Hi
I am trying to use plot functions for the first time in sage - apologies if
this is a dumb question for a change.
I have a square matrix M of fixed complex numbers which are then all
multiplied by a different phase depending on which column they are in. (In
the 2x2 example below M=[a,b;c,d] and column 1 is multiplied by
exp(i*theta) and column 2 is multiplied by exp(i*phi) ). I then take
another fixed matrix A away from M and take f=det(M-A).abs() as my output.
I have explicitly written this formula for A = [1,1;0,0] below. So the
function I would like to plot is f as a function of theta and phi (in this
case).
a = 1/2
b = - i/3
c = 1/4
d = i/5
theta, phi = var('theta,phi')
f(theta,phi) = ( (a*exp(i*theta)-1)*d*exp(i*phi) -
(b*exp(i*phi)-1)*c*exp(i*theta) ) . abs()
plot3d(f, (theta,0,pi), (phi,0,pi))
No matter how I try to do this, even if I explicitly write out the complex
conjugates of each element, I get what for me is a record-length screed of
error stuff ending in 'TypeError: unable to coerce to a real number',
originating
in the command 'plot3d(...etc...)'. I have attached a text file with the
full output of one of my attempts.
I can see that in a way I am asking a lot of the interpreter; but then
again I feel I have explicitly made the thing real by the time it gets to
be an input for the plot3d function.
Is there any way around this, or do I have to start writing complexes as
a+bi etc and do it the hard way?
Many thanks
Gary
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Traceback (most recent call last): theta, phi = var('theta,phi')
File "", line 1, in <module>
File "/tmp/tmpKH82DM/___code___.py", line 13, in <module>
plot3d(f,(theta,_sage_const_0 ,pi),(phi,_sage_const_0 ,pi))
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/plot/plot3d/plot3d.py",
line 840, in plot3d
P=parametric_plot3d.parametric_plot3d((u,v,f), urange, vrange, **kwds)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/plot/plot3d/parametric_plot3d.py",
line 513, in parametric_plot3d
G = _parametric_plot3d_surface(f, urange, vrange, plot_points=plot_points,
boundary_style=boundary_style, **kwds)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/plot/plot3d/parametric_plot3d.py",
line 619, in _parametric_plot3d_surface
g, ranges = setup_for_eval_on_grid(f, [urange,vrange], plot_points)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/plot/misc.py", line
148, in setup_for_eval_on_grid
return fast_float(funcs, *vars,**options), [tuple(range+[range_step]) for
range,range_step in zip(ranges, range_steps)]
File "fast_eval.pyx", line 1357, in sage.ext.fast_eval.fast_float
(sage/ext/fast_eval.c:9278)
File "fast_eval.pyx", line 1372, in sage.ext.fast_eval.fast_float
(sage/ext/fast_eval.c:9483)
File "fast_callable.pyx", line 420, in sage.ext.fast_callable.fast_callable
(sage/ext/fast_callable.c:3619)
File "expression.pyx", line 8954, in
sage.symbolic.expression.Expression._fast_callable_
(sage/symbolic/expression.cpp:36693)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1431, in fast_callable
return FastCallableConverter(ex, etb)()
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 213, in __call__
return self.arithmetic(div, div.operator())
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1371, in arithmetic
return reduce(lambda x,y: self.etb.call(operator, x,y), operands)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1371, in <lambda>
return reduce(lambda x,y: self.etb.call(operator, x,y), operands)
File "fast_callable.pyx", line 685, in
sage.ext.fast_callable.ExpressionTreeBuilder.call
(sage/ext/fast_callable.c:5588)
File "fast_callable.pyx", line 565, in
sage.ext.fast_callable.ExpressionTreeBuilder.__call__
(sage/ext/fast_callable.c:4837)
File "expression.pyx", line 8954, in
sage.symbolic.expression.Expression._fast_callable_
(sage/symbolic/expression.cpp:36693)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1431, in fast_callable
return FastCallableConverter(ex, etb)()
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 214, in __call__
return self.arithmetic(ex, operator)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1371, in arithmetic
return reduce(lambda x,y: self.etb.call(operator, x,y), operands)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1371, in <lambda>
return reduce(lambda x,y: self.etb.call(operator, x,y), operands)
File "fast_callable.pyx", line 685, in
sage.ext.fast_callable.ExpressionTreeBuilder.call
(sage/ext/fast_callable.c:5588)
File "fast_callable.pyx", line 565, in
sage.ext.fast_callable.ExpressionTreeBuilder.__call__
(sage/ext/fast_callable.c:4837)
