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2019-07-30 10:47:49 +0100 | marked best answer | Differential forms and tensors Dear all, A long time ago I was trying to implement a SAGE code for working with Differential Forms with values in a certain Lie algebra, but due to my lack of programming knowledge, I couldn't. This kind of objects are important for working with non-Abelin gauge theories. Question Is it possible to define and work with those objects? So far there is no reference of it in the manual. Thank you! |
2019-05-20 14:11:07 +0100 | marked best answer | Size of Labels on a Plot dear all: I'd like to know if there is any way to change the size of the font of labels (in a plot) without changing the size of the numbers on the ticks. Thank you |
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2019-05-17 21:46:48 +0100 | commented answer | Restricting a variable to a (real) range Thank you @dsejas Yes, your comment was incredible useful! It drove me to a nice solution. Since I had a lot of assumptions, I was trying to find a way to drop the last assumption (still don't know it possible), and looking for that I found the |
2019-05-17 16:18:03 +0100 | asked a question | Restricting a variable to a (real) range Hi. I'm solving a differential equation which depends on two parameters $c1$ and $c2$. They are both positive but in order to solve the equation, assume(c2 - 3 > 0) the equation is solved; But imposing Question Is it possible to set a condition like |
2019-05-14 09:41:24 +0100 | asked a question | Solving an ODE and simplifying the result I'm interested in solving the differential equation $$3 h' + 3 h^2 = c_1,$$ where $c_1$ is a positive real number. The above code works, but it's not solved explicitly for $h$, so This gives something like $$h\left(t\right) = \frac{\sqrt{3} \sqrt{c_{1}} {\left(e^{\left(\frac{2}{3} \, \sqrt{3} C \sqrt{c_{1}} + \frac{2}{3} \, \sqrt{3} \sqrt{c_{1}} t\right)} + 1\right)}}{3 \, {\left(e^{\left(\frac{2}{3} \, \sqrt{3} C \sqrt{c_{1}} + \frac{2}{3} \, \sqrt{3} \sqrt{c_{1}} t\right)} - 1\right)}},$$ in sage notation (non-LaTeX) it starts like Question 1: Is there a way to allocate to the solution (i.e. I had to set by hand (it is ease, but it would be nice to automatize the allocation) Then, by simply looking at the solution it is clear that it can be simplified. I tried things like but none of them returns the expected result, which could be obtained from Mathematica's kernel $$ \sqrt{\frac{c_1}{3}} \tanh\left( \sqrt{\frac{c_1}{3}} (t - 3 c_2) \right) $$ Question 2: How could the expression |
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2018-12-04 09:18:37 +0100 | asked a question | Sagemanifold - Connection components from a tensor (not a metric) Dear community. This might sound dump, but I'm trying to determine whether a tensor satisfy the properties of a metric (under certain conditions). Of course it is a (0,2)-symmetric tensor, call it $S$, but I cannot (to my understanding) calculate the (Levi-Civita-like) connection components that would be associated to $S$... unless I declare it as a metric. The way it is implemented makes sense... and it's solid! What I did...?I defined like a metric and calculate the associated connection (and curvatures) Why should I do something else?In the file Question:Is this possible? |
2018-12-04 08:34:54 +0100 | commented answer | How to get the collection of all functions from X to Y in SageMath Thanks for the theory! |
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2018-12-03 19:20:48 +0100 | commented answer | Subtitute functions - in a differential equation - Sagemanifold hehehehe... Thank you again! I almost got it... but I tried |
2018-12-03 19:18:05 +0100 | commented answer | Sagemanifold - `only_nonredundant = True` by default Excellent! Thank you for the answer, and a wonderful use of the |
2018-12-03 18:37:06 +0100 | asked a question | Sagemanifold - `only_nonredundant = True` by default Hi, I find the option |
2018-12-03 18:33:37 +0100 | asked a question | Subtitute functions - in a differential equation - Sagemanifold Dear community, I have a differential equation that depends on a function $\xi(t)$, but is a component of a tensor (calculated with I'd like to define the restriction to $\xi = 0$, and assign it to a new tensor but I get an I know that it works for functions QuestionIs there a way to substitute functions that are not |
2018-11-28 22:16:13 +0100 | commented question | Sagemanifold: autoparallel curve equations Currently I am not at work, I'll upload it tomorrow. Thanks for the interest. |
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2018-11-28 19:13:43 +0100 | asked a question | Sagemanifold: autoparallel curve equations Hello community. I'm interested in calculating the autoparallel curves defined by an affine connection (it has torsion). Following the recipes from the documentation notebooks in the sagemanifold web page I've achieved the goal with ease. However, in the result there is a function $h$, which is related with the torsion of the connection, shows up in the definition of the curve. I expected this function not to show... because one usually argue that the contribution of the antisymmetric part of the connection to the geodesic (or autoparallel in this case) vanishes, based in symmetry arguments (it is contracted with a symmetric tensor). Is the fact that I'm getting a contribution of the torsion in the equations a mistake in the algorithm of the curve equation or is a personal misunderstanding? |
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2018-11-22 14:25:43 +0100 | commented question | Assignation of components of a differential form (or multivector field) in sagemanifold @eric_g: Thank you! I didn't know that... I was assigning the components one by one! (there was the tedious part) |
2018-11-22 10:30:47 +0100 | asked a question | Assignation of components of a differential form (or multivector field) in sagemanifold Dear all. I've crossed with the task of assigning components to a multivector field, and it's tedious! (specially higher ranks) Question: Is there an efficient way of assigning components to tensors with symmetries? |
2018-11-22 09:30:38 +0100 | asked a question | Tensor density in sagemanifolds? Hello community. I've just realized that within the class Well, more generally... Is there a way to assign a density weight to a tensor? |
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2018-08-28 15:09:20 +0100 | answered a question | How can I calculate this sum? (accept both sage(cocalc) and by hand) I'm certain that the question is not correctly asked. Notice that in the sentence,
there is no sum at all! However, it seems that the OP wants to know if the expresion $$\frac{1}{1 - (x + x^2)^2} = \sum_{n = 0}^\infty (x + x^2)^{2n},$$ is valid. If that is the question... I'd say yes, as long as $(x + x^2)^2 <1.$ |