Rational Point: source code for chart

2025-02-05T17:37:40Z

source code for chart

← Older revision	Revision as of 17:37, 5 February 2025
Line 1:	Line 1:
		<syntaxhighlight lang="R" line="1">
		#! /usr/bin/R -f

		x_data = seq(-5, 5, 0.01)

		Y = function(x) {sqrt(-(x - 4)(x + 3)(x^2 + 1))}
		svg()
		plot( x=c(rev(x_data),x_data), xlab=c("Any 4 points of curve lying on same resolvent parabolic trajectory satisfy resultant","“square dance” equation P (+) Q (+) R (+) S = O with additional “point at infinity” O."),
		y=c(Y(rev(x_data)),-Y(x_data)),
		ylab="Defining algebraic point group operation (+) over a quartic curve:",
		type="l",xlim=c(-3,4),
		main=expression(y^2 == -(x - 4)(x + 3)(x^2 + 1)), lwd=3, col="brown")
		points(-1/2, 15/4)
		points(-1/2, -15/4)
		points(-3, 0)
		points(-3, -0)
		points(4, 0)
		points(4, -0)
		points(3/5, 102/25)
		points(3/5, -102/25)
		points(1077/481, 1723260/231361)
		points(1077/481, -1723260/231361)
		points(-1352/733, 2929542/537289)
		points(-1352/733, -2929542/537289)

		fm4 <- lm(y ~ 1 + x + I(x^2),
		data.frame(x=c(-1/2,3/5,1077/481),
		y=c(-15/4,102/25,1723260/231361)))

		lines(x_data, fm4$coefficients[[3]]x_data^2 + fm4$coefficients[[2]]x_data + fm4$coefficients[[1]], lwd=1.5, col="red")

		fm5 <- lm(y ~ 1 + x + I(x^2),
		data.frame(x=c(-1/2,3/5,1077/481),
		y=c(-15/4,-102/25,1723260/231361)))



		lines(x_data, fm5$coefficients[[3]]x_data^2 + fm5$coefficients[[2]]x_data + fm5$coefficients[[1]])

		fm6 <- lm(y ~ 1 + x + I(x^2),
		data.frame(x=c(-1/2,3/5,1077/481),
		y=c(-15/4,-102/25,-1723260/231361)))



		lines(x_data, fm6$coefficients[[3]]x_data^2 + fm6$coefficients[[2]]x_data + fm6$coefficients[[1]], lwd=1.5, col="blue")


		</syntaxhighlight>

Rational Point at 16:47, 5 February 2025

2025-02-05T16:47:24Z

New page

File:Square dance equations solved.svg - Revision history

Rational Point: source code for chart

Rational Point at 16:47, 5 February 2025