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Returns some c
, where c
is an equation from the basis whose leading monomial divides m
.
Remark: if the current ring does not satisfy the property
∀ (k : Nat) (a : α), k ≠ 0 → OfNat.ofNat (α := α) k * a = 0 → a = 0
then the leading coefficient of the equation must also divide k
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Returns some c
, where c
is an equation from the basis whose leading monomial divides some
monomial in p
.
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Simplifies d.p
using c
, and returns an extended polynomial derivation.
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Simplified d.p
using the current basis, and returns the extended polynomial derivation.
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Simplifies c₁
using c₂
.
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Simplifies c₁
using c₂
exhaustively.
Simplify the given equation constraint using the current basis.
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Returns true
if c.p
is the constant polynomial.
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Simplifies and checks whether the resulting constraint is trivial (i.e., 0 = 0
),
or inconsistent (i.e., k = 0
where k % c != 0
for a comm-ring with characteristic c
),
and returns none
. Otherwise, returns the simplified constraint.
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Tries to convert the leading monomial into a monic one.
It exploits the fact that given a polynomial with leading coefficient k
,
if the ring has a nonzero characteristic p
and gcd k p = 1
, then
k
has an inverse.
It also handles the easy case where k
is -1
.
Remark: if the ring implements the class NoNatZeroDivisors
, then
the coefficients are divided by the gcd of all coefficients.
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Returns true
if c.d.p
is the constant polynomial.