[Merged by Bors] - feat: add circle averages#24427
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PR summary 9cdc811252Import changes for modified filesNo significant changes to the import graph Import changes for all files
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@sgouezel Thank you for the improvements. All implemented. |
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For a function `f` on the complex plane, introduce the notation `circleAverage f c R` as a shorthand for the average of `f` on the circle with center `c` and radius `R`. Averages of this form are typically used in analysis of one complex variable. ### Raison d'Être Like `IntervalAverage,` this notion exists as a convenience. It avoids the hassle of manually eliminating `2 * π` every time an average is computed. At least for the moment, it seems that the simplifier is not built to cancel repeating factors in non-trivial formulas. ### Why not use `IntervalAverage`? Two reasons: - Length: `circleAverage` is shorter and easier to read than the interval average of `f (circleMap c R θ)`, taken over the interval `0..2 * π`. This is an issue in computations, where splitting the circle average of a sum into a sum of circle averages quickly leads for lengthy formulas unfit for human consumption. - Ease of use: Manipulating `IntervalAverage`s by applying standard theorems from mathlib often leads to expressions of the form `(f + g) (circleMap c R θ)`, `f (circleMap c R θ) + g (circleMap c R θ) ` and `(f + g) ∘ (circleMap c R)` that are not equal enough for tactics like `rw`.
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For a function `f` on the complex plane, introduce the notation `circleAverage f c R` as a shorthand for the average of `f` on the circle with center `c` and radius `R`. Averages of this form are typically used in analysis of one complex variable. ### Raison d'Être Like `IntervalAverage,` this notion exists as a convenience. It avoids the hassle of manually eliminating `2 * π` every time an average is computed. At least for the moment, it seems that the simplifier is not built to cancel repeating factors in non-trivial formulas. ### Why not use `IntervalAverage`? Two reasons: - Length: `circleAverage` is shorter and easier to read than the interval average of `f (circleMap c R θ)`, taken over the interval `0..2 * π`. This is an issue in computations, where splitting the circle average of a sum into a sum of circle averages quickly leads for lengthy formulas unfit for human consumption. - Ease of use: Manipulating `IntervalAverage`s by applying standard theorems from mathlib often leads to expressions of the form `(f + g) (circleMap c R θ)`, `f (circleMap c R θ) + g (circleMap c R θ) ` and `(f + g) ∘ (circleMap c R)` that are not equal enough for tactics like `rw`.
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For a function `f` on the complex plane, introduce the notation `circleAverage f c R` as a shorthand for the average of `f` on the circle with center `c` and radius `R`. Averages of this form are typically used in analysis of one complex variable. ### Raison d'Être Like `IntervalAverage,` this notion exists as a convenience. It avoids the hassle of manually eliminating `2 * π` every time an average is computed. At least for the moment, it seems that the simplifier is not built to cancel repeating factors in non-trivial formulas. ### Why not use `IntervalAverage`? Two reasons: - Length: `circleAverage` is shorter and easier to read than the interval average of `f (circleMap c R θ)`, taken over the interval `0..2 * π`. This is an issue in computations, where splitting the circle average of a sum into a sum of circle averages quickly leads for lengthy formulas unfit for human consumption. - Ease of use: Manipulating `IntervalAverage`s by applying standard theorems from mathlib often leads to expressions of the form `(f + g) (circleMap c R θ)`, `f (circleMap c R θ) + g (circleMap c R θ) ` and `(f + g) ∘ (circleMap c R)` that are not equal enough for tactics like `rw`.
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For a function
fon the complex plane, introduce the notationcircleAverage f c Ras a shorthand for the average offon the circle with centercand radiusR. Averages of this form are typically used in analysis of one complex variable.Raison d'Être
Like
IntervalAverage,this notion exists as a convenience. It avoids the hassle of manually eliminating2 * πevery time an average is computed. At least for the moment, it seems that the simplifier is not built to cancel repeating factors in non-trivial formulas.Why not use
IntervalAverage?Two reasons:
Length:
circleAverageis shorter and easier to read than the interval average off (circleMap c R θ), taken over the interval0..2 * π. This is an issue in computations, where splitting the circle average of a sum into a sum of circle averages quickly leads for lengthy formulas unfit for human consumption.Ease of use: Manipulating
IntervalAverages by applying standard theorems from mathlib often leads to expressions of the form(f + g) (circleMap c R θ),f (circleMap c R θ) + g (circleMap c R θ)and(f + g) ∘ (circleMap c R)that are not equal enough for tactics likerw.