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2013-12-15 15:26:45 +0200 | commented answer | Compute the volume of a cube region Thank you a lot... Sage is powerful yet so simple :) |

2013-12-15 15:26:05 +0200 | marked best answer | Compute the volume of a cube region You can construct the 3-dimensional cube as follows: Then construct the polyhedron with the last vertex removed: In our case, the length of the edge is If you want to have a plot of the polyhedron |

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2013-12-15 14:15:52 +0200 | asked a question | Compute the volume of a cube region Hi, I would like to compute the volume $V$ of the lower polyhedron (that does not contain vertex A) let's call it $poly_G$. (let's call $poly_A$ the upper polyhedron that does not contain G). Size is $a=AB=BF=...$ We can compute $V_{poly_A}$ by introducing K and I points and using Pythagore's theorem and median's properties . I can do that by hand using $V_{poly_G}=V_{cube}-V_{poly_A}$ I want to compute the volume with sage, I have tried this code using volume integrations but I am not sure about the result at all... I look at first for the normal vector of plane DBE (cross product) which gives the equation plane $x-y+z$. Then I compute using triple integrations. I would like to know if there are elegant ways of computing this kind of problem in sage ? And in addition, if this require few lines, how can I display the above figure ? Sorry if this looks simple, I am new to Sage. Thanks, |

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