vector

https://www.youtube.com/watch?v=8xsIsyHYrMU 

https://www.youtube.com/watch?v=ZW6OD1kVMAw

三角測量

 law of sin

http://math1.ck.tp.edu.tw/%E6%9E%97%E4%BF%A1%E5%AE%89/%E5%AD%B8%E8%A1%93%E7%A0%94%E7%A9%B6/%E4%B8%8A%E8%AA%B2%E8%AC%9B%E7%BE%A9/%E7%AC%AC%E4%BA%8C%E5%86%8A/2-3%E6%AD%A3%E5%BC%A6%E9%A4%98%E5%BC%A6%E5%AE%9A%E7%90%86.pdf

https://blog.xuite.net/wang620628/twblog/126093831

https://www.youtube.com/watch?v=b5nUmrh90fY

https://www.youtube.com/watch?v=bYAf-3cn4V4

law of cos

Heron's formula

http://www2.chsh.chc.edu.tw/bee/1050206/heron%20formula.pdf

三角形的角平分線

三角形的中線

平行四邊形定理

journal of combinatroics

The Electronic Journal of Combinatorics (E-JC)

https://www.combinatorics.org/ojs/index.php/eljc

graph labeling

Joseph A Gallian

https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS6

Joseph A Gallian

https://scholar.google.com/scholar?hl=zh-TW&as_sdt=0%2C5&q=joseph+a+gallian&oq=joseph+

maxima command

algebra

ratsimp() 化簡

expand() 展開

factor()    因式分解

kill(x)      kill the x variable

kill(all)     kill all variables

 

x:123        assign x=123

f(x):=x^2＋2*x+1    define function of x =x^2+2x+1

sum(i,i,1,10)   sum i , i from 1 to 10

%i            image number

%pi         

%e

%phi        the  golden mean (1+sqrt(5))/2

%gamma    the Euler-Mascheroni constant

inf              real positive  inifinity

minf          real negative inifinity

abs()        absolute

sqrt()       square root

float()      float number

compare()  compare numbers

is()

load("filename")

solve([equation],[variable])

round()

floor()

print()

%i1) powerdisp;
(%o1)                                false
(%i2) x^2+2*x+1;
                                           2
(%o2)                            x  + 2 x + 1
(%i3) powerdisp: true;
(%o3)                                true
(%i4) x^2+2*x+1;
                                                             2
(%o4)                            1 + 2 x + x

radexpand

https://maxima-discuss.narkive.com/K3S0HYnY/radcan-vs-radexpand-and-documentation

 

evaluate

 

Option variable: radexpand

Default value: true

radexpand controls some simplifications of radicals.

When radexpand is all, causes nth roots of factors of a product which are powers of n to be pulled outside of the radical. E.g. if radexpand is all, sqrt (16*x^2) simplifies to 4*x.

More particularly, consider sqrt (x^2).

• If radexpand is all or assume (x > 0) has been executed, sqrt(x^2) simplifies to x.
• If radexpand is true and domain is real (its default), sqrt(x^2) simplifies to abs(x).
• If radexpand is false, or radexpand is true and domain is complex, sqrt(x^2) is not simplified.

Note that domain only matters when radexpand is true 

reference

https://maxima.sourceforge.io/docs/manual/maxima_46.html. 

 

evaluate

 

8.1 Functions and Variables for Evaluation

https://maxima.sourceforge.io/docs/manual/maxima_43.html

4.2 Functions and Variables for Command Line

https://maxima.sourceforge.io/docs/manual/maxima_8.html

 

3. Entering commands

https://maxima.sourceforge.io/docs/xmaxima/xmaxima_3.html

ctl-j

ctl-u

alt-p  to search backwards

alt-n  to search forward

Complex Number

 

cabs                           absolute of complex number

conjugate

carg                           angle of complex number

realpart

imagpart

polarform

rectform

 
For further ways to compute with complex numbers, see the functions rectform, realpart, imagpart, carg, conjugate and polarform.

 

Matrix

https://maxima.sourceforge.io/docs/manual/maxima_113.html#Introduction-to-Matrices-and-Linear-Algebra

 

matrix()

determinant()

invert()

transpose() 

length()

Plot

plot2d([equation],[x,lower, upper])

plot3d([equation],[x,lower,upper],[y,lower,upper])

vector

 https://maxima.sourceforge.io/docs/manual/maxima_116.html#Vectors

a.b        a dot b

axb        a cross b

         load("vect" );

         express(a~b);

 

https://maxima.sourceforge.io/docs/manual/maxima_131.html#Sums-Products-and-Series

permutation/ combination

 

load(functs)

permutation (n, r)

combination (n, r)

sequence/ series

arithmetic (a, d, n)

geometric (a, r, n)

harmonic (a, b, c, n)

geosum (a, r, n)

Set

https://maxima.surceforge.io/docs/manualo/maxima_156.html#Sets

 

Differential/Integrate

 

diff()

integrate()

limit()

 

HP laser jet driver for Linux

 How to install latest HPLIP on my Ubuntu to support my HP printer and/or scanner?

 

真空炮 Vacuum bazooka

 https://archive.iypt.org/problems/

30th IYPT (2017)

17. Vacuum bazooka

A ‘vacuum bazooka’ can be built with a simple plastic pipe, a light projectile, and a vacuum cleaner. Build such a device and maximise the muzzle velocity.

17.真空火箭筒

可以用一個簡單的塑料管，一個輕彈丸和一個真空吸塵器來建造一個“真空火箭筒”。建造這樣的裝置，並使槍口速度最大化。

self avoiding walk

The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk

• Neal Madras & 
• Alan D. Sokal 

 https://link.springer.com/article/10.1007/BF01022990