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

 1 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/ in () /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)  asked Aug 30 '10 allmar 13 ● 3 Kelvin Li 453 ● 1 ● 10 ● 17 you can put
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around the code block to make it more readable (prevent markdown formatting) niles (Aug 30 '10) the same effect has selecting a block of text and clicking the editor button with zeroes and ones. Evgeny (Aug 30 '10) if you select a span of text and click "code formatting" button - the selection will be "backticked" and as a result displayed with a fixed width font. Evgeny (Aug 30 '10)

 2 Hello, Here is a possibility sage: R. = 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 posted Aug 30 '10 vdelecroix 1443 ● 6 ● 22 ● 40 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)