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These are questions asked by MaPal93

I have a system of 3 (very large) nonlinear equations in 3 variables. Since I cannot feed non-algebraic expressions into polynomial solvers, I want to extract only their numerators (which should be algebraic) and solve the three numerators for the 3 variables. These solutions should also solve the non-algebraic system then. 

This is the original system (sorry I don't know why but I was not able to include the massive expression in the startup code):

I think I am not understanding the syntax. To extract the numerators, I am using ((numer@evala@:-Norm@numer)~@eval)(Eqs) (scroll down to the very bottom of my script):

  1. Am I wrong?
  2. What exactly am I doing with this combined command?
  3. Why length(((numer@evala@:-Norm@numer)~@eval)(Eqs)) is much larger than length(Eqs)? Shouldn't it be smaller since I just extract the numerators?

Thank you.

I am using this command: plotsetup(png, plotoutput = "titleofmylistofplots", plotoptions = "width=1920,height=1080")

in the execution block right before a sequence of split execution blocks, each made of plots:-display( seq( plot( [$ 20], series1of8[1..20,j], color=cols1[j]), j=1..3)); (I have 8 series: series1of8, series2of8, series3of8 and so on...)

When I open the output .png file, it only contains the last plot, that is the plot of series8of8. I want my file to contain all 8 plots. How to change the plotsetup() command accordingly?


I have a data structure/plotting question. How do I plot the 3 lambdas (singleaxis) and the 6 betas (dualaxis) for 12 calibrations (1000 runs each)? All the details are in the script Thank you!

For the beta plots and subplots, please follow the dualaxis example output format at the bottom of my script for each of the 12 calibrations.

For the lambda plots, I'd like to combine a few of them as follows (each plot with lambda_1 subplot, lambda_2 subplot, and lambda_3 subplot - note that the lambda plot example at the bottom of the script is dualaxis but I just need singleaxis):

PLOT 1 (singleaxis): lambda_1, _2, _3 for ncal2 and ncal3 (superimposed, 2 data series for each subplot)

PLOT 2 (singleaxis):  lambda_1, _2, _3 for ncal7 and ncal8 (superimposed, 2 data series for each subplot)

PLOT 3 (singleaxis):  lambda_1, _2, _3 for ncal4, ncal5, ncal6 (superimposed, 3 data series for each subplot)

PLOT 4 (singleaxis):  lambda_1, _2, _3 for ncal9, ncal10, ncal11 (superimposed, 3 data series for each subplot)

I have access to a powerful GPU, a NVIDIA Tesla A100.

How to leverage it to solve my system of 3 nonlinear equations in 3 variables? Script:

I don't think that it is just by adding the following two lines right before my solve() block, right?


I also read and but it's still not clear to me. Thanks!

Last execution block is not producing any output. Why?

The 3x3 nonlinear system I am trying to solve is already a stylized version of my problem, as I already:

  1. Calibrated my equations before attempting to solve for them (search for "Calib_1" in my script)
  2. Split the original 6x6 system into two 3x3 sub-systems (since 3 out of 6 variables only appear in 3 out of 6 equations) and solved for one sub-system

What else can you think of? Should I instead use the parallel solver on the whole 6x6 system rather than just the unsolved 3x3 sub-system?

How to find, if exist, singular solutions? That is, some valuation of some parameters that will yield a solution that cannot be obtained by applying the same valuation to a general solution. Carl Love (who I cannot tag) once mentioned: "The parameter valuations that lead to singular solutions can often be guessed by using valuations that would produce zeros in denominators in the general solution. A singular solution can't be expressed as any instantiation of a generic symbolic solution. By instantiation I mean an assigment of numeric values to some parameters. Here's an example:"

#2x2 matrix and 2x1 vector. 5 parameters (a, b, d, x, y). The 2 decision variables are
#unseen and unnamed in this pure matrix-vector form. Their values are the two entries 
#in the solution vectors S0 and S1.

A:= <a, b; 0, d>;  B:= <x, y>;

#Get a generic solution:
S0:= LinearAlgebra:-LinearSolve(A, B);

#Instantiate 3 parameters (a, d, y) to 0 and solve again:
S1:= LinearAlgebra:-LinearSolve(eval([A, B], [a, d, y]=~ 0)[]);

#Note that no possible instantiation of S0 can produce S1.

Thank you!

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