The class degree is used to represent the values returned by the "deg" function applied to power products and (multivariate) polynomials. Recall that in general a degree is a value in Z^k; the value of k and the way the degree is computed (equiv. weight matrix) are specified when creating the PPOrdering object used for making the PPMonoid of the polynomial ring -- see the function NewPolyRing.
If t1 and t2 are two power products then the degree of their product is just the sum of their individual degrees; and naturally, if t1 divides t2 then the degree of the quotient is the difference of their degrees. The degree values are totally ordered using a lexicographic ordering. Note that a degree may have negative components.
A degree object may be created by using one of the following functions:
degree d1(k); -- create a new degree object with value (0,0,...,0), with k zeroes
wdeg(f) -- where f is a RingElem belonging to a PolyRing
wdeg(t) -- where t is a PPMonoidElem (see PPMonoid)
The following functions are available for objects of type degree:
d1 = d2 -- assignment, d1 must be non-const
cout << d -- print out the degree
GradingDim(d) -- get the number of the components
d[s] -- get the s-th component of the degree (as a BigInt) (for 0 <= s < k)
SetComponent(d, k, n) -- sets the k-th component of d to n (mach.int. or BigInt)
d1 + d2 -- sum
d1 - d2 -- difference (there might be no PP with such a degree)
d1 += d2 -- equivalent to d1 = d1 + d2
d1 -= d2 -- equivalent to d1 = d1 - d2
top(d1, d2) -- coordinate-by-coordinate maximum (a sort of "lcm")
cmp(d1, d2) -- (int) result is <0, =0, >0 according as d1 <,=,> d2
The six comparison operators may be used for comparing degrees (using the lexicographic ordering).
IsZero(d) -- return true iff d is the zero degree
So far the implementation is very simple. The primary design choice was to
use C++ std::vector<>s for holding the values -- indeed a degree object is
just a "wrapped up" vector of values of type degree::ElementType. For a
first implementation this conveniently hides issues of memory management
etc. Since I do not expect huge numbers of degree objects to created and
destroyed, there seems little benefit in trying to use MemPools (except it
might be simpler to detect memory leaks...) I have preferred to make most
functions friends rather than members, mostly because I prefer the syntax
of normal function calls.
The CheckCompatible function is simple so I made it inline. Note the type
of the third argument: it is deliberately not (a reference to) a
std::string because I wanted to avoid calling a ctor for a std::string
unless an error is definitely to be signalled. I made it a private
static member function so that within it there is free access to
myCoords, the data member of a degree object; also the call
degree::CheckCompatible makes it clear that it is special to degrees.
As is generally done in CoCoALib the member function mySetComponent only uses
CoCoA_ASSERT for the index range check. In contrast, the non-member fn SetComponent
always performs a check on the index value. The member fn operator[] also
always performs a check on the index value because it is the only way to get
read access to the degree components. I used MachineInt as the type for
the index to avoid the nasty surprises C++ can spring with silent conversions
between various integer types.
In implementations of functions on degrees I have preferred to place the
lengths of the degree vectors in a const local variable: it seems cleaner
than calling repeatedly myCoords.size(), and might even be fractionally
faster.
operator<< no longer handles the case of one-dimensional
degrees specially so that the value is not printed inside parentheses.
The implementation uses BigInts internally to hold the values of the degree
coordinates. The allows a smooth transition to examples with huge degrees
but could cause some run-time performance degradation. If many complaints
about lack of speed surface, I'll review the implementation.
Is public write-access to the components of a degree object desirable? Or is this a bug?
No special handling for the case of a grading over Z (i.e. k=1) other than for printing. Is this really a shortcoming?
Printing via operator<< is perhaps rather crude?
Is the special printing for k=1 really such a clever idea?
GradingDim(const degree&) seems a bit redundant,
but it is clearer than "dim" or "size"
Is use of MachineInt for the index values such a clever idea?