File "expression.pyx", line 8954, in
sage.symbolic.expression.Expression._fast_callable_
(sage/symbolic/expression.cpp:36693)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1431, in fast_callable
return FastCallableConverter(ex, etb)()
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 213, in __call__
return self.arithmetic(div, div.operator())
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1371, in arithmetic
return reduce(lambda x,y: self.etb.call(operator, x,y), operands)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1371, in <lambda>
return reduce(lambda x,y: self.etb.call(operator, x,y), operands)
File "fast_callable.pyx", line 685, in
sage.ext.fast_callable.ExpressionTreeBuilder.call
(sage/ext/fast_callable.c:5588)
File "fast_callable.pyx", line 565, in
sage.ext.fast_callable.ExpressionTreeBuilder.__call__
(sage/ext/fast_callable.c:4837)
File "expression.pyx", line 8954, in
sage.symbolic.expression.Expression._fast_callable_
(sage/symbolic/expression.cpp:36693)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1431, in fast_callable
return FastCallableConverter(ex, etb)()
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 214, in __call__
return self.arithmetic(ex, operator)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1371, in arithmetic
return reduce(lambda x,y: self.etb.call(operator, x,y), operands)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1371, in <lambda>
return reduce(lambda x,y: self.etb.call(operator, x,y), operands)
File "fast_callable.pyx", line 685, in
sage.ext.fast_callable.ExpressionTreeBuilder.call
(sage/ext/fast_callable.c:5588)
File "fast_callable.pyx", line 565, in
sage.ext.fast_callable.ExpressionTreeBuilder.__call__
(sage/ext/fast_callable.c:4837)
File "expression.pyx", line 8954, in
sage.symbolic.expression.Expression._fast_callable_
(sage/symbolic/expression.cpp:36693)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1431, in fast_callable
return FastCallableConverter(ex, etb)()
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 213, in __call__
return self.arithmetic(div, div.operator())
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1371, in arithmetic
return reduce(lambda x,y: self.etb.call(operator, x,y), operands)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1371, in <lambda>
return reduce(lambda x,y: self.etb.call(operator, x,y), operands)
File "fast_callable.pyx", line 685, in
sage.ext.fast_callable.ExpressionTreeBuilder.call
(sage/ext/fast_callable.c:5588)
File "fast_callable.pyx", line 565, in
sage.ext.fast_callable.ExpressionTreeBuilder.__call__
(sage/ext/fast_callable.c:4837)
File "expression.pyx", line 8954, in
sage.symbolic.expression.Expression._fast_callable_
(sage/symbolic/expression.cpp:36693)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1431, in fast_callable
return FastCallableConverter(ex, etb)()
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 220, in __call__
return self.composition(ex, operator)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1409, in composition
return self.etb.call(function, *ex.operands())
File "fast_callable.pyx", line 685, in
sage.ext.fast_callable.ExpressionTreeBuilder.call
(sage/ext/fast_callable.c:5588)
File "fast_callable.pyx", line 565, in
sage.ext.fast_callable.ExpressionTreeBuilder.__call__
(sage/ext/fast_callable.c:4837)
File "expression.pyx", line 8954, in
sage.symbolic.expression.Expression._fast_callable_
(sage/symbolic/expression.cpp:36693)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1431, in fast_callable
return FastCallableConverter(ex, etb)()
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 213, in __call__
return self.arithmetic(div, div.operator())
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1371, in arithmetic
return reduce(lambda x,y: self.etb.call(operator, x,y), operands)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1371, in <lambda>
return reduce(lambda x,y: self.etb.call(operator, x,y), operands)
File "fast_callable.pyx", line 685, in
sage.ext.fast_callable.ExpressionTreeBuilder.call
(sage/ext/fast_callable.c:5588)
File "fast_callable.pyx", line 565, in
sage.ext.fast_callable.ExpressionTreeBuilder.__call__
(sage/ext/fast_callable.c:4837)
File "expression.pyx", line 8954, in
sage.symbolic.expression.Expression._fast_callable_
(sage/symbolic/expression.cpp:36693)
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 1431, in fast_callable
return FastCallableConverter(ex, etb)()
File
"/home/sage/sage-5.7/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py",
line 204, in __call__
raise err
TypeError: unable to coerce to a real number
