tmonteil's profile - activity

Sage does not have any precise recommandation about that. I guess you should just follow Python's PEP 515/, which is not that strict either.

You can start from an empty graphics, and add circles to it directly as follows:

sage: G = Graphics()
sage: for c in lis:
....:     G += circle(c, .05, fill=true,  color='red')

Then, you can show it with:

sage: G

Could you please provide the whole code. In particular, how is im defined ?

Ticket ?

I don't know the problem, but when you write things like sum(j*v[3,j] for i in range(0,7)) are you sure that you do not confuse i and j ?

homework ?

It might depend on how "complex" are the expressions.

Apparently trig_reduce is not idempotent and you have to apply it twice to get the correct result:

sage: produit.apply_map(lambda x: x.trig_reduce().trig_reduce())
[ cos(theta1 + theta2 + theta3) -sin(theta1 + theta2 + theta3)]
[ sin(theta1 + theta2 + theta3)  cos(theta1 + theta2 + theta3)]

Could you please provide the code that you used to construct your matrix ?

a is the square root of 3, as the coefficients of this matrix are defined on the number field with defining polynomial x^2 - 3, see:

sage: M = s[2].canonical_matrix()
sage: M.parent()
Full MatrixSpace of 2 by 2 dense matrices over Number Field in a with defining polynomial x^2 - 3 with a = 1.732050807568878?
sage: M
[ 1  0]
[ a -1]
sage: M[1,0]
a
sage: M[1,0]^2
3

What is wrong ? What did you expect ?

Note that this random generation is not uniform on the simplex, as it comes from the projection of an hypercube (think of a square projected on its diagonal).

If you want to consider all the points satisfying some properties, i guess the best way it to consider those points as forming a set. In your case, the set of points is a polytope. By convenience, you can construct it from a linear program as follows:

sage: p = MixedIntegerLinearProgram()
sage: x = p.new_variable(real=True, nonnegative=True)
sage: p.add_constraint(sum(x[i] for i in range(31)) == 1)
sage: P = p.polyhedron() ; P
A 30-dimensional polyhedron in RDF^31 defined as the convex hull of 31 vertices

Then you can do things like:

sage: P.contains([1/2,1/2,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
True
sage: P.contains([1/2,1/3,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
False

sage: P.random_integral_point()
(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)

sage: P.integral_points_count()
31

sage: P.dim()
30

sage: P.is_simplex()
True

sage: P.vertices_list()
...

Could you please provide all the pieces of code that lead to your conclusions (about Glpk being used despite Coin being installed, about the non-working use of alarm, about the working use of @parallel, etc) ?

Anyway, thanks a lot for your exploration of the problem.

Yes i will, but i have to find some time to confirm your hypothesis.

There are at least two possilbilies:

disable the preparser with preparser(False):

sage: type(1)
<type 'sage.rings.integer.Integer'>
sage: preparser(False)
sage: type(1)
<type 'int'>

or use r suffix to say that the numbers are raw:

sage: type(1)
<type 'sage.rings.integer.Integer'>
sage: type(1r)
<type 'int'>
sage: type(1.0r)
<type 'float'>

See https://doc.sagemath.org/html/en/them... and use the binary=True argument.

It is indeed a bug, thanks for reporting,

That said, you should notice that the symbolic ring does not handle numerical values very well, see for example https://trac.sagemath.org/ticket/14821

So here is a workaround:

sage: f = (x+1)^(1/10)+exp(x)
....: f.taylor(x,0,3)
1171/6000*x^3 + 91/200*x^2 + 11/10*x + 2

Note that it is not Python3 specific, i can reproduce it on a Python2 build.

Could you please provide the code that leads to the issue ?

See https://doc.sagemath.org/html/en/refe...

Indeed ! I was thinking of a tutorial instead of just doc, since the way it works is by overriding a default class, not by calling a function. This is a standard pattern in some Python programs, but not in Sage. In particular, i had to copy a part of the source code to insert my hook, so i guess it is not very handy. Perhaps should we propose a better user interface.

You just have to learn the Python language and put your sequence of computations into a function. Basically, you can se Sage as Python bootsted with mathematical typse such as matrices, graphs, etc. There are tons of nice tutorials about the Python language on the web. See also this piece of doc

I tend not to agree with your last statement, if such a weird %iint appears in Sage, it means that there is a missing corresponding Sage function. It is better not to hide the problem, and instead definite such missing function correctly, and it will come with its own latex representation (e.g. dilog(x) is transformed into {\rm Li}_2\left(x\right), not just \dilog(x)).

Okay, i am not sure to understand your question in whole generality. However, here is a solution that could be generalized and adapted to your needs. Let me assume that you want to rewrite the exponents of your expression and that those exponents are polynomials. Working on polynomials has the good property that instead of doing some pattern matching as in the symbolic ring, you can use quotient rings.

For example, here is what you can do in your previous example:

sage: R.<b_m,b_s> = PolynomialRing(QQ)
sage: R
Multivariate Polynomial Ring in b_m, b_s over Rational Field
sage: S = R.quotient(b_m + (b_s-b_m)^3 - b_m)
sage: S
Quotient of Multivariate Polynomial Ring in b_m, b_s over Rational Field by the ideal (-b_m^3 + 3*b_m^2*b_s - 3*b_m*b_s^2 + b_s^3)
sage: p = -b_m^3 + 3*b_m^2*b_s - 3*b_m*b_s^2 + b_s^3 + b_m
sage: p
-b_m^3 + 3*b_m^2*b_s - 3*b_m*b_s^2 + b_s^3 + b_m
sage: S(p)
b_mbar
sage: lift(S(p))
b_m

Now, what you have to do is to walk along the expression and apply this recipe to all exponents of the powers that are encountered. A power is a kind of arithmetic operation, so you will have to override the arithmetic method of ExpressionTreeWalker. Here is how to:

from sage.symbolic.expression_conversions import ExpressionTreeWalker
class RewritePolynomialPowers(ExpressionTreeWalker):
    def __init__(self, ring):
        self.ring = ring
    def arithmetic(self, ex, op):
        if op is operator.pow:
            base, exponent = ex.operands()
            exponent = SR(str(lift(self.ring(exponent))))
            return base ** exponent
        else:
            return reduce(op, map(self, ex.operands()))

Let us try with your example:

sage: var('a,x,b,b_s,b_m')
(a, x, b, b_s, b_m)
sage: f_m = a*x^b
sage: expr = expand(f_m.subs({b : b_m + (b_s-b_m)^3})).derivative(b_m).full_simplify()
sage: RewritePolynomialPowers(S)(expr)
-(3*a*b_m^2 - 6*a*b_m*b_s + 3*a*b_s^2 - a)*x^b_m*log(x)

Please tell if this is sufficient for your general case. Anyway, you see the TreeWalker strategy, you can also replace other kind of operators (composition, derivation, relation,...), see the (not documented) https://doc.sagemath.org/html/en/refe...

I am not an expert of that part of Sage, but other devs will know more.