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| The documentation only includes examples of RandomPoint used with built-in regions ListPlot[ RandomPoint[ ImplicitRegion[1/2 1] ![enter image description here][1] [1]:... |
| Another example of this technique In[1]:= (* Consider the equation Sin[x^2-y^2]+ Cos[x^2+y^2]==1, with x and y between 0 and 1. It is one equation with two variables and is clearly underdetermined. An obvious solution is... |
| I'll give it a try. I've been using MATLink to get lhc sampling from MATLAB. |
| In[1]:= f = 2 x1 + 3 x2 + 3 y1/2 + 2 y2 - y3/2; c = {x1^2 + y1 == 5/4, x2^(3/2) + 3 y2/2 == 3, x1 + y1 {"DifferentialEvolution", "SearchPoints" -> n}][[ 1]]], {n, 2, 10}] Out[4]= {{0.432374, 8.47632}, {2.24204,... |
| I frequently use IPOPTLink but it won't handle Or constraints, so I'm puzzled that FindMinimum can, with Method -> "IPOPT: |
| In[1]:= (* First polygon is a square centered at the origin,rotated \ by Pi/7, with distances from the center to the vertices equal to 1*) sqr = Polygon[ RotationMatrix[\[Pi]/7] . # & /@ CirclePoints[4] // N]; In[2]:= (*... |
| To summarize, I have always regarded x^(1/3) as being the same as cube root of x. That is not true in Mathematica In[4]:= (-1)^(1/3) // N Out[4]= 0.5 + 0.866025 I In[3]:= CubeRoot[-1] Out[3]= -1 |
| Maple does it correctly int(sqrt((cos(t1) - cos(t2))^2 + (sin(t1) - sin(t2))^2), t1 = 0 .. 2*Pi, t2 = 0 .. 2*Pi)/(2*Pi)^2; 4 -- Pi |
| I would not have expected that fixing the type of the variable would enable a solution. |
| Reduce[12 z^2 (-243 - 27 y + z^2) == 0, {z, y}, Reals] z == 0 || ((z 0) && y == -((243 z^2 - z^4)/(27 z^2))) Limit[-((243 z^2 - z^4)/(27 z^2)), z -> 0] -9 |