How do I Pass a tuple as an argument for a multivariate polynomial?

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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)

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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

link

posted Aug 30 '10

vdelecroix
811 ● 4 ● 11 ● 26

updated Aug 30 '10

And for the many-variable case, you can use `d = dict(zip(R.gens(),v))` and `h.subs(d)` (I think the post above forgot to mention this last part). If v really has to be a vector, you could probably convert it to a tuple or list first. niles (Aug 30 '10)

Niles: for me P.subs(a=5,b=6) does not work for an element of a polynomial ring (but does for symbolic expressions). vdelecroix (Aug 30 '10)

Digression: flatten() is useful in related use-cases. The max_level keyword argument is very useful when there is multiple nesting. ccanonc (Aug 30 '10)

vdelecroix: I think you have to pass the dictionary object to `subs()` niles (Aug 30 '10)

What about the efficiency of each/any of the above methods? In particular, is unpacking the dictionary quicker than unpacking the list? tdstephens3 (Jun 14 '11)

How do I Pass a tuple as an argument for a multivariate polynomial?

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