Generator
reciprocity
A generator in the number library, called 4 times across 1 essays. Below: what it draws at its defaults and at each mode an essay asks for, what it checks while drawing, and everywhere it is used.
reciprocity is one function. Everything below came out of it during this
build, at parameters taken from the essays rather than invented for this page — so a figure
here is the same figure a reader meets in an essay, and if the generator changes, this page
changes with it.
At its defaults
show: "gauss"
What it checks while it draws
Collected by running the family and listening to lib/verify.js, not written
here. The count is how many separate times this build put that claim to the test.
- (p | q) comes out of the count above it ×1
- (q | p) comes out of the count below the line ×1
- 3 folds gives the same answer as Euler's criterion ×1
- and every one of them lands in the bottom half ×1
- and their product is minus one to the power of the whole rectangle ×1
- both are odd primes and they are different ×1
- every point is counted exactly once, on one side or the other ×1
- no lattice point lies on the diagonal, because the primes are coprime ×1
- the first prime is a whole number between 3 and 31 ×1
- the folded values are all different ×1
- the modulus is a whole number between 5 and 31 ×1
- the modulus is an odd prime ×1
- the multiplier is a whole number between 2 and 30 ×1
- the multiplier is not a multiple of the modulus ×1
- the points below the line are the sum of the floors of kq/p ×1
- the second prime is a whole number between 3 and 31 ×1
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.