decisions, decisions vs. conventions, conventions ..

a few minutes ago [1] i was latexing and realised that i needed another name for a function .. yet i had already used f, g, and h ..

argh ..

i can't just call it f' ("f prime") either, because i already used (prime) for differentiation of functions on the real line .. and f₀ just looks .. weird:  

i mean, what's the subscript for?

[runs through alphabet]
[sighs]

i guess i'll use u;
it feels the least strange, to me.

the greek letter φ is close to f, but it looks too much like a smooth, compactly-supported function for my taste ..

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odd, how some conventions become crippling.  to me, for instance,

• a and b are points or parameters (or very rarely, indices)
• c is a constant,
• d is the exterior differential,
• e is base e (and occasionally an embedding*)
• f, g, and h are functions,
• i, j, k are indices (with i sometimes the inclusion map [2])
• l denotes a line,
• m and n are natural numbers,
• o is a base point in a space*
• p and q are either points, exponents, or polynomials,
• r is the radius of a ball (occasionally a third polynomial),
• s and t are parametrisation variables,
• u and v are vectorfields,
• w is a weight function*
• x, y, and z are spatial variables.

as for uppercase letters,

• A is a matrix, sometimes a constant,
• B is a ball,
• C is a constant, subject to change, line by line,
• D is the total derivative map,
• E is the base space for a fibre bundle,
• F and G are mappings between spaces,
• H is used for homology,
• I is the identity map,
• J is used for jacobians,
• K is a distorsion function for quasiconformal mappings*
• L is a linear operator, or a space of integrable functions,
• M and N denote sobolev spaces of functions* (on metric spaces)
• O is an open set,
• P is .. an affine hyperplane?  (i rarely use this: huh ..)
• Q is a cube,
• R is the larger of two radii,
• S is a symmetric tensor,
• T is a linear operator between normed linear spaces,
• U is a unitary operator,
• V and W are vector spaces,
• X, Y, and Z are spaces.

and, of course, greek:

• α and β are multi-indices,
• γ is a curve,
• δ and ε are small numbers,
• ζ is an embedding [2]
• η is a standard, smooth mollifier,
• θ is an angle,
• ι is the inclusion map,
• κ denotes curvature,
• λ is an eigenvalue,
• μ and ν are measures,
• ξ are coordinates on a differentiable structure* (or a phase space variable)
• ο looks too much like an o, so it's still a base point,
• π is either a projection map or a homotopy group,
• ρ is the density function to an absolutely continuous measure,
• σ is surface area measure,
• τ is a dummy variable for integration,
• υ, i never use, though Υ is used for jets* (a la viscosity solutions for PDE)
• φ and ψ are test functions,
• χ is a characteristic (indicator) function,
• ω is a solid angle.

[1] .. and yes, clearly i'm blogging now. q-:

[2] i don't do complex analysis unless absolutely necessary.