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.Wed, 28 Jul 2021 19:15:54 +0200Polynomial ring conversion errorhttps://ask.sagemath.org/question/58137/polynomial-ring-conversion-error/I am trying to recursively solve a (zero-dimensional) system of polynomial equations in multiple variables by calculating elimination ideals, solving the resulting univariate polynomials algebraically and plugging the roots in to the original equations in order to remove a variable.
For this, it is necessary to observe within Sage that after plugging in a value for one variable, the result is then a polynomial in fewer variables. The following code shows an example where the coercion into a polynomial ring in fewer variables works in the first step but fails in the second (although in both steps the polynomial does not even contain the variable to be eliminated):
R.<x, y, s, t> = QQ[]
g = x * y
f1 = PolynomialRing(QQ, t)(t - 1)
L1.<a1> = QQ.extension(f1)
R1 = PolynomialRing(L1, [x, y, s])
g = g.change_ring(L1) # allow coefficients in L1
g = g(x, y, s, a1) # plug in t := a1
g = R1(g) # regard as polynomial in fewer variables
assert parent(g) == R1 # works
f2 = PolynomialRing(L1, s)(s - 1)
L2.<a2> = L1.extension(f2)
R2 = PolynomialRing(L2, [x, y])
g = g.change_ring(L2)
g = g(x, y, a2)
g = R2(g) # fails: "TypeError: not a constant polynomial"
(Note that this is a toy example, my code tries to achieve the same for arbitrary $R$, $f_i$'s and $g$.)Wed, 28 Jul 2021 16:30:25 +0200https://ask.sagemath.org/question/58137/polynomial-ring-conversion-error/Answer by FabianG for <p>I am trying to recursively solve a (zero-dimensional) system of polynomial equations in multiple variables by calculating elimination ideals, solving the resulting univariate polynomials algebraically and plugging the roots in to the original equations in order to remove a variable.</p>
<p>For this, it is necessary to observe within Sage that after plugging in a value for one variable, the result is then a polynomial in fewer variables. The following code shows an example where the coercion into a polynomial ring in fewer variables works in the first step but fails in the second (although in both steps the polynomial does not even contain the variable to be eliminated):</p>
<pre><code>R.<x, y, s, t> = QQ[]
g = x * y
f1 = PolynomialRing(QQ, t)(t - 1)
L1.<a1> = QQ.extension(f1)
R1 = PolynomialRing(L1, [x, y, s])
g = g.change_ring(L1) # allow coefficients in L1
g = g(x, y, s, a1) # plug in t := a1
g = R1(g) # regard as polynomial in fewer variables
assert parent(g) == R1 # works
f2 = PolynomialRing(L1, s)(s - 1)
L2.<a2> = L1.extension(f2)
R2 = PolynomialRing(L2, [x, y])
g = g.change_ring(L2)
g = g(x, y, a2)
g = R2(g) # fails: "TypeError: not a constant polynomial"
</code></pre>
<p>(Note that this is a toy example, my code tries to achieve the same for arbitrary $R$, $f_i$'s and $g$.)</p>
https://ask.sagemath.org/question/58137/polynomial-ring-conversion-error/?answer=58138#post-id-58138The issue is that `x, y` still refer to the old variables in the polynomial ring with four variables. It works when adding the lines
x, y, s = R1.gens()
and
x, y = R2.gens()
respectively.
For debugging `MPolynomial_element`s, the underlying `.dict()` field is helpful.
Wed, 28 Jul 2021 19:15:54 +0200https://ask.sagemath.org/question/58137/polynomial-ring-conversion-error/?answer=58138#post-id-58138