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\deflang1033\pard\ri4\plain\f2\fs36\cf0 Chapter 5  Algebra with MuPAD
\par \plain\f2\fs28\cf0 
\par 5.1 Numbers and domains
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}solve(x^3 - 7*x + 6 = 0, x)
\par {\pntext\f1\'b7\tab}assume(x > 0):
\par {\pntext\f1\'b7\tab}solve(x^3 - 7*x + 6 = 0, x)
\par {\pntext\f1\'b7\tab}assume(x < 0):
\par {\pntext\f1\'b7\tab}solve(x^3 - 7*x + 6 = 0, x)
\par {\pntext\f1\'b7\tab}assume(x <= 1):
\par {\pntext\f1\'b7\tab}solve(x^3 - 7*x + 6 = 0, x)
\par {\pntext\f1\'b7\tab}unassume(x):
\par {\pntext\f1\'b7\tab}equation := (cos(x))^2 = cos(x)
\par {\pntext\f1\'b7\tab}solve(equation, x)
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}assume(x > 0):
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 assume(x < 20, _and):
\par solve(equation, x)
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}assume(x > 100):
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 assume(x < 110,_and):
\par solve(equation, x)
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}unassume(x):
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 assume(x, Type::Interval(PI,3*PI)):
\par solve(equation, x)
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}assume(x, Type::Integer):
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 solve(x^4 - 2/3 = 0, x)
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}assume(x, Type::Real):
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 solve(x^4 - 2/3 = 0, x)
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}assume(x, Type::Complex):
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 solve(x^4 - 2/3 = 0, x)
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}assume(x, Type::Imaginary):
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 solve(x^4 - 2/3 = 0, x)
\par \pard\ri4\plain\f2\fs28\cf0 
\par The most popular types:
\par =====================
\par Type::Arithmetical ---arithmetical expressions,
\par Type::Boolean---logical expressions, 
\par Type::Complex---complex expressions, 
\par Type::Constant---constants,
\par Type::Even---even numbers,
\par Type::Imaginary---imaginary numbers, 
\par Type::Integer---integer numbers, 
\par Type::Interval---interval of real numbers, 
\par Type::NegInt---negative integer numbers, 
\par Type::NegRat---negative rational numbers, 
\par Type::Negative---negative numbers,
\par Type::NonNegInt---non-negative integers, 
\par Type::NonNegRat---non-negative rational numbers, 
\par Type::NonNegative---non-negative numbers,
\par Type::NonZero---non-zero numbers,
\par Type::Odd---odd numbers,
\par Type::PosInt---positive integers,
\par Type::PosRat---positive rational numbers, 
\par Type::Positive---positive numbers,
\par Type::RatExpr---rational expressions, 
\par Type::Rational---rational numbers, 
\par Type::Real---real numbers.
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}solve(x^4 - 2/3 = 0, x) assuming x<0
\par {\pntext\f1\'b7\tab}solve(x^4 - 2/3 = 0, x)
\par \pard\ri4\plain\f2\fs28\cf0 
\par >>>>>>>>>> Time for Exercise 5.1
\par 
\par 5.2 Complex numbers and quaternions
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}reset():
\par {\pntext\f1\'b7\tab}solve(x^2 + 1 = 0, x)
\par {\pntext\f1\'b7\tab}solve(x^3 + 1 = 0, x)
\par {\pntext\f1\'b7\tab}solve(x^4 + 1 = 0, x)
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}A := 3/7 + 7/3*I
\par {\pntext\f1\'b7\tab}B := -4/3 + 5/6*I
\par {\pntext\f1\'b7\tab}A+B, A-B, A*B, A/B
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}abs(A)
\par {\pntext\f1\'b7\tab}sqrt(A)
\par {\pntext\f1\'b7\tab}solve(x^2 - A = 0, x)
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}U := solve(x^3 - 1 = 0, x)
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}x1 := U[1]
\par {\pntext\f1\'b7\tab}x2 := U[2]
\par {\pntext\f1\'b7\tab}x3 := U[3]
\par \pard\ri4\plain\f4\fs28\cf1 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}x1 := rectform(x1)
\par {\pntext\f1\'b7\tab}x2 := rectform(x2)
