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Cheat sheet Mathematics

Ordering cheat sheet

Non-strict orders: ≤ The symbol ≤ denotes a generalization of “less than or equal”, and it defines either a partial or total ordering over a set P (in the table below a,b ∈ P): Constraint (Non-strict) partial order (Non-strict) total order Reflexivity: a ≤ a x x Antisymmetry: if a ≤ b and b ≤ […]

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Cheat sheet Mathematics

Metrics cheat sheet

Question: When can a distance function d(x,y) be called metric, pseudo-metric, quasi-metric or semi-metric? Constraint Metric Pseudo Quasi Semi Non-negativity: d(x,y) ≥ 0 x x x x Identity of indiscernibles: d(x,y)=0 ⇒ x=y x x x Symmetry: d(x,y) = d(y,x) x x x Triangle inequality: d(x,z) ≤ d(x,y)+d(y,z) x x x Table derived from Wikipedia […]

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Cheat sheet Spatial stuff

Pyramidal tile cache cheat sheet

This table lists the number of total tiles for increasing zoom-level in a tile cache. The tile cache is assumed to be pyramidal: . level 1: 1 tile level 2: 5 tiles level 3: 21 tiles level 4: 85 tiles level 5: 341 tiles level 6: 1,365 tiles level 7: 5,461 tiles level 8: 21,845 […]

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Cheat sheet Systems

Google fusion tables cheat sheet

See below for commands using the Fusion Tables API. Example table is the oldschool message wall public table. Note that examples are shown first without the required url-encoding. Authenticating: Getting the auth token To authenticate you may use the following test account myjdoe. account: myjdoe@gmail.com password: JoesSecret curl -H "Content-type: application/x-www-form-urlencoded" -d "accountType=GOOGLE &Email=myjdoe@gmail.com&Passwd=JoesSecret&service=fusiontables&source=skipperkongen.dk" https://www.google.com/accounts/ClientLogincurl […]