Index

Symbols

< <=, [1] <> =

==, [1] >=, [1] ? @interact

A

About Sage About this tutorial abs absolute value add_multiple_of_column add_multiple_of_row addition additive_order AlternatingGroup, [1]

and Anti-derivative append arctan arithmetic matrix aspect_ratio augment, [1] axes_labels

B

Basic Arithmetic Basic Arithmetic and Functions BCH Codes BCHCode

bitbucket bool Booleans

C

Calculus Commands cardinality Cartesian product cayley_table CC ceil ceiling center characteristic characteristic_polynomial check_mat Chinese Remainder Theorem Coding Theory check matrix generating matrix hamming distance hamming weight minimum distance coefficients

Coercion explicit implicit column columns, [1] command line concatenation of strings conditionals Contributing to the tutorial contribution cos count crt Cyclic Codes CyclicCode CyclicPermutationGroup, [1]

D

decimal approximation Declaring Variables decode def defining mathematical functions degree del derivative Derivatives partial det

diagonal DiCyclicGroup dimension direct product divides division, [1] Division and factoring divisors, [1] divmod, [1] dual_code

E

e echelon_form echelonize eigenvectors_right elif elimination_ideal else equations euclidean algorithm

exp exponential function exponentiation exponents extend extended_code external files external programs gap singular

F

factor, [1], [2], [3], [4] factoring False, [1] Field Extensions generating polynomial modulus find_root Finding critical points

floor for for statement fractional powers functions arguments definition multiple arguments return values

G

gcd, [1], [2], [3] gen_mat gen_mat_systematic gens, [1] gens_small Getting Started

GF, [1] Graphics adding two plots aspect_ratio color greatest common divisor groebner_basis groups Cayley table Klein 4 alternating cyclic cyclic; DihedralGroup dihedral generators homomorphisms kernel of homomorphism order permutation subgroup

H

Hamming Codes hamming_weight HammingCode

help DESCRIPTION EXAMPLES INPUT command line How to use this tutorial hyperbolic trigonometric functions

I

ideal Ideals construction gens membership Idempotent Polynomials identity_matrix, [1] if statement if-else statement in, [1] Indeterminants index inequalities integers Integers, [1] integral Integrals definate indefinite interact interactive applets

intersection inverse, [1] inverse trigonometric functions is_abelian is_cyclic is_field, [1] is_idempotent is_integral_domain, [1] is_invertible is_irreducible, [1] is_prime, [1] is_primitive is_principal is_ring is_subgroup is_unit, [1]

J

joining strings Jordan Canonical Form

jordan_form

K

kernel

L

lc lcm least common multiple left_kernel len, [1] length lexicographic monomial ordering limit Limits directional Line tangent to a curve linear algebra Linear Codes dimension length linear congruences

LinearCode linestyle list, [1] append comprehensions concatenation count definition extend index length remove slice sort zip lists map lm ln load load_session loading a file log logarithms loops for while lt

M

map, [1] matrix, [1] column determinant diagonal invertability manipulation row rows matrix arithmetic matrix_from_columns matrix_from_rows matrix_from_rows_and_columns MatrixSpace max maximum mean median min Mini-Topic Idempotent Polynomials

minimum minimum_distance mod mode modular arithmetic modulus Monomial Orderings monomials moving_average multiplication multiplicative_order, [1] Multivariate Polynomial Division Algorithm Multivariate Polynomial Rings monomials

N

n natural base normal coset; conjugation; quotient; homomorphism not

notebook nth root number fields

O

Objects or

order, [1], [2] additive multiplicative Order of operations

P

parametric_plot parent, [1], [2], [3], [4], [5] PermutationGroup PermutationGroupMorphism plot parametric plot3d Plotting 2D 3D aspect_ratio polar polar_plot polynomial

Polynomial Arithmetic Polynomial Rings gcd xgcd PolynomialRing, [1], [2], [3], [4] prime prime_divisors prod, [1] Programming in Sage Properties of Rings punctured

Q

QQ quotient, [1], [2]

Quotient Rings qutient

R

random rank Reduction modulo an ideal remainder remove rescale_col rescale_row reset restore, [1] reStructured Text

return right_kernel rings integers modulo n list order size unit group units Rings characteristic roots row row_space rows RR

S

Sage as a Calculator save_session sessions Set cardinality difference intersection subsets symmetric difference union set difference set_block set_column set_row show sign sin sinh slices solve solve_mod solve_right solving equations Solving equations and inequalities Solving equations with several variables Solving for x sort

source code ?? split, [1] sqrt square root standard deviation Standard functions and constants Statistics std string strings concatenation join len split subgroup subgroups subsets subtraction sum swap_columns swap_rows symbolic variables symmetric difference SymmetricGroup

T

tab completion Tab-completion tan terms thickness

total_degree transpose, [1], [2] trigonometric functions True, [1] tutorial source

U

union unit group unit_gens

unit_group_order Universes Universes and coercion

V

var, [1] variables deleting reset restore Variables assignment symbolic

variance vector, [1] Vector and Matrix Spaces

W

weight_distribution weight_enumerator

while statement

X

xgcd, [1]

Z

zero_matrix zip

ZZ