Example function sometimes provides maple 6 help

Multiple matches found:
linalg,kernel
LinearAlgebra,NullSpace

Examples:
> i := 1;

i := 1

> evaln(i);

i

> evaln(a || i);

a1

> evaln(a || (1..3));

a1, a2, a3

> evaln(t[i]);

t[1]

> evaln(f(i));

f(1)

> divide(x^2,x,evaln(t[i]));

true

> t[i];

x

# If something which does not evaluate to a name is passed to evaln an error is
# returned

> evaln(3);

Error, illegal use of an object as a name

Examples:
> plot3d(sin(x+y),x=-1..1,y=-1..1);
> plot3d(binomial,0..5,0..5,grid=[10,10]);

# can have alternate coordinate systems

> plot3d((1.3)^x * sin(y),x=-1..2*Pi,y=0..Pi,coords=spherical,style=patch);
> plot3d([1,x,y],x=0..2*Pi,y=0..2*Pi,coords=toroidal(10),scaling=constrained);\
> plot3d(sin(x*y),x=-Pi..Pi,y=-Pi..Pi,style=contour);

# can have variable endpoints in some cases

> plot3d(sin(x*y),x=-Pi..Pi,y=-x..x);
> p:= proc(x,y) if x^2 < y then cos(x*y) else x*sin(x*y) end if end proc:
> h:= proc(x) x^2 end proc:
> plot3d(p,-2..2,-1..h);
> plot3d([x*sin(x)*cos(y),x*cos(x)*cos(y),x*sin(y)],x=0..2*Pi,y=0..Pi);
> plot3d(x*exp(-x^2-y^2),x=-2..2,y=-2..2,grid=[49,49]);

# can specify a color function (or procedure)

> plot3d(x*exp(-x^2-y^2),x=-2..2,y=-2..2,color=x);
> plot3d(p,-2..2,-1..h,color=h);

# multiple 3d plots can also be done

> plot3d({sin(x*y), x + 2*y},x=-Pi..Pi,y=-Pi..Pi);
> c1:= [cos(x)-2*cos(0.4*y),sin(x)-2*sin(0.4*y),y]:
> c2:= [cos(x)+2*cos(0.4*y),sin(x)+2*sin(0.4*y),y]:
> c3:= [cos(x)+2*sin(0.4*y),sin(x)-2*cos(0.4*y),y]:
> c4:= [cos(x)-2*sin(0.4*y),sin(x)+2*cos(0.4*y),y]:
> plot3d({c1,c2,c3,c4},x=0..2*Pi,y=0..10,grid=[25,15],style=patch);
> plot3d({c1,c2,c3,c4},x=0..2*Pi,y=0..10,grid=[25,15],style=patch,color=sin(x));\
>

Examples:
> plotsetup(default);
> interface(plotdevice);
> plotsetup(tek, kermit);
> plotsetup(ps,plotoutput=`plot.ps`,plotoptions=`portrait,noborder`);
> plotsetup(x11);

Examples:
> with(plots):
> pointplot({[0,1],[1,-1],[3,0],[4,-3]},axes=BOXED);
> pointplot({seq([n,sin(n/10)],n=0..30)});
> points:= { seq([T^2,T],T=0..40) }:
> pointplot(points);
> pointplot(points,coords=polar,color=red);

Examples:
> with(tensor):

# Define the Schwarzschild covariant metric tensor: In defining the array of
# metric components, we use sparse to cut down on the number of components that
# must be entered. We always use the symmetric indexing function when defining
# the metric components.

> g_compts:=array(symmetric,sparse,1..4,1..4):
> g_compts[1,1]:=(1-2*m/r): g_compts[2,2]:=-1/g_compts[1,1]:
> g_compts[3,3]:=-r^2: g_compts[4,4]:=-r^2*sin(th)^2:

# Now create the metric tensor by assigning the proper values to fields
# index_char and compts of a table (or use tensor[create]).

> g:=create([-1,-1], eval(g_compts));

[1 - 2 m/r 0 0 0 ]
[ ]
[ 1 ]
[ 0 - --------- 0 0 ]
[ 1 - 2 m/r ]
g := table([compts = [ ],
[ 2 ]
[ 0 0 -r 0 ]
[ ]
[ 2 2]
[ 0 0 0 -r sin(th) ]

index_char = [-1, -1]

])

# Verify that the new object "g" is really a tensor_type:

> type(g,tensor_type);

true

# Create a "rank-0" tensor, i.e., a scalar:

> R:= create([], -4/r^2);

4
R := table([compts = - ----, index_char = []])
2
r

# Verify that this object is also really a tensor_type:

> type(R,tensor_type);

true

Examples:
> with(group):
> grouporder(permgroup(8, {a=[[1,2]], b=[[1,2,3,4,5,6,7,8]]}));

40320

Examples:
> with(geometry):

> circle(c,x^2+y^2=1,[x,y],'centername'=o);

c

> detail(c);

name of the object: c
form of the object: circle2d
name of the center: o
coordinates of the center: [0, 0]
radius of the circle: 1
equation of the circle: x^2+y^2-1 = 0

# define the same circle but without the names of the axes in the input

> circle(c,a^2+b^2=1);
> a;
> b;

c

> detail(c);

name of the object: c
form of the object: circle2d
name of the center: center_c
coordinates of the center: [0, 0]
radius of the circle: 1
equation of the circle: a^2+b^2-1 = 0

# define the same circle where the names of the axes are assigned by the two
# environment variables

> _EnvHorizontalName := 'm': _EnvVerticalName := 'n':
> circle(c,[point(oo,0,0),1]);

c

> Equation(c);

2 2
m - 1 + n = 0

# In the above examples, c is assigned to a geometric object (circle), c can
# also be assigned to a list of objects

> line(l2, x + y = 1, [x,y]),circle(c, x^2 + y^2 = 1, [x,y]):
> intersection(H, l2, c, [M,N]);

[M, N]

> H;

[M, N]

> detail(H);

[name of the object: M
form of the object: point2d

coordinates of the point: [0, 1], name of the object: N
form of the object: point2d

coordinates of the point: [1, 0]]

# The following is an example when unknown parameters exist:

> line(l2, x + y = 1,[x,y]), point(A, a, 1/2), point(B,3/5,b):
> IsOnLine({A,B},l2,'cond');

IsOnLine: "hint: the following conditions must be satisfi\
ed: {-1/2+conjugate(a) = 0, -2/5+conjugate(b) = 0}"

FAIL

> cond;

___ ___
(- 1/2 + (a) = 0) &and (- 2/5 + (b) = 0)

> assume(op(cond));
> IsOnLine({A,B},l2);

true

# More examples can be found in examples,geometry.

Multiple matches found:
worksheet,expressions,mathobjects
worksheet,expressions,math
worksheet,expressions,mathfunctions
worksheet,expressions,copyexamples