Simtel MSDOS - Coast to Coast/simteldosarchivecoasttocoast2.iso/calculat/cc4_9206.zip/DEMO2.XPL

Text File | 1992-06-07 | 5KB | 308 lines

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// Demonstration file for X(PLORE) - Version 4
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// This file demonstrates only those features
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  that are new to X(PLORE).  The file
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  DEMO1.XPL demonstrates the features that
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  were already present in CC--The Calculus
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  Calculator
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// Matrices
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A = {1,2,3;4,5,6;7,9,8}  // 3 x 3 matrix
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B = A"                   // Transpose of A
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A + B                    // Sum
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A*B                      // Product
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A^(-1)                   // inverse of A
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A/B                      // A*B^(-1)
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A\B                      // A^(-1)*B
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A = Random(3,5)          // 3 x 5 matrix
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B = RREF(A)              // Row reduced form
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C = B[1:3, 4:5]          // submatrix
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H = Matrix(1/(i+j-1),i = 1 to 4, j = 1 to 4)
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                         // Hilbert Matrix
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H^3                      // third power
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1/H                      // inverse of H
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P = CharPoly(H)          // Characteristic
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                           polynomial
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E = EigenVal(H)          // Eigenvalues
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Rank(H - E[1]*Eye(4))    // Should be 3, since
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                           matrix - eigenvalue
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                           is singular
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F = Eig(H)               // F[1] is diagonal
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                           matrix of eigen-
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                           values, F[2] has
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                           eigenvectors in
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                           its columns.
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F[2]*F[1]/F[2] - H       // Should be 0 or
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                           nearly 0
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// Level Curves
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// We will graph the solution to
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      3    3
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     x  + y  = 1
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Window(-3,3,-2,2)
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LevelC(x^3 + y^3 = 1, x=1, y=1)
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// This level curve is a trajectory through
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                      2      2
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  the vector field (3y , - 3x ).  Let's take
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  a look at this vector field
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Field(3y^2, -3x^2, x, y)
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// Another trajectory through this field
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starts at (-1.1, 1)
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Traj(3y^2, -3x^2, x=-1.1, y=1, 100)
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// Infinite precision numbers
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// A number preceded by & is called an
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infinite precision value and will be
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maintained to infinite precision.  All
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computations with infinite precision values
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results in infinite precision values, and
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quotients of infinite precision values are
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stored as exact fractions reduced to lowest
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terms.
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x = &3/&5                // fraction
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y = &7/4 - &2/3          // exact arithmetic
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z = &3^100               // huge integers
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w = &100!                // very huge integers
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H = Matrix(1/Fix(i+j-1),i = 1 to 4, j = 1 to 4)
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       // 4 x 4 Hilbert matrix.  The function
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         FIX returns a Big Number.  Its
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         complement is FLOAT
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H*H                      // exact product
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1/H                      // exact inverse of H
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//  New Three Dimensional Graphing Commands
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Curve3d(cos(t), sin(t), t, t= 0 to 4pi)
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   // new command for parametric curves
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H = Random(6,6)
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Matrixg(H)
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  // New command:  Graph the data in a matrix
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// New string operations
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q1 = 'abc'|'de'   // concatenation
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q2 = q1[3]        // single character
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q3 = q1[2:4]      // substring
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q4 = upcase(q1)   // upper case transform
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n = pos('de',q1)  // position of substring
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m = asc(q1)       // list of ascii codes
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q5 = chr(m)       // characters from codes
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n1 = val('123 + cos(4)')
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                 // value of a string
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q6 = str(123+cos(4))
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                 // string from a value
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// See subroutine Intersect for new Input@
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command
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Intersect
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// procedure demonstrating use of Input@
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Procedure Intersect
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  // user finds intersection of two curves
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  Window(0,3,-1,1)
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  graphics
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  quickg(cos(x),x)
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  sk(x,x)
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  solve(cos(b)=b,b=1)   // target for user to guess
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  Write@(.1,-.5,'Move crosshairs to intersection of curves, and')
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  Write@(.1,-.6,'enter x-coordinate where curves intersect')
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  Repeat
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      input@(.3,-.8,5,x)
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      ok = x > (b-0.05) and x < (b+0.05)
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      if not ok
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          beep
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        end
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    until ok
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  write@(.1,-.7,x)
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  write@(.1,-.8,'You got it!!')
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  text
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end  // Intersect
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