計算物理

在這個講次當中我們準備了3個程式來加深各位同學對於函數的應用。

範例程式1

def computeHCF(x,y):
    if (x > y):
        smaller = y
    else:
        smaller = x
    for i in range(1, smaller+1):
        if((x % i == 0) and (y % i == 0)):
            hcf = i
            print('公因數=',hcf)
    return hcf
print('計算兩整數的公因數,  請輸入兩個整數：')
num1=int(input("整數1="))
num2=int(input("整數2="))
HCF=computeHCF(num1, num2)
print(num1, num2, '的最大公因數=',HCF)

 
==========================螢幕上的輸出============
計算兩整數的公因數,  請輸入兩個整數：
整數1=12
整數2=18
公因數= 1
公因數= 2
公因數= 3
公因數= 6
12 18 的最大公因數= 6

範例程式2

def rt(a):
    for n in range(1,a+1):
        print('*'*n)
while True:
    b=input("直角三角形的邊長=(輸入0就終止)")
    if(b == 0):  break
    c=int(b)
    rt(c)

==========================螢幕上的輸出============
直角三角形的邊長=(輸入0就終止)3
*
**
***
直角三角形的邊長=(輸入0就終止)6
*
**
***
****
*****
******
直角三角形的邊長=(輸入0就終止)0
直角三角形的邊長=(輸入0就終止)

範例程式3

def fact(n): 	# n是由主程式傳入之參數
    m=1
    for n in range(1,n+1):
        m=m*n
    return m  # 回傳m至主程式的呼叫點
m,n=10,3
Cmn=fact(m)/(fact(n)*fact(m-n))
print ('C(%2d,%2d)=%4d' %(m,n,Cmn))

==========================螢幕上的輸出============
C(10, 3)= 120
=================================================

範例程式4

import math
def root2(a,b,c):
    D=b**2-4.*a*c
    if(D == 0.):
        x1,x2=-b/2./a, -b/2./a
    elif D > 0.:
        x1=(-b+math.sqrt(D))/2./a
        x2=(-b-math.sqrt(D))/2./a
    else:
        import cmath   #有複數的數學函數
        x1=(-b+cmath.sqrt(D))/2./a  #複數開平方
        x2=(-b-cmath.sqrt(D))/2./a
    return (D,x1,x2)  #回傳元組
a,b,c=1.,-2.,-3.
(D,x1,x2)=root2(1.,-2.,-3.)         #以元組方式傳回
print('a,b,c=',a,b,c)
if(D > 0): print('兩實根=',(x1,x2))     #列印元組
else:
    print('D < 0, D=',D)
    print('兩複數根=',x1,x2)
print(' ')
a,b,c=1.,-2.,3.
(D,x1,x2)=root2(1.,-2.,3.)         #以元組方式傳回
print('a,b,c=',a,b,c)
if(D > 0): print('兩實根=',(x1,x2))     #列印元組
else:
    print('D < 0, D=',D)
    print('兩複數根=',x1,x2)

==========================螢幕上的輸出============
a,b,c= 1.0 -2.0 -3.0
兩實根= (3.0, -1.0)
 
a,b,c= 1.0 -2.0 3.0
D < 0, D= -8.0
兩複數根= (1+1.4142135623730951j) (1-1.4142135623730951j)
=================================================

範例程式5

Web VPython 3.2
# filepath: https://physexp.thu.edu.tw/~AP/YC/NUM/HTML/mag-bottle-tr.txt
f = read_local_file(scene.title_anchor)
print(f.name) # The file name
print(f.size) # File size in bytes
print(f.type) # What kind of file
print(f.date) # Creation date if available
print('-------------------')
#print(f.text) # The file contents
f=f.text
a=f
print(type(a))
a=a.strip()
a2=a.split('   ')
b=list(a2)
#print(b)
print('len(b)=',len(b),type(b),type(b[0]),b[0])
for i in range(len(b)):
    b[i]=float(b[i])
    
def traject(b):
    ball = sphere(radius = 0.1, color=vec(1,1,0),make_trail=True, retain=100)
    Nb=len(b)
    #print('Nb=',Nb)
    N=Nb/4
    t=[float(b[i*4+0]) for i in range(N)]
    x=[float(b[i*4+1]) for i in range(N)]
    y=[float(b[i*4+2]) for i in range(N)]
    z=[float(b[i*4+3]) for i in range(N)]
    LX=max(x)
    LY=max(y)
    LZ=max(z)
    sw=LX/100.
    arrX=arrow(pos=vec(0,0,0),axis=vec(LX,0,0),shaftwidth=sw,color=vec(1,0,0))
    arrY=arrow(pos=vec(0,0,0),axis=vec(0,LY,0),shaftwidth=sw,color=vec(0,1,0))
    arrZ=arrow(pos=vec(0,0,0),axis=vec(0,0,LZ),shaftwidth=sw,color=vec(0,0,1))
    ball.pos=vec(x[0],y[0],z[0])
    for i in range(N):
        rate(10)
        ball.pos=vec(x[i],y[i],z[i])    
        #print(t[i],x[i],y[i],z[i])

scene = canvas(width=800, height=800, center=vec(0,0,0),background=vec(0,0,0))
print('====',type(b))
traject(b)

====================螢幕上的輸出============
mag-bottle-tr[1].txt
3.3642e+4
text/plain
2023/3/2
-------------------

len(b)= 3204  
 0.0000
===========================================

PYTHON程式語言的學習-8(函數)