Laurent Claessens's profile - activity

Hi all

I can understand the following somewhat surprising result :

sage: var('x,y')
(x, y)
sage: min(x,y)
x

A friend of mine wants to plot3d the function that a human should write f(x,y)=min(|x|,|y|)

what she does is

sage: f(x,y)=min(abs(x),abs(y))
sage: plot3d(f,(x,-2,2),(y,-2,2))

of course, it does not produce the expected result because of what I said in introduction about min(x,y). By the way :

sage: f(4,1)  
4

So ... well ... what do I have to say to her ? What is the best way to plot a function (in the math sense of the term) when it cannot be managed by a function (in the Sage sense of the term).

The following works :

sage: f=lambda x,y:min(abs(x),abs(y))

I guess that

def f(x,y):
   return min(abs(x),abs(y))

will also work.

So my questions are :

1. why min(x,y)=x ?
2. how can I "predict" if such or such function will not work using the simple declaration f(x,y)=blahblah ?
3. what is the best way to deal with such cases ?

Thanks for any help

have a good night

Laurent Claessens (on the night timezone :) )

Hi all.

I got the following problem:

sage: plot(symbolic_expression(x).function(x))

this raises

ValueError: free variable: x |--> x

If I replace x by anything else (but 1*x) it works fine.

How can I do ?

My rationale behind my question is that I have a class which takes a function as argument and can perform many thinks on it, among other the plot. I made the following :

class MyFunction(object):
    def __init__(self,f):
        self.f=symbolic_expression(f).function(x)
    def plot(self):
        return plot(self.f)

My point in doing so is that I have to accept, as input f expressions like x**2, 2, g.diff(x) (where g is an other function) and so on. In these cases, it turns out that I need to use the symbolic_expression trick in order to be sure that what I have is a function (need for numerical integration for example)

My questions :

1. Can I do otherwise in __init__ in order to be sure to be able to use numerical integration, derivative, ... on self.f ?

2. If not, how can I plot when the input is simply "x" ?

This is a sequel of my question about plotting level set.

In the following, G is a circle :

sage: f(x,y)=x**2+y**2  
sage: G=implicit_plot(f==1,(x,-2,2),(y,-3,3))
sage: G.get_minmax_data()
{'xmin': -2.0, 'ymin': -3.0, 'ymax': 3.0, 'xmax': 2.0}

The "correct" get_minmax_data sould be

{'xmin': -1.0, 'ymin': -1.0, 'ymax': 1.0, 'xmax': 1.0}

As far as I understood the code (and the thread "Retrieving xy data from implicit plots" on Sage-support), the following is the relevant part :

xy_data_arrays = numpy.asarray([[[func(x, y) for x in xsrange(*ranges[0],include_endpoint=True)]
                                 for y in xsrange(*ranges[1], include_endpoint=True)]
                                for func in g],dtype=float)

in ../plot/contour_plot.py

My questions are :

1. can I retrieve that xy_data_array ?

2. If I analyse xy_data_array, I suppose that extracting the point with lowest x-component such that the value is positive will provide me the "correct" xmin of the plot. I'm wrong ?

I'm trying to draw level set of a function f:R^2->R, that is the set of solutions of f(x,y)=h for a given h.

For that purpose I wrote the following

#! /usr/bin/sage -python
# -*- coding: utf8 -*-

from sage.all import *

def level_curve(f,h):
    solutions_list = solve(f==h,y)
return [sol.rhs() for sol in solutions_list]

var('x,y')
f=x+y+2
for g in level_curve(f,3):
print g

print "-----"

f=x**2+y**2
for g in level_curve(f,3):
    print g

This works, but I'm not satisfied principally because I got the level sets under the form of a list of functions. Moreover it will not work if the level set is vertical.

Thus I would prefer to get the solution under the form of a parametric curve.

Does Sage provides something for that ?

Thanks for your answer, tmonteil. That solves the equation with enough accuracy for my purpose but it does not solves my full problem because I have a system. Ultimately I would like to know the intersection points of two curves. In my example the second curve was too easy : y-1=0. Since many painting softwares are able to fill the region between two curves (e.g. pstricks), I guess this is possible ...

Hi all.

I have the equations

y - 1 == 0,
y == 1/3*x + sin(2*x)

and I want solutions. I know by the intermediate value theorem that there are two solutions : about x=0.5 and x=1.25. I'd like Sage to give me these solutions. I already tried to_poly_solve=True and/or explicit_solutions=True.

As an example of failure :

sage: solve(  1/3*x + sin(2*x)==1,x,explicit_solutions=True  )
[]

What can I do ?

Thanks Laurent Claessens

Hello

sage: from __future__ import unicode_literals
sage: R=PolynomialRing(QQ,'x')

TypeError Traceback (most recent call last)

/home/moky/script/<ipython console=""> in <module>()

/home/moky/Sage/local/lib/python2.7/site-packages/sage/rings/polynomial/polynomial_ring_constructor.pyc in PolynomialRing(base_ring, arg1, arg2, sparse, order, names, name, implementation) 425 if R is None: 426 raise TypeError("invalid input (%s, %s, %s) to PolynomialRing function; please see the docstring for that function"%( --> 427 base_ring, arg1, arg2)) 428 429 return R

TypeError: invalid input (Rational Field, x, None) to PolynomialRing function; please see the docstring for that function

I guess this is the same kind of problem that the one in this question

By the way, this is "fixed" by using str :

sage: R=PolynomialRing(QQ,str('x'))
sage: f=R.lagrange_polynomial([(0,1),(1,4)]);f
3*x + 1

Does it answer the question ?

sage:s=sin(x)                                                                  
sage: s
sin(x)
sage: f=s.function(x)
sage: f
x |--> sin(x)

By the way, what is the correct way to know the global xmin,xmax,ymin and ymax of a function ? A 3-digit approximation is enough. Up to now I'm using get_minmax_data, but is it the correct way ?

Hello

I'd like to understand the rationale behind the ymin value in the get_minmax_data of a parametric curve that have always y=0:

sage: f(x)=sin(x)
sage: g(x)=0
sage: P=parametric_plot((f,g),(-pi/2,2*pi))
sage: P.get_minmax_data()['ymin']
-1.0

I would have expected ymin to be 0. Is is a bug or is it something I don't understand ?

Yes, `min_symbolic` is the answer. Thanks :)

I can't find this, but I'm pretty sure there is another question with this on ask.sagemath.org.

sage: var('y')
y
sage: min(x,y)
x
sage: min_symbolic(x,y)
min(x, y)

I think if you use the latter, all should be well. I hope? Don't have time to try now. Good luck!