ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 12 Mar 2020 14:24:18 +0100How can I perform matrix operations in a transcendental extension of Q?https://ask.sagemath.org/question/50223/how-can-i-perform-matrix-operations-in-a-transcendental-extension-of-q/ I have three variables $p_w, p_i, p_f$. I want to construct a matrix whose entries are members are rational polynomials in these variables and perform computations with this matrix (ultimately diagonalize it and obtain a general formula for its $n$-th power). But I want to do this computation symbolically, treating the three variables as transcendental elements adjoined to $\mathbb Q$. How an I do this?JackMThu, 12 Mar 2020 14:24:18 +0100https://ask.sagemath.org/question/50223/polynomials rings over transcendental field extensionshttps://ask.sagemath.org/question/7779/polynomials-rings-over-transcendental-field-extensions/Hi all:
It looks like working with polynomial rings over transcendental field
extensions still doesn't work in Sage. Am i doing something wrong
below? The same computation works in Singular, giving the correct
answer of the ideal generated by x*y.
Alex
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| Sage Version 4.6, Release Date: 2010-10-30 |
| Type notebook() for the GUI, and license() for information. |
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sage: R0.<q> = PolynomialRing(QQ); R0
Univariate Polynomial Ring in q over Rational Field
sage: k= FractionField(R0); k
Fraction Field of Univariate Polynomial Ring in q over Rational Field
sage: R.<x,y> = PolynomialRing(k); R
Multivariate Polynomial Ring in x, y over Fraction Field of Univariate Polynomial Ring in q over Rational Field
sage: I = R.ideal((q*x*y)^2); I
Ideal (q^2*x^2*y^2) of Multivariate Polynomial Ring in x, y over Fraction Field of Univariate Polynomial Ring in q over Rational Field
sage: I.radical()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/Users/arai021/<ipython console> in <module>()
/Applications/sage/local/lib/python2.6/site-packages/sage/rings/polynomial/multi_polynomial_ideal.pyc in __call__(self, *args, **kwds)
405 if not R.base_ring().is_field():
406 raise ValueError("Coefficient ring must be a field for function '%s'."%(self.f.__name__))
--> 407 return self.f(self._instance, *args, **kwds)
408
409 require_field = RequireField
/Applications/sage/local/lib/python2.6/site-packages/sage/rings/polynomial/multi_polynomial_ideal.pyc in wrapper(*args, **kwds)
367 """
368 with RedSBContext():
--> 369 return func(*args, **kwds)
370
371 from sage.misc.sageinspect import sage_getsource
/Applications/sage/local/lib/python2.6/site-packages/sage/rings/polynomial/multi_polynomial_ideal.pyc in radical(self)
1404 import sage.libs.singular
1405 radical = sage.libs.singular.ff.primdec__lib.radical
-> 1406 r = radical(self)
1407
1408 S = self.ring()
/Applications/sage/local/lib/python2.6/site-packages/sage/libs/singular/function.so in sage.libs.singular.function.SingularFunction.__call__ (sage/libs/singular/function.cpp:9618)()
TypeError: Cannot call Singular function 'radical' with ring parameter of type '<class 'sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict_domain'>'
araichevTue, 30 Nov 2010 16:11:34 +0100https://ask.sagemath.org/question/7779/