Git issues 3937 1935

[mikestillman]

This PR should fix issues #3937, #1935. It removes the crash when groebner bases are given a Hilbert function "hint", and the data is not correct (so likely gives errors, but still, it should not crash).

Additionally:

• A function canUseHilbertHint has been added, documented, which allows one (and the GB code) to decide if in a given situation, the Hilbert hint is usable.
• Tests have been added
• The abort when discovering a bad Hilbert function is removed. Instead, an exception is issued.
• Note: multi-graded rings will not use any Hilbert hint. If desired, we can likely add this, but it will take some effort and time. Singly graded rings work, as long as all of the variables have positive degree.

[mahrud]

What's the reason behind this change? If this is correct in this case I wonder about tons of other exponents_t initializations which use newarray_atomic (only three exceptions, and this makes it four). The comment before newarray_atomic in newdelete.hpp says:

// this replaces all uses of the construction "new T[n]", with T containing NO pointers.

[mahrud]

I suspect nobody will actually find this node. How about this: add the example of passing the Hilbert option to one of the many nodes about Grobner bases instead, or add a separate node for the option [gb, Hilbert] and link to it from the documentation of gb. I would imagine canUseHilbertHint can stay internal (except imported when needed by MinimalPrimes) in that case.

[d-torrance]

Should checkHilbertHint be exported? We're getting this error:

ii22 : assert checkHilbertHint generators graphIdeal f
../../../../../Macaulay2/tests/normal/ker.m2:24:23:(3):[5]: error: no method for adjacent objects:
            checkHilbertHint (of class Symbol)
    SPACE   | -p_0^4+p_1 -p_0^5+p_2 -p_0^6+p_3 | (of class Matrix)