>> ch5_symbolic
s1 = sym('x^3-1')
 
s1 =
 
x^3-1
 
factor(s1)   % factor the polynomial
 
ans =
 
(x-1)*(x^2+x+1)
 
pause % hit the carriage return when ready to continue
s2 = sym('(x-3)^2 + (y-4)^2')
 
s2 =
 
(x-3)^2 + (y-4)^2
 
expand(s2)   % multiply all the terms out
 
ans =
 
x^2-6*x+25+y^2-8*y
 
pause % hit the carriage return when ready to continue
collect(s2)  % collect is "kinda" the opposite of "expand"
 
ans =
 
x^2-6*x+9+(y-4)^2
 
pause % hit the carriage return when ready to continue
collect(s2,'y') % the default is to focus on "x", you can force "y"
 
ans =
 
y^2-8*y+(x-3)^2+16
 
pause % hit the carriage return when ready to continue
s3 = sym('sqrt(a^4*b^7)')
 
s3 =
 
sqrt(a^4*b^7)
 
simplify(s3)
 
ans =
 
(a^4*b^7)^(1/2)
 
pause % hit the carriage return when ready to continue
s4 = sym('14*x^2/(22*x*y)')
 
s4 =
 
14*x^2/(22*x*y)
 
simplify(s4)
 
ans =
 
7/11*x/y
 
pause % hit the carriage return when ready to continue
diff(s1)
 
ans =
 
3*x^2
 
pause % hit the carriage return when ready to continue
diff(s2,'x') %differentiate w.r.t. x
 
ans =
 
2*x-6
 
pause % hit the carriage return when ready to continue
diff(s2,'y') %differentiate w.r.t. y
 
ans =
 
2*y-8
 
pause % hit the carriage return when ready to continue
diff(s1,2) % return 2nd derivative
 
ans =
 
6*x
 
pause % hit the carriage return when ready to continue
int('sin(a)')
 
ans =
 
-cos(a)
 
pause % hit the carriage return when ready to continue
int(s1,0.0,2.0) % integrate from x=0 to x=2
 
ans =
 
2
 
pause % hit the carriage return when ready to continue
taylor(s2)
 
ans =
 
9+(y-4)^2-6*x+x^2
 
help taylor % series are powerful

 --- help for sym/taylor.m ---

 TAYLOR Taylor series expansion.
    TAYLOR(f) is the fifth order Maclaurin polynomial approximation to f.
    Three additional parameters can be specified, in almost any order.
    TAYLOR(f,n) is the (n-1)-st order Maclaurin polynomial.
    TAYLOR(f,a) is the Taylor polynomial approximation about point a.
    TAYLOR(f,x) uses the independent variable x instead of FINDSYM(f).
 
    Examples:
       taylor(exp(-x))   returns
          1-x+1/2*x^2-1/6*x^3+1/24*x^4-1/120*x^5
       taylor(log(x),6,1)   returns
          x-1-1/2*(x-1)^2+1/3*(x-1)^3-1/4*(x-1)^4+1/5*(x-1)^5
       taylor(sin(x),pi/2,6)   returns
          1-1/2*(x-1/2*pi)^2+1/24*(x-1/2*pi)^4
       taylor(x^t,3,t)   returns
          1+log(x)*t+1/2*log(x)^2*t^2
 
    See also FINDSYM, SYMSUM.


>> quit

 9426 flops.