Dear supporters,
take two polynomial rings:
sage: R1=PolynomialRing(QQ,['x2','x1'])
sage: R2=PolynomialRing(QQ,['x4', 'x3', 'x1'])
Assume that I have an element p of R1 that only contains x1 but not
x2. I would like to be able to transform it into an element of R2 by
mapping R1('x1') to R2('x2').
Since R2(p) wouldn't work (no coercion map), I see two ways:
sage: f = R1.hom([1,'x1'],R2)
sage: f(p)
and
sage: R2(str(p))
Singular provides the command 'imap' for a reasonably fast name-
preserving map between rings. Is there a similar command in Sage?
If not: I have the above situation rather frequently, but always with
different rings (so that I can not use one homomorphism f repeatedly
for many polynomials).
What method would you recommend?
I see that
sage: timeit('f = R1.hom([1,"x1"],R2)')
625 loops, best of 3: 435 µs per loop
sage: timeit('g = R2(str(R1("x1^2+2*x1")))')
625 loops, best of 3: 216 µs per loop
Does this mean that using the string representation is faster than
creating and using a homomorphism?
Cheers,
Simon
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