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2010-08-30 14:09:34 +0100 marked best answer How do I Pass a tuple as an argument for a multivariate polynomial?

Hello,

Here is a possibility

sage: R.<a,b> = PolynomialRing(QQ,['a','b'])
sage: R
Multivariate Polynomial Ring in a, b over Rational Field
sage: P = a^3*b^5+3*a^2+2*b^4
sage: P
sage: P(5,6)   # standard way
974667
sage: P(a=5,b=6)  # another one
974667
sage: v = (5,6)
sage: P(*v)   # the * operator unfold a tuple as 5,6
974667
sage: d = {'a': 5, 'b': 6}
sage: P(**v)  # the ** operator unfold a dictionary as a=5,b=6
974667

But if v is a vector and not a tuple the trick won't work.

Hoping this would be useful, Vincent

2010-08-30 03:57:29 +0100 asked a question How do I Pass a tuple as an argument for a multivariate polynomial?

I can't find any support documentation on this, but I'm sure it must be possible. To give some context, I'm working on a module for invariant theory which allows for computing matrices acting on polynomials:

Say I define a polynomial h(x1,x2) = a*x1^2 + b*x1x2 + c*x2^2 in QQ[x1,x2], and an ordered pair (2-tuple) v = (x1,-x2). How do I pass v such that h(v) is h(x1,-x2) ? In other words, I want to assign each coordinate of the tuple v to it's corresponding coordinate of the argument of h. Actually, a generalization to a polynomial in n variables which takes an n-tuple as an argument would be the most helpful. Below is the error that I received when trying to do this:

TypeError                                 Traceback (most recent call last)

/home/martin/Sage/sage-4.5.2/<ipython console> in <module>()

/home/martin/Sage/sage-4.5.2/local/lib/python2.6/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression.__call__ (sage/symbolic/expression.cpp:15476)()

/home/martin/Sage/sage-4.5.2/local/lib/python2.6/site-packages/sage/symbolic/callable.pyc in _call_element_(self, _the_element, *args, **kwds)

449         d = dict(zip(map(repr, self.arguments()), args))

450         d.update(kwds)

--> 451         return SR(_the_element.substitute(**d))

/home/martin/Sage/sage-4.5.2/local/lib/python2.6/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression.substitute (sage/symbolic/expression.cpp:14850)()

/home/martin/Sage/sage-4.5.2/local/lib/python2.6/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression.coerce_in (sage/symbolic/expression.cpp:10193)()

/home/martin/Sage/sage-4.5.2/local/lib/python2.6/site-packages/sage/structure/parent_old.so in sage.structure.parent_old.Parent._coerce_ (sage/structure/parent_old.c:3288)()

/home/martin/Sage/sage-4.5.2/local/lib/python2.6/site-packages/sage/structure/parent.so in sage.structure.parent.Parent.coerce (sage/structure/parent.c:7045)()

TypeError: no canonical coercion from Ambient free module of rank 2 over the integral domain Multivariate Polynomial Ring in x1, x2 over Rational Field to Callable function ring with arguments (x1, x2)