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// Demonstration file for CC - Version 4
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// This file demonstrates only those features  
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  that are new to Version 4.  You could run   
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  the demo file for Version 3 to see the      
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  original features of CC, but the 3D graphics
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  commands won't work.  We demonstrate their  
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  new syntax here.
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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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// Big Numbers and Fractions
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// A number preceded by & is called a Big      
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  Number and will be maintained to infinite   
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  precision.  All computations with Big       
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  Numbers and integers result in Big Numbers, 
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  and quotients of Big Numbers are stored as 
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// exact fractions reduced to lowest 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               // big numbers
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w = &100!                // very big numbers
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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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// Version 3's 3d graphing commands have been  
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  simplified, and new commands have been      
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  added, in version 4.
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Graph3d(x^2-y^2,x = -1 to 1, y = -1 to 1)
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    // no longer necessary to specify the third
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      limits or the number of steps
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Paramg3d(sin(s)cos(t), sin(s)sin(t), cos(s),   
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     s = 0 to pi, t = 0 to 2pi)
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   // x,y,z limits and the number of steps     
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     need not be specified, 
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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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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 for new input@ 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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input@(x,y)
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