Struct RealProjectiveSpace 

pub struct RealProjectiveSpace<A: Algebra> {
    algebra: Arc<A>,
    pub min: i32,
    pub max: Option<i32>,
    pub clear_bottom: bool,
}

This is $\mathbb{RP}_{\mathrm{min}}^{\mathrm{max}}$. The cohomology is the subquotient of $\mathbb{F}_2[x^\pm]$ given by elements of degree between min and max (inclusive)

The clear_bottom option, if selected, mods out by the elements in the $A(2)$ submodule generated by degrees less than min. This is useful for approximating $\mathrm{tmf} \wedge \mathbb{RP}_{-\infty}^n$, c.f. Proposition 2.2 of Bailey and Ricka. Note that this quotient always has minimum degree -1 mod 8.

Fields

algebra: Arc<A>

min: i32

max: Option<i32>

clear_bottom: bool

Implementations

impl<A: Algebra> RealProjectiveSpace<A>

where for<'a> &'a A: TryInto<&'a SteenrodAlgebra>,

pub fn new( algebra: Arc<A>, min: i32, max: Option<i32>, clear_bottom: bool, ) -> Self

impl<A: Algebra> RealProjectiveSpace<A>

pub fn from_json(algebra: Arc<A>, json: &Value) -> Result<Self>

pub fn to_json(&self, json: &mut Value)

Trait Implementations

impl<A: Algebra> Display for RealProjectiveSpace<A>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<A: Algebra> Module for RealProjectiveSpace<A>

where for<'a> &'a A: TryInto<&'a SteenrodAlgebra>,

type Algebra = A

fn algebra(&self) -> Arc<A>

The algebra the module is over.

fn min_degree(&self) -> i32

The minimum degree of the module, which is required to be bounded below

fn max_computed_degree(&self) -> i32

The maximum t for which the module is fully defined at t. See Module documentation for more details.

fn dimension(&self, degree: i32) -> usize

The dimension of a module at the given degree

fn basis_element_to_string(&self, degree: i32, _idx: usize) -> String

The name of a basis element. This is useful for debugging and printing results.

fn act_on_basis( &self, result: FpSliceMut<'_>, coeff: u32, op_degree: i32, op_index: usize, mod_degree: i32, mod_index: usize, )

fn max_degree(&self) -> Option<i32>

max_degree is the a degree such that if t > max_degree, then self.dimension(t) = 0.

fn compute_basis(&self, degree: i32)

Compute internal data of the module so that we can query information up to degree degree. This should be run by the user whenever they want to query such information.

fn is_unit(&self) -> bool

Whether this is the unit module.

fn prime(&self) -> ValidPrime

The prime the module is over, which should be equal to the prime of the algebra.

fn max_generator_degree(&self) -> Option<i32>

Maximum degree of a generator under the Steenrod action. Every element in higher degree must be obtainable from applying a Steenrod action to a lower degree element.

fn total_dimension(&self) -> usize

fn act( &self, result: FpSliceMut<'_>, coeff: u32, op_degree: i32, op_index: usize, input_degree: i32, input: FpSlice<'_>, )

The length of input need not be equal to the dimension of the module in said degree. Missing entries are interpreted to be 0, while extra entries must be zero.

fn act_by_element( &self, result: FpSliceMut<'_>, coeff: u32, op_degree: i32, op: FpSlice<'_>, input_degree: i32, input: FpSlice<'_>, )

fn act_by_element_on_basis( &self, result: FpSliceMut<'_>, coeff: u32, op_degree: i32, op: FpSlice<'_>, input_degree: i32, input_index: usize, )

fn element_to_string(&self, degree: i32, element: FpSlice<'_>) -> String

Gives the name of an element. The default implementation is derived from Module::basis_element_to_string in the obvious way.

impl<A: Algebra> PartialEq for RealProjectiveSpace<A>

fn eq(&self, other: &Self) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<A: Algebra> ZeroModule for RealProjectiveSpace<A>

where for<'a> &'a A: TryInto<&'a SteenrodAlgebra>,

fn zero_module(algebra: Arc<A>, min_degree: i32) -> Self

impl<A: Algebra> Eq for RealProjectiveSpace<A>