Design #1653
Discriminant: return value
Description
To which ring should the return value of Discriminant belong?
/**/ use QQ[x,y]; /**/ f := y^2-2; /**/ discriminant(f); 8 /**/ RingOf(It); --> ???
Related issues
History
#1
Updated by John Abbott about 2 years ago
Updated by discriminant is actually two functions: univariate inputs, and multivariate input with specified indet.
The multivariate version has to return a result in the original polynomial ring.
The expectation for the univariate version is that the discriminant is an element of the coeff ring,
BUT at the moment CoCoA returns a result in the poly ring.
We could get an "inconsistency" by supplying a univariate input and specifying its indet:
/**/ use QQ[x,y]; /**/ f := y^2-2; /**/ discriminant(f); 8 /**/ discriminant(f,y); 8
I wanted to find a polynomial whose discriminant is divisible by 30, but my program did not work as expected:
for-loop f := some-univariate-poly in QQ[x] d := discriminant(f); if gcd(d,30) = 30 then println f; endif; endfor;
This code never printed anything... because the gcd was computed in
QQ[x], so always came out to 1.If the discriminant has been in the coeff ring (
QQ) then an error would have been signalled (sinceQQ is not a "true gcd domain"). I wasted some time tracking down the problem.#2
Updated by John Abbott about 2 years ago
- Status changed from New to In Progress
- % Done changed from 0 to 10
Anna agrees with what I'd like to do.
Should something similar be done for resultant too?
#3
Updated by John Abbott about 2 years ago
- Assignee set to John Abbott
- % Done changed from 10 to 20
Since resultant is closely related to discriminant they should have compatible behaviour.
This includes presumably adding a 2-arg version of resultant which requires that its args are univariate.
Strangely, resultant is built-in while discriminant is not. This is inconsistent, and should be remedied!
#4
Updated by John Abbott about 2 years ago
- Related to Bug #1656: SEGV in resultant added
#5
Updated by John Abbott about 2 years ago
- Status changed from In Progress to Resolved
- % Done changed from 20 to 80
There are now 2 resultant functions and 2 discriminant functions(in each case with or without specified indet).
If no indet is specified the inputs must be univariate, and the result is in the coeff ring!
Must still update doc, and add some tests.
Still slightly unsure about some edge cases: e.g. resultant gives error if either poly is zero, and discriminant gives error if the poly is constant.
#6
Updated by John Abbott about 2 years ago
The old impl is still in coclib.cpkg5 but renamed to discriminant_old. I'll delete it soon (after some more testing).
#7
Updated by John Abbott about 2 years ago
- Status changed from Resolved to Closed
- % Done changed from 80 to 100
- Estimated time set to 3.50 h