ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 23 Jun 2023 15:52:37 +0200Keep metric purely symbolichttps://ask.sagemath.org/question/69401/keep-metric-purely-symbolic/Is there an easy way to define a purely symbolic riemannian metric on a manifold?
Or do I need to initialize it like this
`g[0,0] = function('g00')(t,x,y,z)`
for example?Fri, 23 Jun 2023 14:03:08 +0200https://ask.sagemath.org/question/69401/keep-metric-purely-symbolic/Answer by eric_g for <p>Is there an easy way to define a purely symbolic riemannian metric on a manifold?
Or do I need to initialize it like this
<code>g[0,0] = function('g00')(t,x,y,z)</code>
for example?</p>
https://ask.sagemath.org/question/69401/keep-metric-purely-symbolic/?answer=69403#post-id-69403At the moment, all tensor fields on manifolds must have expressions in terms of coordinates in one or more charts, These expressions can involve some unspecified functions though, declared via `function`. So yes, the only way to define a generic metric is what you suggest. But in practice, for dimensions larger than 2 or 3, this can lead to untractable computations. Fri, 23 Jun 2023 15:22:24 +0200https://ask.sagemath.org/question/69401/keep-metric-purely-symbolic/?answer=69403#post-id-69403Comment by Loreno Heer for <p>At the moment, all tensor fields on manifolds must have expressions in terms of coordinates in one or more charts, These expressions can involve some unspecified functions though, declared via <code>function</code>. So yes, the only way to define a generic metric is what you suggest. But in practice, for dimensions larger than 2 or 3, this can lead to untractable computations. </p>
https://ask.sagemath.org/question/69401/keep-metric-purely-symbolic/?comment=69404#post-id-69404oh, that is a pity. both in terms of writing it out and computationally. I will then use cadabra2 in the meantime for this.Fri, 23 Jun 2023 15:52:37 +0200https://ask.sagemath.org/question/69401/keep-metric-purely-symbolic/?comment=69404#post-id-69404