# CHE315 Sample Page

## 2764 days ago by joel.boyd

'Below are several examples of sage utilities that you might find useful in PChem. Note that to execute a line command, you must either click "evaluate" or hit shift-enter on your keyboard.'
 Syntax Error: 'Below are several examples of sage utilities that you might find useful in PChem. Syntax Error: 'Below are several examples of sage utilities that you might find useful in PChem.
solve(x^2+x-6==0,x)
 [x == -3, x == 2] [x == -3, x == 2]
integral(x^2,x)
 1/3*x^3 1/3*x^3
integral(x^2,3,8)
 485/3 485/3
diff(x^2+5*x,x)
 2*x + 5 2*x + 5
diff(x^2+5*x,x,2)
 2 2
diff?
 File: /usr/local/sage/local/lib/python2.6/site-packages/sage/calculus/functional.py Type: Definition: diff(f, *args, **kwds) Docstring: The derivative of f. Repeated differentiation is supported by the syntax given in the examples below. ALIAS: diff EXAMPLES: We differentiate a callable symbolic function: sage: f(x,y) = x*y + sin(x^2) + e^(-x) sage: f (x, y) |--> x*y + e^(-x) + sin(x^2) sage: derivative(f, x) (x, y) |--> 2*x*cos(x^2) + y - e^(-x) sage: derivative(f, y) (x, y) |--> x  We differentiate a polynomial: sage: t = polygen(QQ, 't') sage: f = (1-t)^5; f -t^5 + 5*t^4 - 10*t^3 + 10*t^2 - 5*t + 1 sage: derivative(f) -5*t^4 + 20*t^3 - 30*t^2 + 20*t - 5 sage: derivative(f, t) -5*t^4 + 20*t^3 - 30*t^2 + 20*t - 5 sage: derivative(f, t, t) -20*t^3 + 60*t^2 - 60*t + 20 sage: derivative(f, t, 2) -20*t^3 + 60*t^2 - 60*t + 20 sage: derivative(f, 2) -20*t^3 + 60*t^2 - 60*t + 20  We differentiate a symbolic expression: sage: var('a x') (a, x) sage: f = exp(sin(a - x^2))/x sage: derivative(f, x) -2*e^(sin(-x^2 + a))*cos(-x^2 + a) - e^(sin(-x^2 + a))/x^2 sage: derivative(f, a) e^(sin(-x^2 + a))*cos(-x^2 + a)/x  Syntax for repeated differentiation: sage: R. = PolynomialRing(QQ) sage: f = u^4*v^5 sage: derivative(f, u) 4*u^3*v^5 sage: f.derivative(u) # can always use method notation too 4*u^3*v^5  sage: derivative(f, u, u) 12*u^2*v^5 sage: derivative(f, u, u, u) 24*u*v^5 sage: derivative(f, u, 3) 24*u*v^5  sage: derivative(f, u, v) 20*u^3*v^4 sage: derivative(f, u, 2, v) 60*u^2*v^4 sage: derivative(f, u, v, 2) 80*u^3*v^3 sage: derivative(f, [u, v, v]) 80*u^3*v^3  File: /usr/local/sage/local/lib/python2.6/site-packages/sage/calculus/functional.py Type: Definition: diff(f, *args, **kwds) Docstring: The derivative of f. Repeated differentiation is supported by the syntax given in the examples below. ALIAS: diff EXAMPLES: We differentiate a callable symbolic function: sage: f(x,y) = x*y + sin(x^2) + e^(-x) sage: f (x, y) |--> x*y + e^(-x) + sin(x^2) sage: derivative(f, x) (x, y) |--> 2*x*cos(x^2) + y - e^(-x) sage: derivative(f, y) (x, y) |--> x  We differentiate a polynomial: sage: t = polygen(QQ, 't') sage: f = (1-t)^5; f -t^5 + 5*t^4 - 10*t^3 + 10*t^2 - 5*t + 1 sage: derivative(f) -5*t^4 + 20*t^3 - 30*t^2 + 20*t - 5 sage: derivative(f, t) -5*t^4 + 20*t^3 - 30*t^2 + 20*t - 5 sage: derivative(f, t, t) -20*t^3 + 60*t^2 - 60*t + 20 sage: derivative(f, t, 2) -20*t^3 + 60*t^2 - 60*t + 20 sage: derivative(f, 2) -20*t^3 + 60*t^2 - 60*t + 20  We differentiate a symbolic expression: sage: var('a x') (a, x) sage: f = exp(sin(a - x^2))/x sage: derivative(f, x) -2*e^(sin(-x^2 + a))*cos(-x^2 + a) - e^(sin(-x^2 + a))/x^2 sage: derivative(f, a) e^(sin(-x^2 + a))*cos(-x^2 + a)/x  Syntax for repeated differentiation: sage: R. = PolynomialRing(QQ) sage: f = u^4*v^5 sage: derivative(f, u) 4*u^3*v^5 sage: f.derivative(u) # can always use method notation too 4*u^3*v^5  sage: derivative(f, u, u) 12*u^2*v^5 sage: derivative(f, u, u, u) 24*u*v^5 sage: derivative(f, u, 3) 24*u*v^5  sage: derivative(f, u, v) 20*u^3*v^4 sage: derivative(f, u, 2, v) 60*u^2*v^4 sage: derivative(f, u, v, 2) 80*u^3*v^3 sage: derivative(f, [u, v, v]) 80*u^3*v^3 
plot(sin(x),x,-pi,pi)  diff(sin(x))
 cos(x) cos(x)
diff(cos(x))
 -sin(x) -sin(x)
integral(sin(x),x,-pi,pi)
 0 0
diff(3*x^2*a+y,x)
 6*a*x 6*a*x
a,y=var('a,y')