# semi colons add new line and are important to the outcome of code
# how to multiply
3*5 ;
# how to divide
8/4 ;
# how to add
2+3 ;
# how to subtract
5-2 ;
# how to solve exponents
2^3 ;
# how to solve integer division
8//4 ;
# how to write square root
sqrt(36) ;
# not an exact square root
numerical_approx(sqrt(30)) ;
# numerical apporximation shortcut is uppercase N
N(sqrt(30)) ;
# if you want to find the Nth root ; 16 to the 4th root
16^(1/4) ;
# how to find factorial
factorial (5) ;
# the approximation of pi
N(pi)
# how to make the amount of place values you want , comma digits
N(pi,digits=4)
# print natural log (ln)
N(log(1))
# common log you add ,10
N(log(10),10)
#a log with your own base
N(log(4),2)
#exponential function.. e to the power of (number)
N(exp(2))
# practice proble #1
N((5^3)-(3/(2^3)))
#practice problem #2
N(log(9),digits=4)-7*(4/15)
# practice #3 solution is t=ln(7/5)/ln(1+.004)
N((ln(7/5))/(ln(1+0.004)))
#all variations of sqrt
sqrt(4,all=true)
sqrt(-4,all=true)
#how to find trig functions
#sine function
N(sin(pi/17))
sin(pi)
#defining variables
x,y,z=var('x,y,z')
print(4*x-5*y-z==9)
#value of variables and find missing one
x=0;
y=-2;
z=4*x-5*x-9
print('the value of z',z)
# -x+2y=5
# 2x-y=-1
#coefficient matrix
A=matrix(2,2,[-1,2,2,-1])
print(A)
C=matrix(1,2,[5,1])
print(C)
#augmented matrix
B=matrix(2,3,[-1,2,5,2,-1,-1])
D=B.rref()
print(D)
print('x=',D[0,2],',y=',D[1,2])