MATH 3600 2020-11-20 Matrix multiplication

365 days ago by calkin

 
       
A[0,0] 
       
1
1
A[0,0]=1 
       
A=matrix(2,2,[1,1,1,0]) for i in srange(1000000): A=A^2 A[0,0]=A[0,0]%10^20 A[1,0]=A[1,0]%10^20 A[0,1]=A[0,1]%10^20 A[1,1]=A[1,1]%10^20 show(A) 
       

How many digits in $3^{CUID}$?

log(3.^99000000)/log(10.) 
       
4.72350042172466e7
4.72350042172466e7
log(factorial(52).n())/log(10.) 
       
67.9066483922048
67.9066483922048
int(bin(100),5) 
       
Traceback (click to the left of this block for traceback)
...
ValueError: invalid literal for int() with base 5: '0b1100100'
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_18.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("aW50KGJpbigxMDApLDUp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpbr4E_Y/___code___.py", line 3, in <module>
    exec compile(u'int(bin(_sage_const_100 ),_sage_const_5 )
  File "", line 1, in <module>
    
ValueError: invalid literal for int() with base 5: '0b1100100'
b=bin(100) 
       
int(b,10) 
       
Traceback (click to the left of this block for traceback)
...
ValueError: invalid literal for int() with base 10: '0b1100100'
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_21.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("aW50KGIsMTAp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpCSLd2P/___code___.py", line 3, in <module>
    exec compile(u'int(b,_sage_const_10 )
  File "", line 1, in <module>
    
ValueError: invalid literal for int() with base 10: '0b1100100'