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I am trying to numerically integrate a function with respect to one variable, although the function is of more than one variable. An example:

var('x')
var('a')
f(x,a)=a*x
f(x,a)

integral(f(x,a),x,0,1)

produces the correct result of 1/2*a

g(x,a)=(f(x,a).nintegral(x, 0, 1))

Errors with "ValueError: Maxima (via quadpack) cannot compute the integral", but I probably don't have the syntax correct even if that function can do this. Even if a is given a value prior to the g(x,a) definition, it doesn't work.

g(x,a)=numerical_integral(f(x,a),0,1)

Errors with "ValueError: Integrand has wrong number of parameters". I can understand this, as it doesn't quite know what to do with 'a'.

g(x,a)=numerical_integral(f(x,a),0,1, params=[a])
g(x,6)

Gives an incorrect result of 0.3333

g(x,a)=numerical_integral(f(x,a),0,1, params=[6])
g(x,a)

Gives the correct result of 2.99996

h(x,a)=integral(f(x,a),x,0,1)
h(x,6)

Gives the correct result of 3

What is going on with g(x,a) and the "params" vector? Is what I am attempting to do possible?

I would like to make a plot of g(x,a) across a range of a. This is a simplified example, where I could obviously just do it by hand or with a non-numerical integral. The f(x,a) that I am really trying to work with is much more complex. I can upload a .sws workbook with these equations if that helps.

The documentation at http://www.sagemath.org/doc/reference/calculus/sage/gsl/integration.html don't give much to go on with respect to params or nintegral. Any other docs out there I am missing?

Similar to above, the following worked for me from the notebook interface of sage:

os.environ["PATH"]+=":/opt/local/bin"

Octave was installed on my system using MacPorts.

I found that octave.eval('2+2') worked immediately in the notebook, but octave(2+2), required:

octave = Octave()
octave._start()

otherwise it errored with "ValueError: The octave session in which this object was defined is no longer running."

Note: octave.eval returns a string, usually with "ans =", whereas octave() returns a number that I could perform further operations on.

You may want to put octave.quit(True) at the end. I don't understand what is actually going on well, so take my advice with caution.

see also: http://www.sagemath.org/doc/reference/interfaces/sage/interfaces/octave.html