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20200509 16:15:18 0500  commented answer  Implicitization by symmetric polynomials Thank you, this is precisely what I was after. 
20200509 07:52:05 0500  commented question  Implicitization by symmetric polynomials Actually, I made a mistake there. I should have substituted $e_i$ back in after eliminating the variables, and indeed evaluating the elements of at 
20200509 07:37:08 0500  commented question  Implicitization by symmetric polynomials @rburing Unfortunately, your suggestion doesn't seem to work, assuming I understand it correctly: outputs instead of 
20200509 07:19:23 0500  commented question  Implicitization by symmetric polynomials @rburing I had to clean up my code a little, but here it is. 
20200509 04:16:22 0500  asked a question  Implicitization by symmetric polynomials Let $p_1,\dotsc,p_m$ be real polynomials (although rational can do as well) in $t$ variables.
At the moment I am doing this for $t = 1$ by iterating the following simple algorithm over $d \geq 1$:
This works reasonably well when the degrees of $p_1,\dotsc,p_m$ are small, but otherwise iterating over each $d$ involves quite a bit of work and it doesn't scale very well. I know that the equivalent problem for $s \in \Bbb{Q}[X_1,\dotsc,X_m]$ is "readily" solved through variable elimination via Gröbner bases, but I have yet to find a way to make this work for symmetric polynomials. I also thought that I might compute the relevant ideal and then try to find the subset fixed by the symmetric group in $m$ variables, but I couldn't find any facilities in Sage to compute fixed sets under a group action (which I guess is a hard problem in general). This is my current code: And here's a sample output: 
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20180110 07:00:59 0500  asked a question  Drawing a planar multigraph with loops I would like to draw a planar graph with multiple edges and loops in Sage. Unfortunately, the default algorithm draws may intersecting edges and Sage is unable to compute an embedding for graphs with loops multiple edges. Fortunately I know a planar embedding of this graph, so I tried using the Is there a way to achieve what I need? 
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20151130 18:21:35 0500  answered a question  Fast evaluation of big polynomials The problem with the code sample you posted in your second comment isn't the part you highlighted, but the first loop, i.e. the generation of the polynomials. Indeed, on my 5 year old Intel Core i5 2500K I get which suggests that the time to generate a random polynomial of degree at most $8$ in $256$ variables scales linearly with the number of terms. Now, the total number of monomials of degree at most $8$ is $$ \sum_{k=0}^8 {{256}\choose{k}} = 423203101008289 $$ (which I computed with On the other hand, you could try to speed this up with the although I almost ran out of my 8 GB of RAM with the last one, so unless you have access to lots of memory it is unlikely that you would be able to store the result of Final note: If you don't need to use your polynomials more than once, you could try to directly generate their evaluation at some given point, although I fear that won't help much. Anyway, since this is for your master thesis I suggest you bring the problem up with your advisor. 
20151130 13:25:09 0500  commented question  Late binding and lazy symbolic thence numeric math I don't understand: what does lazy evaluation have to do with symbolic simplifications? By the way, your second line of code fails in my Sage although this works 
20151130 10:38:09 0500  commented question  Piecewise function of several variables and how to display it I don't think so, although you could use 
20151130 10:07:22 0500  commented question  jmol cannot run while plot3d Did you restart Sage after installing 
20151130 09:57:00 0500  commented answer  How can I make a 3D scatter plot?

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20151129 14:20:48 0500  answered a question  present sage output as "normal" mathematics If you're working from the notebook you can use the will display 
20151129 10:29:16 0500  asked a question  How can I make a 3D scatter plot? I would like to get an idea of the behaviour of a function that takes an integer and a real number as arguments and returns an integer, so I set out to make a 3D scatter plot over a discretisation of its domain. The problem is that I cannot find any 3D scatter plot function in the documentation. To make a 2D scatter plot I could use either the aptly named instead of a plot of three points in Euclidean space. Using a viewer different from 
20151129 08:50:51 0500  answered a question  How can I programmatically define constraints for minimize_constrained? With a bit of effort, due to how Python handles lambda functions, I found a way. Given the above setup, the following code returns a list of constraints for 
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20151129 06:20:53 0500  asked a question  How can I programmatically define constraints for minimize_constrained? I'd like to run a minimization problem in several different dimensions, and then find a minimum over the results (for more information on the problem see here). I can easily define both the objective function and the main constraint in a dimensonindependent way with a simple combination of On the other hand, I'm not sure on how to express the fact that every variable should be an element of the interval but I'm worried that using those instead of a pair of constraints for every variable would have a negative effect on 
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20151112 15:21:26 0500  commented answer  Is there a more efficient way to compute the first digit of a number? By the way, is there a particular reason why you used 
20151112 14:29:03 0500  commented answer  Is there a more efficient way to compute the first digit of a number? Can you explain how this works? I have no trouble with the concept of lazy evaluation, but why doesn't 
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20151111 04:33:44 0500  asked a question  Is there a more efficient way to compute the first digit of a number? I need to compute the first digit of some large numbers. So far I've been converting them to strings, although it can be somewhat slow. For example: Is there a faster way to to do this? For my purpose you can assume that all the numbers involved are powers of some small base. 