\par \pard\ri4\plain\f4\fs28\cf1 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}arg(x1), arg(x2)
\par {\pntext\f1\'b7\tab}A := plot::Point2d([Re(U[1]),Im(U[1])]):
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 B := plot::Point2d([Re(U[2]),Im(U[2])]):
\par C := plot::Point2d([Re(U[3]),Im(U[3])]):
\par C1 := plot::Circle2d(1, [0,0]):
\par plot(A,B,C,C1, PointSize=3, PointColor=RGB::Red)
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}A := plot::Arrow2d([0,0],[Re(U[1]),Im(U[1])]):
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 B := plot::Arrow2d([0,0],[Re(U[2]),Im(U[2])]):
\par C := plot::Arrow2d([0,0],[Re(U[3]),Im(U[3])]):
\par C1 := plot::Circle2d(1, [0,0]):
\par plot(A,B,C,C1, PointSize=3, PointColor=RGB::Red)
\par \pard\ri4\plain\f4\fs28\cf1  \plain\f2\fs28\cf0    
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}A := 3/2 + 2/3*I
\par {\pntext\f1\'b7\tab}abs(A)
\par {\pntext\f1\'b7\tab}sign(A)
\par {\pntext\f1\'b7\tab}rectform(%)
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}a := Dom::Quaternion([2,5,-1,4])
\par {\pntext\f1\'b7\tab}b := Dom::Quaternion(3 + 3*i + 6*j + 7*k)
\par {\pntext\f1\'b7\tab}a+b, a-b
\par {\pntext\f1\'b7\tab}3*a - 4*b
\par {\pntext\f1\'b7\tab}a/b
\par {\pntext\f1\'b7\tab}a^3
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}b := Dom::Quaternion(1+ i + j + k)
\par {\pntext\f1\'b7\tab}Im(b)
\par {\pntext\f1\'b7\tab}Re(b)
\par {\pntext\f1\'b7\tab}conjugate(b)
\par {\pntext\f1\'b7\tab}abs(b)
\par {\pntext\f1\'b7\tab}sign(b)
\par \pard\ri4\plain\f2\fs28\cf0 >>>>>>>>>> Time for Exercise 5.2
\par 
\par 5.3 Polynomials
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}reset():
\par {\pntext\f1\'b7\tab}poly1 := x^3 - 13*x +12
\par {\pntext\f1\'b7\tab}poly2 := x^3 - 11*x^2 + 31*x - 21
\par {\pntext\f1\'b7\tab}poly1*poly2
\par {\pntext\f1\'b7\tab}expand(%)
\par {\pntext\f1\'b7\tab}factor(poly2)
\par {\pntext\f1\'b7\tab}solve(poly2=0,x)
\par {\pntext\f1\'b7\tab}factor(poly1/poly2)
\par {\pntext\f1\'b7\tab}degree(poly1*poly2)
\par {\pntext\f1\'b7\tab}evalp(poly1, x=2.1)
\par {\pntext\f1\'b7\tab}gcd(poly1,poly2)
\par {\pntext\f1\'b7\tab}lcm(poly1,poly2)
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}poly1 := poly(a*x^3 - 13*x +12,[x])
\par {\pntext\f1\'b7\tab}poly2 := poly(x^2 + x^3*y*z + y^2*z^2 + 5*z+3,[x,y])
\par {\pntext\f1\'b7\tab}poly3 := poly(x^2 + x^3*y*z + y^2*z^2 + 5*z+3,[x])
\par {\pntext\f1\'b7\tab}poly4 := poly(x^2 + x^3*y*z + y^2*z^2 + 5*z+3,[y])
\par {\pntext\f1\'b7\tab}poly2list(poly1)
\par {\pntext\f1\'b7\tab}poly2list(poly2)
\par \pard\ri4\plain\f2\fs28\cf0 
\par 
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}A := poly(x^3 + 11*x - 34,[x], Dom::IntegerMod(3))
\par {\pntext\f1\'b7\tab}B := poly(x^4 + 21*x + 17,[x], Dom::IntegerMod(3))
\par {\pntext\f1\'b7\tab}A+B
\par {\pntext\f1\'b7\tab}A*B
\par \pard\ri4\plain\f2\fs28\cf0 
\par >>>>>>>>>> Time for Exercise 5.3
\par 
\par 5.4 Systems of linear equations
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}equations := \{
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1    x - 2*y - 3*z + t = 7,
\par    x + y + z + t = 1,
\par    5*x - 3*y - 3*z = 2
\par \}
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}solve(equations, \{x,y,z\})
\par {\pntext\f1\'b7\tab}linsolve(equations, \{x,y,z\})
\par {\pntext\f1\'b7\tab}linsolve(equations, [z,y,x])
\par {\pntext\f1\'b7\tab}linsolve(
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1    \{5*cos(x)+3*exp(x) = 1, cos(x)-2*exp(x) = 0\},
\par    \{cos(x), exp(x)\}
\par )
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}linsolve(\{5*x+3*y = 1, -2*x - 5*y = 0\}, \{x,y\},
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1    Domain = Dom::IntegerMod(7)
\par )
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}eq1 := x + 2*z = 1:
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 eq2 := y + 4*z = 7:
\par eq3 := 6*x + y = 1:
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}linsolve(\{eq1,eq2,eq3\}, \{x,y,z\})
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}// finding a point on each plane
