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Re: Factoring
Posted:
Apr 15, 1998 12:54 PM


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 = 2Dplot 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



