### matlab numerical inverse function

This script demonstrates using the included Talbot and Euler algorithms for numerical approximations of the inverse Laplace transform. View source: R/inv.R. A prompt for students to write a discussion post on the most difficult topic in a chapter. I am trying to find the inverse of an function, g, numerically, as the explicit form of it is complex. Numerical Tours of Signal Processing. If f contains more than one variable, use the next syntax to specify the independent variable. https://www.mathworks.com/matlabcentral/answers/441843-how-to-find-the-inverse-of-a-function-numerically#comment_664856, https://www.mathworks.com/matlabcentral/answers/441843-how-to-find-the-inverse-of-a-function-numerically#comment_664858, https://www.mathworks.com/matlabcentral/answers/441843-how-to-find-the-inverse-of-a-function-numerically#comment_664867, https://www.mathworks.com/matlabcentral/answers/441843-how-to-find-the-inverse-of-a-function-numerically#comment_664869, https://www.mathworks.com/matlabcentral/answers/441843-how-to-find-the-inverse-of-a-function-numerically#comment_664870, https://www.mathworks.com/matlabcentral/answers/441843-how-to-find-the-inverse-of-a-function-numerically#comment_664881, https://www.mathworks.com/matlabcentral/answers/441843-how-to-find-the-inverse-of-a-function-numerically#comment_664890, https://www.mathworks.com/matlabcentral/answers/441843-how-to-find-the-inverse-of-a-function-numerically#comment_664893, https://www.mathworks.com/matlabcentral/answers/441843-how-to-find-the-inverse-of-a-function-numerically#comment_664895, https://www.mathworks.com/matlabcentral/answers/441843-how-to-find-the-inverse-of-a-function-numerically#answer_358300, https://www.mathworks.com/matlabcentral/answers/441843-how-to-find-the-inverse-of-a-function-numerically#comment_664908, https://www.mathworks.com/matlabcentral/answers/441843-how-to-find-the-inverse-of-a-function-numerically#comment_664962. Applied Numerical Methods Using MATLAB ®, Second Edition begins with an introduction to MATLAB usage and computational errors, covering everything from input/output of data, to various kinds of computing errors, and on to parameter sharing and passing, and more. The notable differences between Matlab’s and NumPy’s & and | operators are: Non-logical {0,1} inputs: NumPy’s output is the bitwise AND of the inputs. We are given a Input, specified as a symbolic expression or function. How to arrange the matrix for such function, Torsten? Good work.I will be grateful if someone helps me with an implicit runge-kutta matlab code for the solution of ode. However, the inverse of a 2 x 2 matrix The inverse of a 3 x 3 matrix requires us to evaluate nine 2 x 2 determinants. g = finverse(f) returns the inverse of function f, such that f(g(x)) = x. Description. The following Matlab project contains the source code and Matlab examples used for numerical inverse laplace transform. Create a script file and type the following code − independent variable. Your equation reduces to, b*m2 + (a + b*m1)*zeta - z*zeta^2 + (a*m1 + b)*zeta^3 + (a*m2)*zeta^4 == 0. Of the coefficients of the above equation, all are apparently known, and have fixed values. Inverse of a matrix in MATLAB is calculated using the inv function. MathWorks is the leading developer of mathematical computing software for engineers and scientists. But for now, how do we find those 4 values? Based on your location, we recommend that you select: . Details. Only a few of the summaries are listed -- use Matlab's help function to see more. thanks. Which of them would you like to choose ? Thus, the function invlap can solve fractional problems and invert functions Fs containing (ir)rational or transcendental expressions.. Value. Matlab treats any non-zero value as 1 and returns the logical AND. Example. Compute functional inverse for this trigonometric function. Returns a list with components x the x-coordinates and y the y-coordinates representing the original function in the interval [t1,t2]. If Limitations. symbolic variable var as the independent variable, such that Contribute to gpeyre/numerical-tours development by creating an account on GitHub. I normally choose the last solution. Accelerating the pace of engineering and science. You don't want me to write the entire expression in here, as it is a massive mess of terms. Inverse Matrix Function Basics: Brief Tutorial ... a matrix is a means via which a numerical data set can be organized and represented by an ordered row and column of variables. It is easy to do so if the function can be converted in a polynomial, but in my case, the function seems to be complicated. MATLAB FUNCTION DESCRIPTIONS . These lists are copied from the help screens for MATLAB Version 4.2c (dated Nov 23 1994). It seems that mathematically a closed inverse Laplace form for this function cannot be found out, so ilaplace function is returning the input transfer function. function f, such that f(g(x)) = x. Assuming the parameters of your Hill function are [10 25 2], and you want to find the point where the value of the function is 9, this point is given by: The default value of false indicates that fun is a function that accepts a vector input and returns a vector output. ... is the function name used in Matlab… How do I do that in MATLAB for USF students For example (3 & 4) in NumPy is 0, while in Matlab both 3 and 4 are considered logical true and (3 & 4) returns 1. Numerical Derivative We are going to develop a Matlab function to calculate the numerical derivative of any unidimensional scalar function fun(x) at a point x0.The function is going to have the following functionality: Usage: D = Deriv(fun, x0) Like Like  ... will have an inverse. But you wrote you already used "roots" on the example: Torsten, the original question does not allow me to make such matrix. Here I wrote the inverse function by solving through the fzero command, however, I don't know why it … But it is not pretty. Reload the page to see its updated state. Find the treasures in MATLAB Central and discover how the community can help you! So there are 4 roots. Recent posts. You can also select a web site from the following