I borrowed/adapted the following code for carrying out a line integral
from a published notebook
var('x,y,t')
F=vector([x^2,x*y])
r=vector([cos(t), sin(t)])
tstart=0
tend=2*pi
integrand = F(x=r[0], y=r[1])*diff(r,t)
As one may observe, integrand is identically 0. The idea is now to
carry out the command
numerical_integral(integrand, tstart, tend)
but that results in the error:
Traceback (most recent call last):
File "", line 1, in <module>
File "/tmp/tmpsnEB5U/___code___.py", line 11, in <module>
numerical_integral(integrand, tstart, tend)
File "", line 1, in <module>
File "integration.pyx", line 207, in
sage.gsl.integration.numerical_integral (sage/gsl/integration.c:1535)
ValueError: Integrand has wrong number of parameters
What is odd is that, if I do a commands like
g(t) = sin(t)^2 + cos(t)^2 - 1
print type(g)
print type(integrand)
numerical_integral(g, tstart, tend)
Sage will tell me both integrand and g are of the same type, and
evaluate the numerical integral for g just fine. I tried also doing
the following: adding an argument on the left-hand side of the
definition for integrand
integrand(t) = F(x=r[0], y=r[1])*diff(r,t)
numerical_integral(integrand, tstart, tend)
which seems to make things suddenly work, and then dropping the
argument on the left side of the definition of g, as in
g = sin(t)^2 + cos(t)^2 - 1
numerical_integral(g, tstart, tend)
which I might have presumed would result in an error, but produced a
value as well. I'm afraid I've gotten very confused about the role of
an argument in the definition of a function. Could someone illuminate
me?
Also, is this a question better suited for sage-edu or some other group?
Thomas L. Scofield
--------------------------------------------------------
Associate Professor
Department of Mathematics and Statistics
Calvin College
--------------------------------------------------------
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