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2020-07-24 15:18:24 +0100 | commented answer | can't solve inequality for independent variable Unfortunately, it does help demonstrating that Mathematica does no better. I guess this is the answer ("Sage can't do what you want"), but I'll give a few days to see if anyone knows more. Thanks. |

2020-07-23 17:26:30 +0100 | asked a question | can't solve inequality for independent variable One of the frustrations I'm always having with Sage is how it tries to "solve" inequalities. For a random example: Which I knew already (since it's just the numerator). Ok, so various signs and things matter, but the fact that it can't even tell me is frustrating. Is there a reason, or a way to convince Sage to actually "solve" these in some way? |

2020-06-04 21:22:28 +0100 | commented answer | abstract index notation and differential geometry Ok that does seem to be a partial solution, but it doesn't allow the metric to be represented with abstract indices. For example, the answer to this problem is generically $C^c_{ab}=2\delta ^c_{(a}\nabla_{b)}\ln \Omega-g_{ab}g^{cd}\nabla_d \ln \Omega$. |

2020-06-02 00:43:51 +0100 | commented answer | abstract index notation and differential geometry Thanks: I will have to work out getting the latest version on my system before testing/marking correct, but it does seem that you've got a solution here. |

2020-05-29 19:40:41 +0100 | asked a question | abstract index notation and differential geometry I am wondering if there are ways to use abstract index notation in sage. For example, could I define the tensor: $$C^c_{ab}=\frac{1}{2}g^{cd}(\tilde{\nabla_a} g_{bd}+\tilde{\nabla_b} g_{ad} - \tilde{\nabla_d} g_{ab})$$ this particular object describes the difference between two connections, $\nabla_a$ and $\tilde{\nabla}_b$. Can we define objects like this an manipulate them in Sage? My confusion comes from the common definition of the connection, a la Which is not directly a 1-tensor. Specifically, I would like to define a metric, $g_{ab}$, and a conformal transformation $\tilde{g_{ab}}=\Omega^2 g_{ab}$, the corresponding connections, and determine the tensor $C^a_{bc}$ for this particular case. (and of course, we know the answer because this the standard approach to conformal transformations in GR). |

2020-02-19 23:01:01 +0100 | commented answer | Can't substitute H=dot(a)/a in SageMath Well, since this is my major frustration with Sage, I |

2020-02-14 21:55:09 +0100 | asked a question | Can't substitute H=dot(a)/a in SageMath Hello all, I'm working with the Friedman equations, and I've gotten them down to the common form presented in terms of the scale factor. MWE incoming: With the result being Which is great, but I really want this to be in terms of the Hubble paramter $H=\dot{a}/a$. I can't make that substitution happen: just spits out the same thing, Any ideas? |

2020-01-18 01:53:44 +0100 | commented answer | Unable to use substitute_function in SageManifolds Tried it both ways and they work. Thanks very much! So the .operator() returns the function, and the .expr() gives the expression of that function? |

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2018-05-07 23:30:42 +0100 | asked a question | Alternating symbols with SageManifolds I would like to utilize the alternating symbol $\epsilon_{abcd}$ in SageManifolds. I've worked out that you can define the volume form like And I can turn this into "the alternating 1-form" by dividing by the determinant of the metric. However, if I try to find the totally upper symbol $\epsilon^{abcd}$, which should just have components +1 and -1, I get Which is just happening because at some point Sage has figured it out needs to keep track of the sign of a. Is there a direct way to define $\epsilon_{abcd}$ without accessing to the volume form at all? Essentially, I want to directly calculate things like the Euler Characteristic (and signature), which look like $$R_{abcd}R_{efgh}\epsilon^{abef}\epsilon^{cdgh}$$ |

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