list: Select the China site (in Chinese or English) for best site performance. The examples cover functions with known inverses so that the accuracy can easily be assessed. f(g(var)) = var. Learn more about inverse function In that case, zeta==0 would be one of the roots of the above equation. MATLAB: How to solve this matrix using inverse function inverse I want to use the inverse function (inv) on this 10 x 10 matrix but I keep getting all this Inf in place of the numbers. For the above example, what would be the input? How to find the inverse of a function numerically. Description Usage Arguments Details Value Note See Also Examples. Can someone tell me how is it possible to find the inverse of this function, I used Matlab function "roots" to solve the following inversion problem. Accelerating the pace of engineering and science. Numerical approximation of the inverse Laplace transform for use with any function defined in "s". This MATLAB function returns the Inverse Sine (sin-1) of the elements of X in radians. You clicked a link that corresponds to this MATLAB command: Run the command by entering it in the MATLAB Command Window. Unable to complete the action because of changes made to the page. Most physical problems can be written in the form of mathematical equations (differential, integral, etc.). How do I suppose to transform the following matrix into polynomial so that I can use "roots"? The transform Fs may be any reasonable function of a variable s^a, where a is a real exponent. If the determinant of the matrix is zero, then the inverse does not exist and the matrix is singular. We do not give the general procedure here because we will soon explain how to use MATLAB to compute a matrix inverse. The problem is, the "inverse" is a rather nasty mess of a function of z. Description. g = finverse (f,var) uses the … To use "roots" we need a matrix as the input, aren't we? vpa(expand(subs(zetaroots,{a,b,m1,m2},[-2.0800,4.0800,0.5,-0.03])),5), - (0.16667*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2))/(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/6) - (0.16667*(10680.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3)*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2) - 70.15*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2) - 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3)*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2) - 256.82*z^2*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2) + 2868.6*z*(5.1962*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 6767.6*z - 8231.4*z^3 - 125699.0)^(1/2) + 106211.0*(5.1962*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 6767.6*z - 8231.4*z^3 - 125699.0)^(1/2) + 192.31*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3)*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2))^(1/2))/((0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/6)*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/4)) - 12.179, (0.16667*(10680.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3)*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2) - 70.15*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2) - 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3)*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2) - 256.82*z^2*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2) + 2868.6*z*(5.1962*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 6767.6*z - 8231.4*z^3 - 125699.0)^(1/2) + 106211.0*(5.1962*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 6767.6*z - 8231.4*z^3 - 125699.0)^(1/2) + 192.31*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3)*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2))^(1/2))/((0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/6)*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/4)) - (0.16667*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2))/(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/6) - 12.179, (0.16667*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2))/(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/6) - (0.16667*(10680.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3)*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2) - 70.15*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2) - 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3)*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2) - 256.82*z^2*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2) - 2868.6*z*(5.1962*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 6767.6*z - 8231.4*z^3 - 125699.0)^(1/2) - 106211.0*(5.1962*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 6767.6*z - 8231.4*z^3 - 125699.0)^(1/2) + 192.31*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3)*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2))^(1/2))/((0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/6)*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/4)) - 12.179, (0.16667*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2))/(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/6) + (0.16667*(10680.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3)*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2) - 70.15*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2) - 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3)*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2) - 256.82*z^2*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2) - 2868.6*z*(5.1962*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 6767.6*z - 8231.4*z^3 - 125699.0)^(1/2) - 106211.0*(5.1962*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 6767.6*z - 8231.4*z^3 - 125699.0)^(1/2) + 192.31*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3)*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/2))^(1/2))/((0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/6)*(96.154*z*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 5340.2*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(1/3) + 9.0*(0.096225*(2.07e6*z^4 + 7.6638e7*z^3 + 1.1346e6*z^2 + 6.3008e7*z + 5.8506e8)^(1/2) - 125.33*z - 152.43*z^3 - 2327.6)^(2/3) + 256.82*z^2 + 70.15)^(1/4)) - 12.179. 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