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StringJoin[string1, string2, ...] or string1 <> string2 <> ... concatenates two or more strings to form a new string whose length is equal to the sum of the individual string lengths. StringLength[string] returns the number of characters in string. StringPosition[string, substring] returns a list of the start and end positions of all occurrances of substring within string. StringReplace[string, string1 newstring1] replaces string1 by newstring1 whenever it appears in string. StringReplace[string, {string1 newstring1, string2 newstring2, . . .}] replaces string1 by newstring1, string2 by newstring2, . . . whenever they appear in string. StringReverse[string] reverses the characters in string. StringTake[string, n] returns the first n characters of string. StringTake[string, n] returns the last n characters of string. StringTake[string, {n}] returns the nth character of string. StringTake[string, { n}] returns the nth character from the end of string. StringTake[string, {m, n}] returns characters m through n of string. Subsets[list] returns a list containing all subsets of list, including the empty set, i.e., the power set of list. Subtract[a, b] computes the difference of a and b. Only two arguments are permitted. Subtract[a, b] is equivalent to a b. SubtractFrom[x, y] or x = y subtracts y from x and returns the new value of x.
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a[i] evaluates the sum a .
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a[i] evaluates the sum
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i = imin imax
a.
Sum[a[i],{i, imin, imax, increment}] evaluates the sum Summation continues as long as i imax.
imax jmax
i = imin
in steps of increment.
imax jmax i =1 j =1
a[i, j] evaluates the sum a . Sum[a[i,j],{i,imin,imax},{j,jmin,jmax}] or a[i, j] evaluates the sum a .
Sum[a[i, j],{i, imax},{j,jmax}] or
imax jmax i, j i=1 j=1 imax jmax i=imin j=jmin i = imin j = jmin i, j
Sum[a[i, j],{i,imin,imax,i_increment},{j,jmin,jmax, j_increment}]
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evaluates the sum
i = imin j = jmin
jmax
ai , j in steps of i_increment and j_increment.
SurfaceOfRevolution[f[x], {x, xmin, xmax}] generates the surface of revolution obtained by rotating the curve z = f(x) about the z-axis. SurfaceOfRevolution[f[x], {x, xmin, xmax}, { , min, max}] generates the surface of revolution obtained by rotating the curve z = f(x) about the z-axis, for min max. SurfaceOfRevolution[{x[t], z[t]}, {t, tmin, tmax}] generates the surface of revolution obtained by rotating the curve defined parametrically by x = x(t), z = z(t), about the z-axis. Table[expression, {n}] generates a list containing n copies of the object expression. Table[expression, {k, n}] generates a list of the values of expression as k varies from 1 to n. Table[expression, {k, m, n}] generates a list of the values of expression as k varies from m to n. Table[expression, {k, m, n, d}] generates a list of the values of expression as k varies from m to n in steps of d. Table[expression,{m},{n}] generates a two-dimensional list, each element of which is the object expression. Table[expression,{i, mi, ni},{j, mj, nj}] generates a nested list whose values are expression, computed as j goes from mj to nj and as i goes from mi to ni. The index j varies most rapidly. TableForm[list] prints list the same way as MatrixForm except the surrounding parentheses are omitted.
APPENDIX
TableForm[list, options] allows the use of various formatting options in determining the appearance of a table. Take[list, n] returns a list consisting of the first n elements of list. Take[list, n] returns a list consisting of the last n elements of list. Take[list, {n}] returns a list consisting of the nth element of list. Take[list, { n}] returns a list consisting of the nth element from the end of list. Take[list, {m, n}] returns a list consisting of the elements of list in positions m through n inclusive. Take[list, {m, n, k}] returns a list consisting of the elements of list in positions m through n in increments of k. Times[a, b,...] computes the product of a, b, . . . Times[a, b] is equivalent to a * b. TimesBy[x,y] or x *= y multiplies x by y and returns the new value of x. Timing[expression] evaluates expression, and returns a list of time used, in seconds, together with the result obtained. Together[expression] combines the terms of expression using a common denominator. Any common factors in the numerator and denominator are cancelled. Total[list] gives the sum of the elements of list. Tr[matrix] computes the trace of matrix. TraditionalForm[expression] prints expression in a traditional mathematical format. TranslateShape[object, {x, y, z}] translates object by the vector {x, y, z}]. Transpose[matrix] computes the transpose of matrix. TrigExpand[expression] expands expression, splitting up sums and multiples that appear in arguments of trigonometric functions and expanding out products of trigonometric functions into sums and powers, taking advantage of trigonometric identities whenever possible. TrigFactor[expression] converts expression into a factored expression of trigonometric functions of a single argument. TrigReduce[expression] rewrites products and powers of trig functions in expression as trigonometric expressions with combined arguments, reducing expression to a linear trig function (i.e., without powers or products). TrigToExp[expression] converts trigonometric and hyperbolic functions to exponential form. Unequal[x, y] or x!= y or x y is True if and only if x and y have different values. Union[list1, list2] combines lists list1 and list2 into one sorted list, eliminating any duplicate elements. Although only two lists are presented in this description, any number of lists may be used. As a special case, Union[list] will eliminate duplicate elements in list. list1 list is equivalent to Union[list1, list2]. UnitStep[x] returns a value of 0 if x < 0 and 1 if x 0. Variables[polynomial] gives a list of all independent variables in polynomial. VectorPlot[{Fx, Fy}, {x, xmin, xmax}, {y, ymin, ymax}] produces a vector field plot of the two-dimensional vector function F, whose components are Fx and Fy. While[condition, expression] evaluates condition, then expression, repetitively, until condition is False. WireFrame[object] shows all polygons used in the construction of object as transparent. It may be used on any Graphics3D object that contains the primitives Polygon, Line, and Point. Xor[p, q] is True if p or q (but not both) are True; False otherwise.
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