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NullSpace[a] returns the basis vectors of the null space of a. Numerator[fraction] returns the numerator of fraction. Opacity[a]specifies the degree of transparency of a graphics object. The value of a must be between 0 and 1, with 0 representing perfect transparency and 1 representing complete opaqueness. Or[p,q ] or p  q or p q is True if p or q (or both) are True; False otherwise. Orthogonalize[vectorlist] uses the GramSchmidt method to produce an orthonormal set of vectors whose span is vectorlist. Orthogonalize[vectorlist, f] produces an orthonormal set of vectors with respect to the inner product defined by f. Outer[Times, v1, v2] computes the outer product of v1 and v2. PaddedForm[expression, {n, f}] prints the value of expression leaving space for a total of n digits, f of which are to the right of the decimal point. The fractional portion of the number is rounded if any digits are deleted. PaddedForm[expression, n] prints the value of expression leaving space for a total of n digits. This form of the command can be used for integers or real number approximations. The decimal point is not counted as a position. ParametricPlot[{x[t], y[t]}, {t, tmin, tmax}] plots the parametric equations x = x(t), y = y(t) over the interval tmin t tmax. ParametricPlot[{{x1[t], y1[t]}, {x2[t], y2[t]}, ...}, {t, tmin, tmax}] plots several sets of parametric equations over tmin t tmax. ParametricPlot3D[{x[t], y[t], z[t]}, {t, tmin, tmax}] plots a space curve in three dimensions for tmin t tmax. ParametricPlot3D[{x[s, t], y[s, t], z[s, t]}, {s, smin, smax}, {t, tmin, tmax}] plots a surface in three dimensions. Part[list, k] or list[[k]] returns the kth element of list. Part[list, k] or list[[ k]] returns the kth element from the end of list. Part[list, m, n] or list[[m, n]] returns the nth entry of the mth element of list, provided list has depth of at least 2. Partition[list, k] converts list into sublists of length k. If list contains k n + m elements, where m < k, Partition will create n sublists and the remaining m elements will be dropped. Partition[list, k, d] partitions list into sublists of length k offsetting each sublist from the previous sublist by d elements. In other words, each sublist (other than the first) begins with the d + 1st element of the previous sublist. Pi or p is the ratio of the circumference of a circle to its diameter. PieChart[datalist] draws a simple pie chart. datalist is a list of numbers enclosed within braces. PieChart[{datalist1, datalist2, ...}] draws a pie chart containing data from multiple data sets. Each data set is a list of numbers enclosed within braces. Plot[f[x], {x, xmin, xmax} plots a twodimensional graph of the function f[x] on the interval xmin x xmax. Plot[{f[x], g[x]}, {x, xmin, xmax}] plots the graphs of f[x] and g[x] from xmin to xmax on the same set of axes. This command can be generalized in a natural way to plot three or more functions. Plot3D[f[x, y], {x, xmin, xmax}, {y, ymin, ymax}] plots a threedimensional graph of the function f[x,y] above the rectangle xmin x xmax, ymin y ymax. Plot3D[{f1[x, y], f2[x, y], ...}, {x, xmin, xmax}, {y, ymin, ymax}] plots several threedimensional surfaces on one set of axes. Plus[a, b,...] computes the sum of a, b, . . . Plus[a, b] is equivalent to a + b. PolarPlot[f[p], {p, pmin, pmax}] generates a plot of the polar equation r = f ( ) as varies from min to max. PolarPlot[{f1[p], f2[p],...}, {p, pmin, pmax}] plots several polar graphs on one set of axes. PolynomialGCD[p1, p2,...] computes the greatest common divisor of the polynomials p1, p2, . . .

