Programs for the Algebra FX2.0 Calculator

This Program solves a two by two system of equations

Finds the determinant of a two by two matrix

Solves a three by three system of equations

Finds the determinant of a three by three matrix

Calculates the slope, distance, and midpoint if given two points

This program finds area, perimeter and Diagonal of a Rectangle

Rotates a triangle through a given angle of rotation about a vertex

Reflects a triangle about the X axis

Reflects a triangle about the Y axis

Shifts a triangle in the x or y direction by a distance

Generates a random pair of numbers 1-6

Reflects a triangle about the line y=x

Reflects a triangle about the line y=-x

Calculates the roots of quatdratic equations

Calculates the discriminant of quadratic equations

This program converts a number from one base to another. Any base from 2 through 36 can be used. List 5 and List 6 of the active file are used by the program.

This program finds any power of a complex number.

This program finds and displays the N complex solutions of z^N=c where c is any complex (or real) number and N is a positive integer

This set of programs solves a system of equations over the complex numbers. The cases of 2 equations with 2 unknowns, 3 equations with 3 unknowns, and 4 equations with 4 unknowns can be solved.

This program analyzes and reports the properties of a general conic. The input can be the coefficients of Ax^2+Cy^2+Dx+Ey+F=0 or of y=Ax^2+Bx+C or of x=Ay^2+By+C. The type of conic is identified. For parabolas, the vertex, axis, focus, and directrix are reported along with the direction of opening. For ellipses, the center, semi-major axis, semi-minor axis, and center to focus distances are reported along with the major axis direction. For hyperbolas, the center, center to vertex, center to imaginary vertex, and center to focus distances are reported along with the transverse axis direction.

integral(a,b) integral(f4,f5) f6(x,y) dA = sum f6(xi,yi)
delta xi 
delta yi 

where (xi,yi) is the midpoint of the rectangular subinterval. As suggested by how the integral is written, the integrand is stored in f6 and the possibly variable limits of the first integration are stored in f4 and f5, respectively. The integration can be done in either order. The program is structured to use the same number of divisions in each direction; consequently, the square of that number of points is summed to approximate the integral. The number of subintervals to be used in each direction is chosen during execution

This program converts terminating or repeating decimals to fraction form.

This program plots the Euler's method solution of the differential equation dy/dx=f6(x,y) using a step size equal to the distance between pixels. Before executing, the window should be adjusted so that the antiderivative has no vertical asymptote within the window. Since the program does not compute a point at the first or last pixel, a vertical asymptote can occur at the edges of the window.

This program uses the Euler's method solution of the differential equation dy/dx=f6(x,y) to compute the value of the antiderivative at x=B. Either the step size or the number of steps can be chosen during execution.

This program numerically solves the differential equation dy/dx=f6(x) and plots the antiderivative F(x)=F(a)+Integral(a,x) f6(t)dt. Before executing, the window should be adjusted so that F(x) has no vertical asymptote within the window. Since the program does not compute a point at the first or last pixel, a vertical asymptote can occur at the edges of the window. 

This program finds the greatest common divisor (GCD) and the least common multiple (LCM) of any two positive integers.

This program graphs the general conic Ax^2+Bxy+Cy^2+Dx+Ey+F=0.

This program plots the implicitly defined graph given by F(x,y)=0. The function F(x,y) is assumed to be stored in f6. As the program is configured, up to sixteen values of x can be found and plotted for each value of y. The y value corresponding to every other row of pixels is used to speed up the plotting. A "Ma ERROR" signifies that that chosen y value and the internally guessed x value combination corresponds to a point at which the function is undefined. A modification to the View Window should avoid that. To graph the relation with a changed View Window, reexecute the program.

This program solves a linear programming problem by the simplex method. The initial tableau is presumed stored as Matrix A. The program identifies the pivot elements and performs the pivots until a final tableau is achieved. The final tableau is stored as Matrix F and is displayed at the end. The initial tableau remains unchanged in Matrix A.

This program performs a multiple linear regression. Values for up to five different x's (x1, x2, ... , x5) are assumed to be in List 1 through List 5 respectively and the corresponding y values are assumed to be in List 6. The data is fit with a function that is linear in each of the x's.

This program allows any computation involving "phasors" to be performed. A "phasor" is a complex number (or a two dimensional vector) expressed in magnitude, direction form. The program as written allows up to five phasors to be involved in the calculation (it can easily be modified to allow for more) and reports the result in the same magnitude, direction form. The angle for the result will be expressed using the default angle setting of the calculator.

This program computes P(x)/Q(x) and reports the quotient and the remainder.

This program factors any polynomial P(x) having integer coefficients over the integers. It will find any common numerical factor and any linear factors of the polynomial. If none of these are found, it will report that P(x) has no linear factors over the integers. Note, however, that P(x) might have quadratic factors that are irreducible over the integers.

This program computes P(x)Q(x) and reports the product.

This program determines whether a number is prime or composite. If the number is composite, its lowest prime divisor is reported.

This program lists all the prime numbers from 2 through a specified number.

This program reports the prime factors of a number and their multiplicity in a matrix format. The first column lists the prime factors of the number, while the second column lists the exponent for that factor.

This program factors Ax^2 +Bx+C for any integers A, B, C subject to A not zero and to B and C not both zero. If possible, the factors contain integer coefficients with the greatest common factor of the coefficients in front. If this form cannot be achieved, the root factored form is presented; that is, A(x-R1)(x-R2) where R1 and R2 are the roots of the quadratic. In any case, radicals are presented in simplified form.

This program simplifies and computes roots. Various simplified forms are presented along with the numerical value. For even roots greater two, the input must be positive; otherwise, the input can be positive or negative. Fractions can be entered either in fraction or division form.

Integral(a,b) f6(x)dx = Sum f6(xi) delta xi

where xi can be chosen to be the left endpoint of the subinterval, the right endpoint of the subinterval, the midpoint of the subinterval, or the trapezoidal rule estimate. The integrand is stored in f6; the number of subintervals is chosen during execution.

This program graphs a polynomial given its leading coefficient and its roots. The window is adjusted to show all the roots and the maximum and minimum values of the polynomial between the roots.

This program row reduces Matrix A to reduced row echelon form. The result is displayed as Matrix R; the original Matrix A is left unchanged. If desired, each step of the row reduction can be displayed.

This program approximates the integral Integral(a,b) f6(x)dx by Simpson's rule for any even number of subintervals. The integrand is stored in f6; the even number of subintervals is chosen during execution.

This program graphs the slope field of the differential equation dy/dx=f6(x,y) . The relationship to the antiderivative can be dramatically seen by over-graphing. If the graph window is changed, reexecute the program to replot the slope field. The program is structured so that the lines of the slope field never overlap. If f6 is a function of x only, the numerical antiderivative can be plotted via the Fundamental Theorem Program. In all cases, an approximate antiderivative can be plotted via the Euler's Method Graphical Program.

This program approximates a triple integral numerically by integral(a,b) integral(f2,f3) integral(f4,f5) f6(x,y,z) dV = sum f6(xi,yi,zi) delta xi delta yi delta zi where (xi,yi,zi) is the midpoint of the rectangular subregion. As suggested by how the integral is written, the integrand is stored in f6, the possibly variable limits of the first integration are stored in f4 and f5, respectively, and the possibly variable limits of the second integration are stored in f2 and f3, respectively. The integration can be done in any order. The program is structured to use the same number of divisions in each direction; consequently, the cube of that number of points is summed to approximate the integral. The number of subintervals to be used in each direction is chosen during execution.