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APPENDIX
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PolynomialLCM[p1, p2,...] computes the least common multiple of the polynomials p1, p2, . . . PolynomialQ[expression, variable] yields True if expression is a polynomial in variable, and False otherwise. PolynomialQuotient[p, s, x] gives the quotient upon division of p by s expressed as a function of x. Any remainder is ignored. PolynomialRemainder[p, s, x] returns the remainder when p is divided by s. The degree of the remainder is less than the degree of s. c Power[a, b] computes a b, Power[a, b, c] produces a b , etc. PowerExpand[expression] expands nested powers, powers of products and quotients, roots of products and quotients, and their logarithms. PreDecrement[x] or x decreases the value of x by 1 and returns the new value of x. PreIncrement[x] or ++ x increases the value of x by 1 and returns the new value of x. Prepend[list, x] returns list with x inserted to the left of its first element. Prime[n] returns the nth prime. PrimeQ[expression] yields True if expression is a prime number, and yields False otherwise. Print[expression] prints expression, followed by a line feed. Print[expression1, expression2, . . .] prints expression1, expression2, . . . followed by a single imax imax line feed. Product[a[i], {i, imax}] or a[i] evaluates the product ai .
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Product[a[i], {i, imin, imax}] or
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a[i] evaluates the product
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Product[a[i], {i, imin, imax, increment}] evaluates the product ai in steps of i = imin increment. imax jmax imax jmax Product[a[i, j], {i, imax}, {j, jmax}] or a[i, j] evaluates the product ai , j .
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imax
Product[a[i,j],{i,imin,imax},{j,jmin,jmax}] or the product
i = imin j = jmin
a
imax
jmax
i=imin j=jmin
jmax
a[i, j] evaluates
i, j
jmax
Product[a[i,j],{i,imin,imax,i_increment},{j,jmin,jmax, j_increment}] evaluates the product
i = imin j = jmin
a
imax
i, j
in steps of i_increment and j_increment.
Projection[vector1, vector2] returns the orthogonal projection of vector1 onto vector2. Projection[vector1, vector2, f ] returns the orthogonal projection of vector1 onto vector2 with respect to an inner product defined by f. Quotient[m, n] returns the quotient when m is divided by n. Random[ ] gives a uniformly distributed, real, pseudorandom number in the interval [0, 1]. Random[type] returns a uniformly distributed pseudorandom number of type type, which is either Integer, Real, or Complex. Its values are between 0 and 1, in the case of Integer or Real, and contained within the square determined by 0 and 1 + , if type is Complex. Random[type, range] gives a uniformly distributed pseudorandom number in the interval or rectangle determined by range. range can be either a single number or a list of two numbers such as {a,b} or {a + b I, c + d I}. A single number m, is equivalent to {0,m}. Random[type, range, n] gives a uniformly distributed pseudorandom number to n significant digits in the interval or rectangle determined by range. RandomComplex[] returns a pseudorandom complex number lying within the rectangle whose opposite vertices are 0 and 1+I. RandomComplex[zmax] returns a pseudorandom complex number that lies in the rectangle whose opposite vertices are 0 and zmax. RandomComplex[{zmin, zmax}] returns a pseudorandom complex number that lies in the rectangle whose opposite vertices are zmin and zmax. RandomComplex[{zmin, zmax},n] returns a list of n pseudorandom complex numbers each of which lies in the rectangle whose opposite vertices are zmin and zmax.
APPENDIX
RandomComplex[{zmin, zmax},{m, n}] returns an m n list of pseudorandom complex numbers each of which lies in the rectangle whose opposite vertices are zmin and zmax. RandomInteger[ ] returns 0 or 1 with equal probability. RandomInteger[imax] returns a pseudorandom integer between 0 and imax. RandomInteger[{imin, imax}] returns a pseudorandom integer between imin and imax. RandomInteger[{imin, imax},n] returns a list of n pseudorandom integers between xmin and xmax. This extends in a natural way to lists of higher dimension. RandomInteger[{imin, imax},{m, n}] returns an m n list of pseudorandom integers between xmin and xmax. This extends in a natural way to lists of higher dimension. RandomPrime[n] returns a pseudorandom prime number between 2 and n. RandomPrime[{m, n}] returns a pseudorandom prime number between m and n. RandomPrime[{m, n}, k] returns a list of k pseudorandom primes, each between m and n. RandomReal[ ] returns a pseudorandom real number between 0 and 1. RandomReal[xmax] returns a pseudorandom real number between 0 and xmax. RandomReal[{xmin, xmax }] returns a pseudorandom real number between xmin and xmax. RandomReal[{xmin, xmax},n] returns a list of n pseudorandom real numbers between xmin and xmax. RandomReal[{xmin, xmax},{m, n}] returns an m n list of pseudorandom real numbers between xmin and xmax. This extends in a natural way to lists of higher dimension. RandomSample[{e1, e2, . . . , en}] gives a pseudorandom permutation of the list of ei. RandomSample[{e1, e2, . . . , en}, k] gives a pseudorandom sample of k of the ei. Range[n] generates a list of the first n consecutive integers. Range[m, n] generates a list of numbers from m to n in unit increments. Range[m, n, d] generates a list of numbers from m through n in increments of d. Reduce[equations, variables] simplifies equations, attempting to solve for variables. If equations is an identity, Reduce returns the value True. If equations is a contradiction, the value False is returned. Remove[symbol] removes symbol completely. symbol will no longer be recognized unless it is redefined. ReplacePart[list, x, n] replaces the object in the nth position of list by x. ReplacePart[list, x, n] replaces the object in the nth position from the end by x. ReplacePart[list, i new] replaces the ith part of list with new. ReplacePart[list, { i 1 new1,i 2 new2, ..., i n newn} ] replaces parts i 1, i2,...,in with new1, new2, . . . , newn, respectively. ReplacePart[list,{{i1},{i2},...,{in}} new] replaces all elements in positions i1, i2,...,in with new. ReplacePart[list, {i, j} new] replaces the element in position j of the ith outer level entry with new. ReplacePart[list, {i1,j1} new1, {i2, j2} new2,...,{in, jn} newn] replaces the entries in positions jk of entry ik in the outer level with newk. ReplacePart[list, {{i1,j1}, {i2, j2}, ... , {in, jn}} new] replaces all entries in positions jk of entry ik in the outer level with new. Rest[list] returns list with its first element deleted. Reverse[list] reverses the order of the elements of list. RevolutionPlot3D[f[x], {x, xmin, xmax}] plots the surface generated by rotating the curve z = f(x) , xmin x xmax, completely around the z-axis. RevolutionPlot3D[f[x], {x, xmin, xmax}, {p, pmin, pmax}] plots the surface generated by rotating the curve z = f(x) , xmin x xmax, around the z-axis for min max where is the angle measured counterclockwise from the positive x-axis. RevolutionPlot3D[{f[t],g[t]}, {t, tmin, tmax}] generates a plot of the surface generated by rotating the curve x = f(t), z = g(t), tmin t tmax, completely around the z-axis. RevolutionPlot3D[{f[t],g[t]}, {t, tmin, tmax},{p, pmin, pmax}] generates a plot of the surface generated by the curve x = f(t), z = g(t), tmin t tmax, around the z-axis for min max where is the angle measured counterclockwise from the positive x-axis.