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Topic: Re: Factoring
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Dave Slomer

Posts: 244
Registered: 12/6/04
Re: Factoring
Posted: Apr 15, 1998 12:54 PM
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Jerry Uhl wrote:
>Mathematica does plot implicit functions.


>At 10:13 PM -0400 4/13/98, Dave Slomer wrote:

Actually, so does Derive, even if the implicitness seems 'insolveable=
'. I
just did:

x+y=3D3
x^2+y^2=3D9
sin(x*y)=3D.3
SIN(x=B7y) + COS(x=B7y) =3D 0.2
SIN(x=B7y) + COS(y) =3D 0.2
LN(x + y) + SIN(x + y) + =EA^y + COS(x) =3D 0

=2E..the last several of which produced very interesting plots!

=46rom Derive's 'help' on 'implicit plots':

<<
"Functions implicitly defined by an equation may be plotted using a
relatively efficient algorithm of linear interpolation upon triangles=
..

The implicit plotting algorithm starts in the top left corner of the =
2D-plot
window, plotting points in a top to bottom, left to right fashion. U=
nlike
most explicit plots, implicit plots may not be automatically scaled; =
nor may
an implicit plot line be traced.

Explicit plots are faster and somewhat more accurate than implicit pl=
ots.
Before plotting, when possible, DERIVE automatically converts a funct=
ion
implicitly defined by an equation into a function explicitly defined =
by an
equation of the form y =3D u where y is a variable and u is a univari=
ate
expression in another variable...

An alternate method for generating explicit solutions for implicitly =
defined
equations is to substitute polar coordinates for the variables and so=
lve for
the distance from the origin in terms of the angle...

Implicit 2D plots of a family of plot lines can also be used to make =
contour
of functions of two variables. Simplifying and then plotting an expre=
ssion
of the form

VECTOR (z =3D u, z, m, n, s)

produces a contour plot of the function z =3D u where u is a function=
of x and
y as z varies from m to n in steps of size s. The Calculus Vector co=
mmand
is an easy way to enter such expressions."
>>

Dave Slomer
AP Calculus and computer science teacher
Winton Woods HS, Cinti, OH 45240
http://www.geocities.com/capecanaveral/lab/8692






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