Tuesday, March 27, 2012

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]

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 ..

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.

1 comment:

Anonymous said...

You could use capital greek letters such as Gamma, Delta, Sigma, Pi, Lambda, and Omega. Wait, can't use those either. About the only thing left is the Batman symbol.