25p32zi - p64p43p26p52p35zi + p64p43p36p52p25zi + p45p54p62p36p23zi + p45p54p26p63p32zi - p45p24p56p63p32zi - p45p24p62p36p53zi + p45p24p63p36p52zi - p45p34p56p62p23zi + p45p34p62p26p53zi - p45p34p26p63p52zi - p54p42p65p36p23zi - p54p42p26p63p35zi + p54p42p63p36p25zi - p54p43p65p26p32zi + p54p43p62p26p35zi - p54p43p62p36p25zi + p42p24p65p36p53zi + p42p24p56p63p35zi + p42p34p65p56p23zi - p42p34p65p26p53zi - p42p34p56p63p25zi + p24p43p65p56p32zi - p24p43p65p36p52zi - p24p43p56p62p35zi + p43p34p65p26p52zi + p43p34p56p62p25zi)/(p44 + p11 + p66 + p55 + p22 + p33 - p44p11 - p44p66 - p11p66 + p41p14 - p44p55 - p44p22 - p11p55 - p44p33 - p11p22 - p11p33 + p46p64 - p66p55 - p66p22 - p66p33 + p61p16 - p55p22 - p55p33 - p22p33 + p45p54 + p42p24 + p51p15 + p43p34 + p21p12 + p31p13 + p65p56 + p62p26 + p63p36 + p52p25 + p53p35 + p23p32 + p44p11p66 + p44p11p55 + p44p11p22 - p66p41p14 + p44p11p33 + p44p66p55 + p44p66p22 - p11p46p64 + p11p66p55 + p44p66p33 + p11p66p22 - p44p61p16 + p11p66p33 - p41p14p55 - p41p14p22 + p41p64p16 + p14p46p61 - p41p14p33 + p44p55p22 + p44p55p33 + p11p55p22 + p44p22p33 + p11p55p33 + p11p22p33 - p46p64p55 - p46p64p22 + p66p55p22 - p46p64p33 + p66p55p33 + p66p22p33 - p61p16p55 - p61p16p22 - p61p16p33 - p11p45p54 - p44p51p15 - p11p42p24 - p44p21p12 - p11p43p34 - p44p31p13 - p66p45p54 - p66p42p24 + p41p54p15 + p14p45p51 + p55p22p33 - p66p51p15 + p41p24p12 + p14p42p21 - p66p43p34 - p66p21p12 + p41p34p13 + p14p43p31 - p66p31p13 - p44p65p56 - p11p65p56 - p44p62p26 - p11p62p26 - p44p63p36 - p11p63p36 - p22p45p54 + p46p54p65 + p64p45p56 - p55p42p24 - p33p45p54 + p46p24p62 + p64p42p26 - p33p42p24 - p55p43p34 - p22p51p15 + p61p15p56 + p16p51p65 - p22p43p34 + p46p34p63 + p64p43p36 - p55p21p12 - p33p51p15 + p61p12p26 + p16p21p62 - p33p21p12 - p55p31p13 - p22p31p13 + p61p13p36 + p16p31p63 - p22p65p56 - p55p62p26 - p33p65p56 - p33p62p26 - p55p63p36 - p22p63p36 - p44p52p25 - p11p52p25 - p44p53p35 - p11p53p35 - p44p23p32 - p11p23p32 + p45p24p52 + p54p42p25 - p66p52p25 + p45p34p53 + p54p43p35 + p51p12p25 + p15p21p52 - p66p53p35 + p42p34p23 + p24p43p32 - p66p23p32 + p51p13p35 + p15p31p53 + p21p13p32 + p12p31p23 + p65p26p52 + p56p62p25 - p33p52p25 - p22p53p35 + p65p36p53 + p56p63p35 - p55p23p32 + p62p36p23 + p26p63p32 + p52p35p23 + p25p53p32 - p44p11p66p55 - p44p11p66p22 - p44p11p66p33 - p44p11p55p22 + p66p41p14p55 - p44p11p55p33 + p66p41p14p22 - p44p11p22p33 + p66p41p14p33 - p44p66p55p22 + p11p46p64p55 - p44p66p55p33 + p11p46p64p22 - p11p66p55p22 - p44p66p22p33 + p44p61p16p55 + p11p46p64p33 - p11p66p55p33 + p44p61p16p22 - p11p66p22p33 + p44p61p16p33 + p41p14p55p22 - p41p64p16p55 - p14p46p61p55 + p41p14p55p33 - p41p64p16p22 - p14p46p61p22 + p41p14p22p33 - p41p64p16p33 - p14p46p61p33 + p11p66p45p54 - p44p55p22p33 + p44p66p51p15 + p11p66p42p24 - p11p55p22p33 + p44p66p21p12 + p11p66p43p34 + p44p66p31p13 + p46p64p55p22 + p44p11p65p56 + p46p64p55p33 - p66p41p54p15 - p66p14p45p51 + p46p64p22p33 - p66p55p22p33 + p44p11p62p26 - p66p41p24p12 - p66p14p42p21 + p61p16p55p22 + p61p16p55p33 + p44p11p63p36 - p66p41p34p13 - p66p14p43p31 + p61p16p22p33 + p11p22p45p54 - p11p46p54p65 - p11p64p45p56 + p11p55p42p24 + p11p33p45p54 + p44p22p51p15 - p44p61p15p56 - p44p16p51p65 - p11p46p24p62 - p11p64p42p26 + p44p55p21p12 + p44p33p51p15 + p11p33p42p24 + p11p55p43p34 - p44p61p12p26 - p44p16p21p62 + p11p22p43p34 - p11p46p34p63 - p11p64p43p36 + p44p33p21p12 + p44p55p31p13 + p44p22p31p13 - p44p61p13p36 - p44p16p31p63 + p66p22p45p54 + p66p55p42p24 + p66p33p45p54 - p41p22p54p15 - p14p22p45p51 - p41p14p65p56 + p41p64p15p56 + p41p16p54p65 + p14p46p51p65 + p14p61p45p56 - p46p64p51p15 + p46p61p54p15 + p64p16p45p51 - p61p16p45p54 + p66p33p42p24 - p41p55p24p12 - p14p55p42p21 + p66p55p43p34 - p41p33p54p15 - p14p33p45p51 + p66p22p51p15 + p66p22p43p34 - p41p14p62p26 + p41p64p12p26 + p41p16p24p62 + p14p46p21p62 + p14p61p42p26 - p46p64p21p12 + p46p61p24p12 + p64p16p42p21 - p61p16p42p24 + p66p55p21p12 + p66p33p51p15 - p41p33p24p12 - p14p33p42p21 - p41p55p34p13 - p14p55p43p31 - p41p22p34p13 - p14p22p43p31 + p66p33p21p12 - p41p14p63p36 + p41p64p13p36 + p41p16p34p63 + p14p46p31p63 + p14p61p43p36 - p46p64p31p13 + p46p61p34p13 + p64p16p43p31 - p61p16p43p34 + p66p55p31p13 + p66p22p31p13 + p44p22p65p56 + p44p55p62p26 + p44p33p65p56 + p11p22p65p56 + p11p55p62p26 + p11p33p65p56 + p44p33p62p26 + p44p55p63p36 + p44p22p63p36 + p11p33p62p26 + p11p55p63p36 + p11p22p63p36 - p46p22p54p65 - p64p22p45p56 + p22p33p45p54 - p46p55p24p62 - p64p55p42p26 - p46p33p54p65 - p64p33p45p56 + p44p11p52p25 + p55p33p42p24 + p55p22p43p34 - p46p33p24p62 - p64p33p42p26 - p46p55p34p63 - p64p55p43p36 - p61p22p15p56 - p16p22p51p65 + p44p11p53p35 - p46p22p34p63 - p64p22p43p36 + p22p33p51p15 - p61p55p12p26 - p16p55p21p62 - p61p33p15p56 - p16p33p51p65 + p55p33p21p12 + p44p11p23p32 + p55p22p31p13 - p61p33p12p26 - p16p33p21p62 - p61p55p13p36 - p16p55p31p63 - p61p22p13p36 - p16p22p31p63 + p44p66p52p25 - p11p45p24p52 - p11p54p42p25 + p11p66p52p25 - p44p51p12p25 - p44p15p21p52 + p44p66p53p35 - p11p45p34p53 - p11p54p43p35 + p11p66p53p35 + p44p66p23p32 - p44p51p13p35 - p44p15p31p53 - p11p42p34p23 - p11p24p43p32 + p11p66p23p32 - p44p21p13p32 - p44p12p31p23 - p66p45p24p52 - p66p54p42p25 - p41p14p52p25 + p41p54p12p25 + p41p24p15p52 + p14p45p21p52 + p14p42p51p25 - p45p54p21p12 + p45p24p51p12 + p54p42p15p21 - p42p24p51p15 - p66p45p34p53 - p66p54p43p35 + p22p33p65p56 + p55p33p62p26 - p66p51p12p25 - p66p15p21p52 - p66p42p34p23 - p66p24p43p32 - p41p14p53p35 + p41p54p13p35 + p41p15p34p53 + p14p45p31p53 + p14p51p43p35 - p45p54p31p13 + p45p51p34p13 + p54p15p43p31 - p51p15p43p34 + p55p22p63p36 - p66p51p13p35 - p66p15p31p53 - p41p14p23p32 + p41p24p13p32 + p41p34p12p23 + p14p42p31p23 + p14p43p21p32 - p42p24p31p13 + p42p34p21p13 + p24p43p12p31 - p43p34p21p12 - p66p21p13p32 - p66p12p31p23 - p44p65p26p52 - p44p56p62p25 + p44p33p52p25 - p11p65p26p52 - p11p56p62p25 + p44p22p53p35 - p44p65p36p53 - p44p56p63p35 + p11p33p52p25 + p44p55p23p32 + p11p22p53p35 - p11p65p36p53 - p11p56p63p35 - p44p62p36p23 - p44p26p63p32 + p11p55p23p32 - p11p62p36p23 - p11p26p63p32 - p46p64p52p25 + p46p54p62p25 + p46p24p65p52 + p64p45p26p52 + p64p42p56p25 - p45p54p62p26 + p45p24p56p62 + p54p42p65p26 - p42p24p65p56 - p33p45p24p52 - p33p54p42p25 - p22p45p34p53 - p22p54p43p35 + p66p33p52p25 - p46p64p53p35 + p46p54p63p35 + p46p34p65p53 + p64p45p36p53 + p64p43p56p35 - p45p54p63p36 + p45p34p56p63 + p54p43p65p36 - p43p34p65p56 - p55p42p34p23 - p55p24p43p32 + p66p22p53p35 - p61p16p52p25 + p61p15p26p52 + p61p12p56p25 + p16p51p62p25 + p16p21p65p52 - p51p15p62p26 + p51p12p65p26 + p15p21p56p62 - p21p12p65p56 - p46p64p23p32 + p46p24p63p32 + p46p34p62p23 + p64p42p36p23 + p64p43p26p32 - p42p24p63p36 + p42p34p26p63 + p24p43p62p36 - p43p34p62p26 + p66p55p23p32 - p33p51p12p25 - p33p15p21p52 - p22p51p13p35 - p22p15p31p53 - p61p16p53p35 + p61p15p36p53 + p61p13p56p35 + p16p51p63p35 + p16p31p65p53 - p51p15p63*p36 + …

7

I see. I don’t think there is really a way to get around this.

8

That’s what I feared. Many thanks anyway! :slight_smile:

Best,
Francis