Defining your polynomial as
p[x_, a_, b_, c_] := the formula
I'd do this :
Manipulate[ CountRoots[ p[x, a, b, c], {x, 0, Infinity}],
{a, -100, 100}, {b, -100, 100}, {c, -100, 100}]
If a plot is needed one can proceed this way :
ListContourPlot3D[ Table[ CountRoots[ p[x, a, b...
This works (it's obvious the same will hold for negative integers):
Reduce[a^2 + b^2 == c^2 && 0 < a < 100 && 0 < b < 100 && 0 < c < 100, {a, b, c}, Integers]
And if you're up for an interesting visualization, here is my take:
ListPlot3D[{a, b, c} /...
I try to plot the following, but something seems to be wrong in my code and I can't figure out how to fix it:
RegionPlot3D[{CountRoots[\[Sigma]q33[\[Omega], V1, V2,
V3], {\[Omega], 0, Infinity} == 0],
CountRoots[\[Sigma]q33[\[Omega], V1, V2,
V3], {\[Omega], 0, Infinity} == 1],
...
ee[v1_?NumericQ,v2_?NumericQ,v3_?NumericQ]:= CountRoots[σq33[ω,v1,v2,v3],{ω,0,Infinity}];
Show[Table[RegionPlot3D[
ee[v1, v2, v3] == i, {v1, 0, 50}, {v2, 0, 50}, {v3, 0, 100},
Mesh -> None, LabelStyle -> (FontSize -> 14),
PlotStyle -> Directive[GrayLevel[ i/10 + 1/10, 3/10...
We’ve all heard the stories of seemingly trivial patents being used to mug technology companies. There was the patent on the “Interactive Web” which a troll named Eolas used to extract $521 million from Microsoft–until a jury in East Texas threw out the patents. There are the four patents Lodsys is using to send threatening letters to software developers everywhere–trivial patents that Google says never should have been granted, in fact, Google and Oracle have submitted mountains of prior art to show that the patents should be invalid. …
