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Roots Or Zeros Modules

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CALCULATOR MODULE : Maths Array And Vector   ±

Calculate vector (array sum, average, root mean square (RMS), and dot product) and matrix operations (matrix inverse, transpose, determinant, Crout factorisation (LU factorisation), and cross product). Enter each matrix row as a comma separated list, with a new line for each row. For large matrices the rows will sometimes wrap around to the next line. If the lines wrap, you must still enter a new line (enter key) for each new row. Matrices should have an equal number of elements in each row.

Solve a set of linear equations using matrix and vector operations. The matrix must be square (equal number of rows and columns), and must have an equal number of elements in each row. The matrix rows must be independent, and well conditioned.

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CALCULATOR MODULE : Maths Polynomial   ±

Calculate polynomial coefficients, roots or zeros, maximum and minimum, points of inflection, and interpolate polynomial value, slope and curvature.

Polynomials can be calculated for linear (first order), quadratic (second order), cubic (third order), quartic (fourth order), quintic (fifth order), sextic (sixth order), septic (seventh order), octic (eighth order) or nth degree. For polynomials with all real roots, all roots can sometimes be solved simultaneously using the Durand Kerner method. In other cases solve for individual roots. The maximum or minimum points (slope equals zero) and the inflection points (curvature equals zero) can also be calculated. Use a plot page to plot the polynomial and identify the approximate root values if any.

Lagrange's method is used to interpolate between data points. This method is useful for interpolating between data points, but can give poor results when extrapolating outside the data range. Evenly spaced data points can result in cyclic behaviour.

Polynomial coefficients can be calculated from the real roots, and the nth coefficient. There are an infinite number of polynomials with the same roots. The nth coefficient is required in order to calculate unique coefficients. This method only applies if all of the roots are real. Polynomial coefficients can also be calculated from XZ data points.

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CALCULATOR MODULE : Maths Polynomial Root Maximum And Minimum And Point Of Inflection   ±

Calculate maths polynomial roots, maximum and minimum and points of inflection.

Multiple roots, maximum and minimum or points of inflection are calculated using the Durand Kerner method. This method is only valid if all roots, maximum and minimum or points of inflection are real. Use the single root calculators for polynomials with imaginary roots. The single root calculators can only calculate real roots, maximum and minimum or points of inflection. The value Xu is used as the initial guess for calculating the roots, maximum and minimum or points of inflection. Use the plot options to select suitable guess values.

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CALCULATOR MODULE : User Programmable   ±

Use the user programmable calculator to write your own programs, with inbuilt plots and tables etc. Select the number of X input variables and Z output variables on the setup page. For example if you have one equation with two input variables select two X input variables, and one Z output variable.

The calculators use Javascript so you can use the full range of programming constructs: if, else, for, while. You can also define functions and objects to use in your code. Enter Javascript statements to define all of the output variables z1, z2, z3... in terms of the input variables x1, x2, x3.... and any previously defined variables. Each Javascript statement should be on a new line and must end with a semi colon ';' eg : z1 = x1 + 2 * x2;. You can also reference the variables by index eg: for(i=0: i<3; i++){x[i] = sin(z[i]);}. Refer to the help page in Resources for more details.

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