# Revision history [back]

Regarding your question (1), you can not pass a list of "variables" since they are not defined yet (or there is a chicken-and-egg stuff there). However, you can pass the names of the indeterminates as a list of strings as follows:

sage: B = PolynomialRing(QQ,['a','b','c'])
sage: B
Multivariate Polynomial Ring in a, b, c over Rational Field


Now, if you want the Python name a point to the polynomial indeterminate a, and so on, you have to do:

sage: B.inject_variables()
Defining a, b, c


Regarding your question (2), if i understand your question, it seems you are doing things in the reverse order. What you want are polynomial whose indeterminates are x,y,z, so you will define them over the ring which is made of the polynomials over QQ with variables a,b,c:

sage: B.<a,b,c> = QQ[]; B
Multivariate Polynomial Ring in a, b, c over Rational Field
sage: A.<x,y,z>=B[] ; A
Multivariate Polynomial Ring in x, y, z over Multivariate Polynomial Ring in a, b, c over Rational Field
sage: ex = (1-a^2)*x*y^2+(a-b^2+c)*x*y*z+(b^2-c^2-a)*x^2*z
sage: ex
(-a^2 + 1)*x*y^2 + (b^2 - c^2 - a)*x^2*z + (-b^2 + a + c)*x*y*z
sage: ex.coefficients()
[-a^2 + 1, b^2 - c^2 - a, -b^2 + a + c]
sage: ex.monomials()
[x*y^2, x^2*z, x*y*z]


But also:

sage: ex.dict()
{(1, 1, 1): -b^2 + a + c, (1, 2, 0): -a^2 + 1, (2, 0, 1): b^2 - c^2 - a}
sage: dict(ex)
{-b^2 + a + c: x*y*z, b^2 - c^2 - a: x^2*z, -a^2 + 1: x*y^2}
sage: list(ex)
[(-a^2 + 1, x*y^2), (b^2 - c^2 - a, x^2*z), (-b^2 + a + c, x*y*z)]


Regarding your question (1), you can not pass a list of "variables" since they are not defined yet (or there is a chicken-and-egg stuff there). However, you can pass the names of the indeterminates as a list of strings as follows:

sage: B = PolynomialRing(QQ,['a','b','c'])
sage: B
Multivariate Polynomial Ring in a, b, c over Rational Field


Now, if you want the Python name a point to the polynomial indeterminate a, and so on, you have to do:

sage: B.inject_variables()
Defining a, b, c


Regarding your question (2), if i understand your question, it seems you are doing things in the reverse order. What you want are polynomial whose indeterminates are x,y,z, so you will define them over the ring which is made of the polynomials over QQ with variables a,b,c:

sage: B.<a,b,c> = QQ[]; B
Multivariate Polynomial Ring in a, b, c over Rational Field
sage: A.<x,y,z>=B[] ; A
Multivariate Polynomial Ring in x, y, z over Multivariate Polynomial Ring in a, b, c over Rational Field
sage: ex = (1-a^2)*x*y^2+(a-b^2+c)*x*y*z+(b^2-c^2-a)*x^2*z
sage: ex
(-a^2 + 1)*x*y^2 + (b^2 - c^2 - a)*x^2*z + (-b^2 + a + c)*x*y*z
sage: ex.coefficients()
[-a^2 + 1, b^2 - c^2 - a, -b^2 + a + c]
sage: ex.monomials()
[x*y^2, x^2*z, x*y*z]


But also:

sage: list(ex)
[(-a^2 + 1, x*y^2), (b^2 - c^2 - a, x^2*z), (-b^2 + a + c, x*y*z)]
sage: dict(ex)
{-b^2 + a + c: x*y*z, b^2 - c^2 - a: x^2*z, -a^2 + 1: x*y^2}
sage: ex.dict()
{(1, 1, 1): -b^2 + a + c, (1, 2, 0): -a^2 + 1, (2, 0, 1): b^2 - c^2 - a}
sage: dict(ex)
{-b^2 + a + c: x*y*z, b^2 - c^2 - a: x^2*z, -a^2 + 1: x*y^2}
sage: list(ex)
[(-a^2 + 1, x*y^2), (b^2 - c^2 - a, x^2*z), (-b^2 + a + c, x*y*z)]