﻿ maxima軟體使用的問題(頁 1) - 數學軟體 - Math Pro 數學補給站

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### maxima軟體使用的問題

１、不等式求解，例如2x+5<8
２、絕對值求解，例如|3x-7|=8
３、有理化分母，例如1/(sqrt(3)+sqrt(2))會變成sqrt(3)-sqrt(2)

[color=green]不等式求解[/color]
[color=red](%o1)[/color]　C:/PROGRA~1/MAXIMA~1.2/share/maxima/5.19.2/share/contrib/solve_rat_ineq.mac

[color=green]解一次不等式[/color]
[color=red](%i2)[/color]　[color=blue]solve_rat_ineq(2*x+5<8);[/color]
[color=red](%o2)[/color]　$$\displaystyle [ [x<\frac{3}{2}] ]$$

[color=green]解二次不等式[/color]
[color=red](%i3)[/color]　[color=blue]solve_rat_ineq(x^2+3*x+2>=0);[/color]
[color=red](%o3)[/color]　$$\displaystyle [ [x \le -2],[x \ge -1] ]$$

[color=green]解高次不等式[/color]
[color=red](%i4)[/color]　[color=blue]solve_rat_ineq((x-2)^3*(x+5)^5*(x-1)>0);[/color]
[color=red](%o4)[/color]　$$\displaystyle [ [x>-5,x<1],[x>2] ]$$

[color=green]絕對值求解[/color]
[color=red](%o5)[/color]　C:/PROGRA~1/MAXIMA~1.2/share/maxima/5.19.2/share/contrib/fourier_elim/fourier_elim.lisp

[color=green]解絕對值方程式[/color]
[color=red](%i6)[/color]　[color=blue]fourier_elim([abs(3*x-7)=8],[x]);[/color]
[color=red](%o6)[/color]　$$\displaystyle [x=5]$$ or $$[x=-\frac{1}{3}]$$

[color=green]解絕對值不等式
[url=http://www.ma.utexas.edu/pipermail/maxima/2008/011599.html]http://www.ma.utexas.edu/pipermail/maxima/2008/011599.html[/url][/color]
[color=red](%i7)[/color]　[color=blue]fourier_elim([abs(x - abs(5-x)) < 1],[x]);[/color]
[color=red](%o7)[/color]　$$\displaystyle [2<x,x<3]$$

[color=green]有理化分母

I have two expressions, test1=1/sqrt(2) and test2=2*sqrt(2-sqrt(2))/sqrt(2)...[/color]
[color=red](%i8)[/color]　[color=blue]algebraic : true;[/color]
[color=red](%o8)[/color]　true

[color=red](%i9)[/color]　[color=blue]ratsimp(1/(sqrt(3) + sqrt(2)));[/color]
[color=red](%o9)[/color]　$$\sqrt{3}-\sqrt{2}$$

[color=red](%i10)[/color]　[color=blue]ratsimp(1/(5^(1/3) - 2^(1/3)));[/color]
[color=red](%o10)[/color]　$$\displaystyle \frac{5^{2/3}+2^{1/3}5^{1/3}+2^{2/3}}{3}$$

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[url]http://www.math.utexas.edu/pipermail/maxima/2009/[/url]