Re: [sage-support] Re: naive question
Thanks. I was wondering why declaring the polynomial ring helped, but
this helps me understand.
Fernando
On 3/7/2020 3:00 PM, Simon King wrote:
On 2020-03-07, Eric Gourgoulhon wrote:
You should use simplify_full() instead of simplify():
Or you should rather use *polynomials* instead of general symbolic
variables, provided of course that all your expressions are multivariate
rational functions (which is the case here):
sage: var('s t')
(s, t)
sage: R. = QQ[]
sage: thirdroot = ((s^2 - 1)*t^2 - s^2 + 1)/(s^2 + 2*s*t + t^2)
sage: thirdroot = ((s^2 - 1)*t^2 - s^2 + 1)/(s^2 + 2*s*t + t^2)
sage: factor(thirdroot + 1)
(s*t + 1)^2/(s + t)^2
sage: factor(thirdroot + 1)
(s + t)^-2 * (s*t + 1)^2
sage: a = thirdroot + 1 - (s*t + 1)^2/(s+t)^2
sage: a
((s^2 - 1)*t^2 - s^2 + 1)/(s^2 + 2*s*t + t^2) - (s*t + 1)^2/(s + t)^2 + 1
sage: a.simplify_full()
0
sage: a = thirdroot + 1 - (s*t + 1)^2/(s+t)^2; a
0
That's because thirdroot is an element of the quotient field of a
polynomial ring, which does automatic simplifications (which in the
special context of polynomials is a lot easier than in the general
context of symbolic variables).
Best regards,
Simon
--
==
Fernando Q. Gouvea
Carter Professor of Mathematics
Colby College
Mayflower Hill 5836
Waterville, ME 04901
fqgou...@colby.edu http://www.colby.edu/~fqgouvea
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[sage-support] Re: naive question
On 2020-03-07, Eric Gourgoulhon wrote:
> You should use simplify_full() instead of simplify():
Or you should rather use *polynomials* instead of general symbolic
variables, provided of course that all your expressions are multivariate
rational functions (which is the case here):
> sage: var('s t')
> (s, t)
sage: R. = QQ[]
> sage: thirdroot = ((s^2 - 1)*t^2 - s^2 + 1)/(s^2 + 2*s*t + t^2)
sage: thirdroot = ((s^2 - 1)*t^2 - s^2 + 1)/(s^2 + 2*s*t + t^2)
> sage: factor(thirdroot + 1)
> (s*t + 1)^2/(s + t)^2
sage: factor(thirdroot + 1)
(s + t)^-2 * (s*t + 1)^2
> sage: a = thirdroot + 1 - (s*t + 1)^2/(s+t)^2
> sage: a
> ((s^2 - 1)*t^2 - s^2 + 1)/(s^2 + 2*s*t + t^2) - (s*t + 1)^2/(s + t)^2 + 1
> sage: a.simplify_full()
> 0
sage: a = thirdroot + 1 - (s*t + 1)^2/(s+t)^2; a
0
That's because thirdroot is an element of the quotient field of a
polynomial ring, which does automatic simplifications (which in the
special context of polynomials is a lot easier than in the general
context of symbolic variables).
Best regards,
Simon
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[sage-support] Re: naive question
You should use simplify_full() instead of simplify():
sage: var('s t')
(s, t)
sage: thirdroot = ((s^2 - 1)*t^2 - s^2 + 1)/(s^2 + 2*s*t + t^2)
sage: factor(thirdroot + 1)
(s*t + 1)^2/(s + t)^2
sage: a = thirdroot + 1 - (s*t + 1)^2/(s+t)^2
sage: a
((s^2 - 1)*t^2 - s^2 + 1)/(s^2 + 2*s*t + t^2) - (s*t + 1)^2/(s + t)^2 + 1
sage: a.simplify_full()
0
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