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These look like `P_{n,k}(x,y) = U_n(x * cos(k*pi/(n+1)) + y * sin(k*pi/(n+1)))`, orthogonal on the unweighted unit disk.
Sparse differentiation is trivial (using ultraspherical generalizations), bu…
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Hi! I'm working on problems with data defined on the n-sphere (n >= 128 or so). From looking around the documentation it seems like this library doesn't support that--do I have the right? Are you fami…
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This continues on from the discussion from #395. I just found another class of operator being the diagonal conversion between Ultraspherical and Jacobi, which requires the recurrence.
One pattern…
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This metaticket tracks efforts to remove the usage of pexpect for calling maxima, either by using `maxima_lib` or replacing it altogether. Code that is dependent on the maxima expect interface is in…
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I am somewhat puzzled about what exactly is happening when computing derivatives and conversions on 2d Chebyshev product spaces. Some enlightenment would be greatly appreciated. This is also related t…
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This is perhaps a duplicate request, but I couldn't find a previous issue about this.
Currently, the display of union types makes it difficult to detect where one type ends and the other begins:
!…
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At the moment just the Chebyshev polynomials are symbolic. Missing are `hermite`, `laguerre`, `legendreP`, `legendreQ`, `ultraspherical` (=`gegenbauer`), and, while the Stirling and Euler polynomial…
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running Helmholtz rectangle PDE example on this page
https://github.com/JuliaApproximation/ApproxFunExamples/blob/master/PDEs/Rectangle%20PDEs.ipynb
```julia
d = (-1.0..1.0)^2
Δ = Laplacian(d…
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If `L` is a linop, `spy(L)` should draw a continuous figure, and that's what it does in v4. At present in v5, however, it draws a discrete matrix. I understand from @asgeirbirkis that this may have …
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There are issues with the current connection coefficient matrix introducing bad conditioning:
```julia
V = SymTriOperator([zeros(5); -ones(6); zeros(10); -ones(7)],zeros(4))
J = -Δ + V
Λ, U = eig(…