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--- status: moved August 2022
--- author(s):
--- notes: implemented in newring.m2
doc ///
Node
Key
newRing
(newRing, QuotientRing)
(newRing, PolynomialRing)
[newRing, DegreeLift]
[newRing, DegreeMap]
[newRing, DegreeRank]
[newRing, DegreeGroup]
[newRing, Degrees]
[newRing, Global]
[newRing, Heft]
[newRing, Constants]
[newRing, Inverses]
[newRing, Join]
[newRing, Local]
[newRing, MonomialOrder]
[newRing, MonomialSize]
[newRing, VariableBaseName]
[newRing, Variables]
[newRing, SkewCommutative]
[newRing, Weights]
[newRing, WeylAlgebra]
Headline
make a copy of a ring, with some features changed
Usage
S = newRing(R, options)
Inputs
R:{PolynomialRing,QuotientRing}
Variables => List -- see @TO [monoid, Variables]@
VariableBaseName => Symbol -- see @TO [monoid, VariableBaseName]@
Global => Boolean -- see @TO [monoid, Global]@
Local => Boolean -- see @TO [monoid, Local]@
Inverses => Boolean -- see @TO [monoid, Inverses]@
Weights => List -- see @TO [monoid, Weights]@
Degrees => List -- see @TO [monoid, Degrees]@
DegreeMap => Boolean -- see @TO [monoid, DegreeMap]@
DegreeLift => Boolean -- see @TO [monoid, DegreeLift]@
DegreeRank => ZZ -- see @TO [monoid, DegreeRank]@
Heft => List -- see @TO [monoid, Heft]@
Join => Boolean -- see @TO [monoid, Join]@
Constants => Boolean -- see @TO [monoid, Join]@
MonomialOrder => List -- see @TO [monoid, MonomialOrder]@
MonomialSize => ZZ -- see @TO [monoid, MonomialSize]@
SkewCommutative => Boolean -- see @TO [monoid, SkewCommutative]@
WeylAlgebra => List -- see @TO [monoid, WeylAlgebra]@
Outputs
S:Ring
a new ring, constructed in the same way @TT "R"@ was, over the same coefficient
ring, but with the newly specified options overriding those used before.
See @TO monoid@ for a description of those options. If @TT "R"@ was a quotient
ring, then the number of variables must be the same, and S will be a quotient
ring, too, with defining ideal obtained from the old by substituting the new
variables for the old, preserving their order.
Description
Text
If a different number of variables is given with @TO Variables@, then the list
of degrees in @TT "R"@ will be ignored. If a new degree rank is specified with
@TO DegreeRank@ then the list of degrees and the heft vector of @TT "R"@ will be
ignored. If a new nonempty list of degrees is specified with @TO Degrees@, then
the degree rank and the heft vector of @TT "R"@ will be ignored.
Example
R = QQ[x,y, MonomialOrder => Lex, Degrees => {3,5}];
describe newRing(R, MonomialOrder => GRevLex)
describe newRing(R, Variables => 4)
describe newRing(R, Heft => {2})
S = R/(x^2+y^3);
describe newRing(R, Variables => 2)
Text
The default values for the options of @TT "newRing"@ are all set to a
non-accessible private symbol whose name is @TT "nothing"@.
///
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