MISSING TITLE¶
- class sage.categories.ore_modules.OreModules(ore)[source]¶
- Bases: - Category_over_base_ring- Category of Ore modules. - ore_ring(var='x')[source]¶
- Return the underlying Ore polynomial ring. - INPUT: - var(default;- x) – the variable name
 - EXAMPLES: - sage: from sage.categories.ore_modules import OreModules sage: K.<a> = GF(5^3) sage: Frob = K.frobenius_endomorphism() sage: cat = OreModules(K, Frob) sage: cat.ore_ring() Ore Polynomial Ring in x over Finite Field in a of size 5^3 twisted by a |--> a^5 sage: cat.ore_ring('y') Ore Polynomial Ring in y over Finite Field in a of size 5^3 twisted by a |--> a^5 - >>> from sage.all import * >>> from sage.categories.ore_modules import OreModules >>> K = GF(Integer(5)**Integer(3), names=('a',)); (a,) = K._first_ngens(1) >>> Frob = K.frobenius_endomorphism() >>> cat = OreModules(K, Frob) >>> cat.ore_ring() Ore Polynomial Ring in x over Finite Field in a of size 5^3 twisted by a |--> a^5 >>> cat.ore_ring('y') Ore Polynomial Ring in y over Finite Field in a of size 5^3 twisted by a |--> a^5 
 - super_categories()[source]¶
- Return the immediate super categories of this category. - EXAMPLES: - sage: from sage.categories.ore_modules import OreModules sage: K.<a> = GF(5^3) sage: Frob = K.frobenius_endomorphism() sage: cat = OreModules(K, Frob) sage: cat.super_categories() [Category of vector spaces over Finite Field in a of size 5^3] - >>> from sage.all import * >>> from sage.categories.ore_modules import OreModules >>> K = GF(Integer(5)**Integer(3), names=('a',)); (a,) = K._first_ngens(1) >>> Frob = K.frobenius_endomorphism() >>> cat = OreModules(K, Frob) >>> cat.super_categories() [Category of vector spaces over Finite Field in a of size 5^3] 
 - twisting_derivation()[source]¶
- Return the underlying twisting derivation. - EXAMPLES: - sage: from sage.categories.ore_modules import OreModules sage: R.<t> = QQ[] sage: d = R.derivation() sage: cat = OreModules(R, d) sage: cat.twisting_derivation() d/dt - >>> from sage.all import * >>> from sage.categories.ore_modules import OreModules >>> R = QQ['t']; (t,) = R._first_ngens(1) >>> d = R.derivation() >>> cat = OreModules(R, d) >>> cat.twisting_derivation() d/dt - If the twising derivation is zero, nothing is returned: - sage: K.<a> = GF(5^3) sage: Frob = K.frobenius_endomorphism() sage: cat = OreModules(K, Frob) sage: cat.twisting_derivation() - >>> from sage.all import * >>> K = GF(Integer(5)**Integer(3), names=('a',)); (a,) = K._first_ngens(1) >>> Frob = K.frobenius_endomorphism() >>> cat = OreModules(K, Frob) >>> cat.twisting_derivation() 
 - twisting_morphism()[source]¶
- Return the underlying twisting morphism. - EXAMPLES: - sage: from sage.categories.ore_modules import OreModules sage: K.<a> = GF(5^3) sage: Frob = K.frobenius_endomorphism() sage: cat = OreModules(K, Frob) sage: cat.twisting_morphism() Frobenius endomorphism a |--> a^5 on Finite Field in a of size 5^3 - >>> from sage.all import * >>> from sage.categories.ore_modules import OreModules >>> K = GF(Integer(5)**Integer(3), names=('a',)); (a,) = K._first_ngens(1) >>> Frob = K.frobenius_endomorphism() >>> cat = OreModules(K, Frob) >>> cat.twisting_morphism() Frobenius endomorphism a |--> a^5 on Finite Field in a of size 5^3 - If the twising morphism is the identity, nothing is returned: - sage: R.<t> = QQ[] sage: d = R.derivation() sage: cat = OreModules(R, d) sage: cat.twisting_morphism() - >>> from sage.all import * >>> R = QQ['t']; (t,) = R._first_ngens(1) >>> d = R.derivation() >>> cat = OreModules(R, d) >>> cat.twisting_morphism()