I want to construct a table with a header like
$[\alpha_{0,0}, \alpha_{0,1},...\alpha_{1,0},\alpha_{1,1},...]$
but I do not want to enter the indices by hand. How can I do ?
Also I find the show result of the following command a little bit strange
α = var("α_", n=11,latex_name='\alpha_')
αα = list(α)
show(αα)
αα
Can some one explain
Doubly indexed variables are often useful.
No easy construct exists like for simply indexed ones though.
That said, list comprehension makes it relatively easy.
Here is one way to obtain the requested indexing.
sage: α = [var(f"α_{i}_{j}", latex_name=fr"\alpha_{{{i},{j}}}")
....: for i in range(3) for j in range(3)]
Not sure of what your "double indexed variable means. One possible interpretation is a two-dimensionnal array of symbolic variables, flattened as needed :
sage: DIVar=[[var("alpha_%d_%d"%(u,v), latex_name="\\alpha_{%d,%d}"%(u, v)) for v in range(3)] for u in range(2)]
which is $$ \left[\left[{\alpha_{0,0}}, {\alpha_{0,1}}, {\alpha_{0,2}}\right], \left[{\alpha_{1,0}}, {\alpha_{1,1}}, {\alpha_{1,2}}\right]\right] $$
and can be used as:
sage: table([[f(u) for u in flatten(DIVar)] for f in (sin, cos, tan)], header_row=flatten(DIVar), header_column=[function("f")]+[sin, cos, tan])
f | alpha_0_0 alpha_0_1 alpha_0_2 alpha_1_0 alpha_1_1 alpha_1_2
+-----+----------------+----------------+----------------+----------------+----------------+----------------+
sin | sin(alpha_0_0) sin(alpha_0_1) sin(alpha_0_2) sin(alpha_1_0) sin(alpha_1_1) sin(alpha_1_2)
cos | cos(alpha_0_0) cos(alpha_0_1) cos(alpha_0_2) cos(alpha_1_0) cos(alpha_1_1) cos(alpha_1_2)
tan | tan(alpha_0_0) tan(alpha_0_1) tan(alpha_0_2) tan(alpha_1_0) tan(alpha_1_1) tan(alpha_1_2)
[ No LaTeX output here : the generated latex code uses tabular, not understood by ask.sagemath.org's Markdown. I know that there is a way to create an HTML version accepted here, but, for dear life, I'm unable to remember it... ].
HTH,
Asked: 2022-10-20 17:14:02 +0100
Seen: 165 times
Last updated: Oct 22 '22
Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.
I think you should use
'\\alpha'for the latex_name instead. Two slashes at the start because a backslash is a special character and needs to be "escaped". No trailing_because Sage seems to insert that automatically in LaTeX names for indexed variables like this.Your example gives one index. Can you give us an example with two indexes ?