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 solve(subs(eq1, x=0, y=0), z)
\par \pard\ri4\plain\f4\fs28\cf1 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}solve(subs(eq2,x=0, y=0),z)
\par {\pntext\f1\'b7\tab}solve(subs(eq3,x=0, z=0),y)
\par \pard\ri4\plain\f4\fs28\cf1 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}// declare planes and the point
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 A := plot::Plane([0,0,1/2],[1,0,2]):
\par B := plot::Plane([0,0,7/4],[0,1,4]):
\par C := plot::Plane([0,1,0],[6,1,0]):
\par P := plot::Point3d([-1/2,4,3/4]):
\par plot(A,B,C,P)
\par \pard\ri4\plain\f4\fs28\cf1 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}eq1 :=   x + 3*y + 2*z = 1:
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 eq2 := 2*x + 6*y + 4*z = 7:
\par eq3 :=  -x - 3*y - 2*z = 3:
\par linsolve(\{eq1,eq2,eq3\}, \{x,y,z\})
\par \pard\ri4\plain\f2\fs28\cf0  >>>>>>>>>> Time for Exercise 5.4   
\par 5.5 Declarations of matrices
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}matrix(3, 3, [[0,1,2], [1,0,3], [4,5,0]])
\par {\pntext\f1\'b7\tab}matrix(4, 4, [[0,1,2], [1,0,3], [4,5,0]])
\par {\pntext\f1\'b7\tab}matrix(4, 3, [[0,1,2], [1,0,3], [4,5,0]])
\par {\pntext\f1\'b7\tab}matrix(4, 5, [5,3,2,5,8], Diagonal)
\par {\pntext\f1\'b7\tab}matrix(5, 5, [1,2,3,4,5,6,7,8,9], Banded)
\par {\pntext\f1\'b7\tab}matrix(5, 5, [5,3,3,5,8], Banded)
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}matrix(4, 4, (n,m) -> exp(n + m))
\par {\pntext\f1\'b7\tab}matrix(4, 4, n -> exp(n), Diagonal)
\par {\pntext\f1\'b7\tab}linalg::hilbert(5)
\par {\pntext\f1\'b7\tab}linalg::randomMatrix(5, 5, Dom::Integer)
\par {\pntext\f1\'b7\tab}linalg::randomMatrix(4, 4, Dom::Integer, 0..9)
\par {\pntext\f1\'b7\tab}linalg::randomMatrix(6, 6,
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1    Dom::Integer, 0..100, Diagonal
\par )
\par \pard\ri4\plain\f2\fs28\cf0 
\par >>>>>>>>>> Time for Exercise 5.5   
\par 
\par 5.6 Visualization of matrices
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}B := linalg::randomMatrix(5,5, Dom::Integer, -10..10)
\par {\pntext\f1\'b7\tab}plot(plot::Matrixplot(B))
\par \pard\ri4\plain\f2\fs28\cf0 
\par 5.7 Operations on matrices
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}A := matrix(3,3,[[7,6,0],[8,0,3],[6,1,9]]);
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 B := matrix(3,3,[[9,7,0],[0,6,1],[0,0,8]]);
\par C := matrix(2,3,[[7,1,7],[0,8,4]]);
\par F := matrix(3,2,[[1,8],[7,5],[7,0]]);
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}A + B
\par {\pntext\f1\'b7\tab}3*A + 5*B
\par {\pntext\f1\'b7\tab}A*B  // this operation can be done
\par {\pntext\f1\'b7\tab}B*F  // this operations can be done also
\par {\pntext\f1\'b7\tab}F*B // this operations cannot be done
\par {\pntext\f1\'b7\tab}A^(-1)
\par {\pntext\f1\'b7\tab}float(A^(-1))
\par {\pntext\f1\'b7\tab}linalg::transpose(A)
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}g := x -> x*exp(-x*3);
\par {\pntext\f1\'b7\tab}A := matrix([[7,6,0], [8,0,3], [6,1,9]]):
\par {\pntext\f1\'b7\tab}map(A, g)
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}map(A, x -> x*exp(-x*3))
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}f := (x,y) -> x*y:
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 zip(A,B,f)
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}f := (x,y)->max(x,y):
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 zip(A,B,f)
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}g := (x,y)->min(x,y):
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 zip(A,B,g)
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}h := (n,m) -> gcd(n,m):
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf1 zip(A,B,h)
\par \pard\ri4\plain\f2\fs28\cf0 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf1 {\pntext\f1\'b7\tab}A := matrix(3,3,[[3, 2, 5],[-1, 5, 3],[1, 2, -5]])
\par {\pntext\f1\'b7\tab}linalg::det(A)
\par \pard\ri4\plain\f2\fs28\cf0 
\par >>>>>>>>>> Time for Exercise 5.7 
\par }